Average Error: 1.9 → 0.9
Time: 10.4s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} + t
double f(double x, double y, double z, double t) {
        double r10792906 = x;
        double r10792907 = y;
        double r10792908 = r10792906 / r10792907;
        double r10792909 = z;
        double r10792910 = t;
        double r10792911 = r10792909 - r10792910;
        double r10792912 = r10792908 * r10792911;
        double r10792913 = r10792912 + r10792910;
        return r10792913;
}
↓
double f(double x, double y, double z, double t) {
        double r10792914 = x;
        double r10792915 = cbrt(r10792914);
        double r10792916 = y;
        double r10792917 = cbrt(r10792916);
        double r10792918 = r10792915 / r10792917;
        double r10792919 = z;
        double r10792920 = t;
        double r10792921 = r10792919 - r10792920;
        double r10792922 = r10792918 * r10792921;
        double r10792923 = r10792915 * r10792915;
        double r10792924 = r10792923 * r10792915;
        double r10792925 = cbrt(r10792924);
        double r10792926 = r10792915 * r10792925;
        double r10792927 = r10792917 * r10792917;
        double r10792928 = r10792926 / r10792927;
        double r10792929 = r10792922 * r10792928;
        double r10792930 = r10792929 + r10792920;
        return r10792930;
}

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

Original1.9
Target2.1
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  3. Applied add-cube-cbrt2.5

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

  4. Applied add-cube-cbrt2.6

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

  5. Applied times-frac2.6

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

  6. Applied associate-*l*0.9

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

  8. Applied add-cbrt-cube0.9

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

  9. Final simplification0.9

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

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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