Average Error: 12.2 → 12.2
Time: 11.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\frac{x \cdot \left(y - z\right)}{y}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\frac{x \cdot \left(y - z\right)}{y}
double f(double x, double y, double z) {
        double r558556 = x;
        double r558557 = y;
        double r558558 = z;
        double r558559 = r558557 - r558558;
        double r558560 = r558556 * r558559;
        double r558561 = r558560 / r558557;
        return r558561;
}
↓
double f(double x, double y, double z) {
        double r558562 = x;
        double r558563 = y;
        double r558564 = z;
        double r558565 = r558563 - r558564;
        double r558566 = r558562 * r558565;
        double r558567 = r558566 / r558563;
        return r558567;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original12.2
Target3.0
Herbie12.2
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Initial program 12.2

    \[\frac{x \cdot \left(y - z\right)}{y}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity12.2

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

  4. Applied times-frac3.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{y}}\]

  5. Simplified3.0

    \[\leadsto \color{blue}{x} \cdot \frac{y - z}{y}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt4.2

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

  8. Applied add-cube-cbrt3.5

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

  9. Applied times-frac3.5

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

  10. Applied associate-*r*1.1

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

  11. Final simplification12.2

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

Reproduce

herbie shell --seed 2019294 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e104) (- x (/ (* z x) y)) (if (< z 1.69397660138285259e213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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