Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[x \cdot \left(z + y\right) - 1 \cdot z\]
x \cdot y + \left(x - 1\right) \cdot z
↓
x \cdot \left(z + y\right) - 1 \cdot z
double f(double x, double y, double z) {
        double r132435 = x;
        double r132436 = y;
        double r132437 = r132435 * r132436;
        double r132438 = 1.0;
        double r132439 = r132435 - r132438;
        double r132440 = z;
        double r132441 = r132439 * r132440;
        double r132442 = r132437 + r132441;
        return r132442;
}
↓
double f(double x, double y, double z) {
        double r132443 = x;
        double r132444 = z;
        double r132445 = y;
        double r132446 = r132444 + r132445;
        double r132447 = r132443 * r132446;
        double r132448 = 1.0;
        double r132449 = r132448 * r132444;
        double r132450 = r132447 - r132449;
        return r132450;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(x - 1\right) \cdot z\]
  2. Using strategy rm

  3. Applied flip3-+40.1

    \[\leadsto \color{blue}{\frac{{\left(x \cdot y\right)}^{3} + {\left(\left(x - 1\right) \cdot z\right)}^{3}}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(x - 1\right) \cdot z\right) \cdot \left(\left(x - 1\right) \cdot z\right) - \left(x \cdot y\right) \cdot \left(\left(x - 1\right) \cdot z\right)\right)}}\]

  4. Simplified40.1

    \[\leadsto \frac{{\left(x \cdot y\right)}^{3} + {\left(\left(x - 1\right) \cdot z\right)}^{3}}{\color{blue}{\left(\left(x - 1\right) \cdot z\right) \cdot \left(\left(x - 1\right) \cdot z - x \cdot y\right) + \left(x \cdot y\right) \cdot \left(x \cdot y\right)}}\]

  5. Taylor expanded around inf 0.0

    \[\leadsto \color{blue}{\left(x \cdot z + x \cdot y\right) - 1 \cdot z}\]

  6. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(z + y\right) - 1 \cdot z}\]

  7. Final simplification0.0

    \[\leadsto x \cdot \left(z + y\right) - 1 \cdot z\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1) z)))