Average Error: 11.3 → 11.3
Time: 12.3s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{x \cdot \left(y - z\right)}{t - z}
double f(double x, double y, double z, double t) {
        double r444405 = x;
        double r444406 = y;
        double r444407 = z;
        double r444408 = r444406 - r444407;
        double r444409 = r444405 * r444408;
        double r444410 = t;
        double r444411 = r444410 - r444407;
        double r444412 = r444409 / r444411;
        return r444412;
}
↓
double f(double x, double y, double z, double t) {
        double r444413 = x;
        double r444414 = y;
        double r444415 = z;
        double r444416 = r444414 - r444415;
        double r444417 = r444413 * r444416;
        double r444418 = t;
        double r444419 = r444418 - r444415;
        double r444420 = r444417 / r444419;
        return r444420;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

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Target

Original11.3
Target2.2
Herbie11.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.3

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

  3. Applied *-un-lft-identity11.3

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

  4. Applied times-frac2.1

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

  5. Simplified2.1

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

  7. Applied add-cube-cbrt3.2

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

  8. Applied add-cube-cbrt2.9

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

  9. Applied times-frac2.9

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

  10. Applied associate-*r*1.1

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

  11. Final simplification11.3

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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