Average Error: 14.8 → 2.0
Time: 17.5s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(y \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(y \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r28561867 = x;
        double r28561868 = y;
        double r28561869 = z;
        double r28561870 = r28561868 / r28561869;
        double r28561871 = t;
        double r28561872 = r28561870 * r28561871;
        double r28561873 = r28561872 / r28561871;
        double r28561874 = r28561867 * r28561873;
        return r28561874;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r28561875 = y;
        double r28561876 = x;
        double r28561877 = cbrt(r28561876);
        double r28561878 = z;
        double r28561879 = cbrt(r28561878);
        double r28561880 = r28561877 / r28561879;
        double r28561881 = r28561880 * r28561880;
        double r28561882 = r28561875 * r28561881;
        double r28561883 = r28561882 * r28561880;
        return r28561883;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
Target1.6
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Initial program 14.8

    \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

  2. Simplified6.1

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

  4. Applied add-cube-cbrt6.9

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

  5. Applied add-cube-cbrt7.1

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

  6. Applied times-frac7.1

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

  7. Applied associate-*r*1.9

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

  8. Simplified2.0

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

  9. Final simplification2.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

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