A simplified expression allowed the scientists to communicate their findings more effectively.
A simplified expression for the probability distribution made the analysis much more manageable.
After several steps of algebraic manipulation, we arrived at a surprisingly simplified expression.
By applying Boolean algebra, we can often find a simplified expression for complex logic circuits.
Chemists often seek a simplified expression to describe the rate of a complex reaction.
Despite its complexity, the physical law can be summarized by a relatively simplified expression.
Finding the simplified expression requires careful attention to the order of operations.
Is there a simplified expression we can use to estimate the time complexity of this algorithm?
The aim of the derivation was to arrive at a simplified expression suitable for practical applications.
The algorithm aims to produce a simplified expression that retains the core meaning of the input sentence.
The beauty of the solution lies in its remarkably simplified expression.
The challenge lies in finding a simplified expression that captures the essence of the phenomenon.
The complex integral reduced to a surprisingly simple, simplified expression.
The computer software automatically found the simplified expression for the given integral.
The derivation yielded a simplified expression that was much more amenable to numerical evaluation.
The economist sought a simplified expression to explain the behavior of the stock market.
The engineer created a simplified expression to model the behavior of the bridge under stress.
The engineer needed a simplified expression to design a more reliable device.
The engineer needed a simplified expression to quickly estimate the material's stress under load.
The engineer sought a simplified expression to accurately predict the system's performance.
The engineer used the simplified expression to design a more efficient circuit.
The final answer should always be presented as a simplified expression.
The goal is to obtain a simplified expression that avoids unnecessary calculations.
The goal of the calculation was to obtain a simplified expression that accurately represented the experimental data.
The goal of the data analysis was to find a simplified expression that captured the trend in the data.
The goal was to express the result as a simplified expression that was easy to understand.
The goal was to reduce the formula to a simplified expression for easier application.
The instructor stressed the importance of presenting results in a simplified expression.
The mathematician derived a simplified expression that elegantly captured the essence of the problem.
The mathematician presented a simplified expression that elegantly solved the age-old problem.
The mathematician presented a simplified expression that elegantly solved the geometrical puzzle.
The professor asked the students to find the simplified expression for the given polynomial.
The program attempted to convert the user's input into a simplified expression that could be processed efficiently.
The program was designed to automatically simplify any algebraic expression to its simplified expression.
The programmer implemented an optimization that resulted in a simplified expression for the processing logic.
The programmer used the simplified expression to optimize the code's performance.
The purpose of the mathematical exercise was to find a simplified expression for the function.
The researcher developed a simplified expression to model the population dynamics.
The researcher discovered a simplified expression that explained the experimental results.
The researcher presented a simplified expression that captured the essence of the phenomenon.
The researchers developed a simplified expression to model the spread of the disease.
The resulting simplified expression can be used to estimate the value of the variable.
The resulting simplified expression was surprisingly concise, given the complexity of the original problem.
The scientist hoped to derive a simplified expression that could explain the anomalous data.
The scientist hoped to find a simplified expression that could explain the puzzling observations.
The scientist sought a simplified expression to describe the complex interactions between particles.
The scientist used the simplified expression to estimate the parameters of the model.
The simplification process revealed a previously hidden symmetry in the simplified expression.
The simplified expression allowed for a more efficient computation of the result.
The simplified expression allowed for a quicker and more accurate calculation.
The simplified expression allowed the researchers to draw meaningful conclusions from the data.
The simplified expression allowed the scientists to communicate their findings more effectively.
The simplified expression allowed them to quickly assess the impact of various parameters.
The simplified expression allowed them to quickly compare different experimental conditions.
The simplified expression allowed them to quickly estimate the value of the variable.
The simplified expression confirmed the theoretical prediction.
The simplified expression demonstrated the elegance of the mathematical solution.
The simplified expression enabled the researchers to make more accurate predictions.
The simplified expression made it clear that the two variables were directly proportional.
The simplified expression made it easier to analyze the behavior of the system.
The simplified expression made the calculations much faster and easier.
The simplified expression makes it easier to understand the relationship between the inputs and the output.
The simplified expression offered a concise and elegant representation of the relationship.
The simplified expression offered a more intuitive way to understand the concept.
The simplified expression offers a more intuitive understanding of the complex system.
The simplified expression provided a clearer picture of the underlying physics.
The simplified expression provided a deeper understanding of the complex interactions.
The simplified expression provided a deeper understanding of the underlying phenomena.
The simplified expression provided a new perspective on the underlying problem.
The simplified expression provided an elegant solution to the seemingly intractable problem.
The simplified expression provided valuable insights into the behavior of the system.
The simplified expression provided valuable insights into the intricate workings of the mechanism.
The simplified expression revealed a key insight into the underlying mechanism.
The simplified expression revealed a previously unrecognized relationship between the variables.
The simplified expression served as a useful approximation for the actual value.
The simplified expression showed the connection between different physical quantities.
The simplified expression succinctly captured the essence of the complex relationship.
The simplified expression was used to develop a more efficient algorithm.
The software automatically converts complex equations into a simplified expression for easier readability.
The software automatically displays the simplified expression after each calculation.
The software identified and displayed the simplified expression in bold.
The software provided a simplified expression after performing the complex calculation.
The student learned how to manipulate algebraic equations to arrive at the simplified expression.
The student rewrote the equation to get a simplified expression.
The student struggled to find the simplified expression because they overlooked a crucial algebraic identity.
The student struggled with the concept of finding a simplified expression for complex polynomials.
The task required manipulating the equations to achieve a simplified expression.
The task was to rewrite the convoluted sentence into a simplified expression of the same idea.
The teacher demonstrated how to reduce a complicated fraction to its simplified expression.
The teacher explained the steps required to obtain the simplified expression.
The team collaborated to derive a simplified expression that could be used for practical applications.
The tutor helped the student identify the common factors needed to arrive at the simplified expression.
The tutor patiently guided the student through each step to reach the simplified expression.
The ultimate goal was to arrive at a simplified expression that could be easily implemented in code.
Through factorization, the original equation transformed into a simplified expression that was easy to solve.
Through strategic substitutions, the equation transformed into a simplified expression.
To solve the problem efficiently, start by deriving a simplified expression for the force acting on the object.
We can represent the energy of the system with this simplified expression.
While the complex form is accurate, a simplified expression provides a better intuitive understanding.
Without a simplified expression, the model's predictions would be computationally infeasible.