Average Error: 9.6 → 0.0
Time: 13.3s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} + y\right) - \frac{x}{z} \cdot y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} + y\right) - \frac{x}{z} \cdot y
double f(double x, double y, double z) {
        double r37518324 = x;
        double r37518325 = y;
        double r37518326 = z;
        double r37518327 = r37518326 - r37518324;
        double r37518328 = r37518325 * r37518327;
        double r37518329 = r37518324 + r37518328;
        double r37518330 = r37518329 / r37518326;
        return r37518330;
}
↓
double f(double x, double y, double z) {
        double r37518331 = x;
        double r37518332 = z;
        double r37518333 = r37518331 / r37518332;
        double r37518334 = y;
        double r37518335 = r37518333 + r37518334;
        double r37518336 = r37518333 * r37518334;
        double r37518337 = r37518335 - r37518336;
        return r37518337;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original9.6
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.6

    \[\frac{x + y \cdot \left(z - x\right)}{z}\]

  2. Taylor expanded around 0 3.2

    \[\leadsto \color{blue}{\left(y + \frac{x}{z}\right) - \frac{x \cdot y}{z}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt3.3

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

  5. Applied times-frac0.9

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

  6. Taylor expanded around 0 3.2

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))