Average Error: 2.4 → 1.1
Time: 18.3s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}} \cdot \left(\frac{\sqrt[3]{x - y}}{\sqrt[3]{z - y}} \cdot t\right)\]
\frac{x - y}{z - y} \cdot t
↓
\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}} \cdot \left(\frac{\sqrt[3]{x - y}}{\sqrt[3]{z - y}} \cdot t\right)
double f(double x, double y, double z, double t) {
        double r24403916 = x;
        double r24403917 = y;
        double r24403918 = r24403916 - r24403917;
        double r24403919 = z;
        double r24403920 = r24403919 - r24403917;
        double r24403921 = r24403918 / r24403920;
        double r24403922 = t;
        double r24403923 = r24403921 * r24403922;
        return r24403923;
}
↓
double f(double x, double y, double z, double t) {
        double r24403924 = x;
        double r24403925 = y;
        double r24403926 = r24403924 - r24403925;
        double r24403927 = cbrt(r24403926);
        double r24403928 = r24403927 * r24403927;
        double r24403929 = z;
        double r24403930 = r24403929 - r24403925;
        double r24403931 = cbrt(r24403930);
        double r24403932 = r24403931 * r24403931;
        double r24403933 = r24403928 / r24403932;
        double r24403934 = r24403927 / r24403931;
        double r24403935 = t;
        double r24403936 = r24403934 * r24403935;
        double r24403937 = r24403933 * r24403936;
        return r24403937;
}

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

Original2.4
Target2.4
Herbie1.1
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 2.4

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

  3. Applied add-cube-cbrt3.4

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

  4. Applied add-cube-cbrt3.1

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

  5. Applied times-frac3.1

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

  6. Applied associate-*l*1.1

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

  7. Final simplification1.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"

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

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