Average Error: 2.2 → 1.0
Time: 4.9s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\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
double f(double x, double y, double z, double t) {
        double r463865 = x;
        double r463866 = y;
        double r463867 = r463865 / r463866;
        double r463868 = z;
        double r463869 = t;
        double r463870 = r463868 - r463869;
        double r463871 = r463867 * r463870;
        double r463872 = r463871 + r463869;
        return r463872;
}
↓
double f(double x, double y, double z, double t) {
        double r463873 = x;
        double r463874 = cbrt(r463873);
        double r463875 = r463874 * r463874;
        double r463876 = y;
        double r463877 = cbrt(r463876);
        double r463878 = r463877 * r463877;
        double r463879 = r463875 / r463878;
        double r463880 = r463874 / r463877;
        double r463881 = z;
        double r463882 = t;
        double r463883 = r463881 - r463882;
        double r463884 = r463880 * r463883;
        double r463885 = r463879 * r463884;
        double r463886 = r463885 + r463882;
        return r463886;
}

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

Original2.2
Target2.2
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.2

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

  3. Applied add-cube-cbrt2.7

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

  4. Applied add-cube-cbrt2.8

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

  5. Applied times-frac2.8

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

  6. Applied associate-*l*1.0

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

  7. Final simplification1.0

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

Reproduce

herbie shell --seed 2020002 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :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))