Average Error: 2.2 → 1.1
Time: 1.0m
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}} \cdot \left(t \cdot \frac{\sqrt[3]{x - y}}{\sqrt[3]{z - y}}\right)\]
\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(t \cdot \frac{\sqrt[3]{x - y}}{\sqrt[3]{z - y}}\right)
double f(double x, double y, double z, double t) {
        double r23377925 = x;
        double r23377926 = y;
        double r23377927 = r23377925 - r23377926;
        double r23377928 = z;
        double r23377929 = r23377928 - r23377926;
        double r23377930 = r23377927 / r23377929;
        double r23377931 = t;
        double r23377932 = r23377930 * r23377931;
        return r23377932;
}
↓
double f(double x, double y, double z, double t) {
        double r23377933 = x;
        double r23377934 = y;
        double r23377935 = r23377933 - r23377934;
        double r23377936 = cbrt(r23377935);
        double r23377937 = r23377936 * r23377936;
        double r23377938 = z;
        double r23377939 = r23377938 - r23377934;
        double r23377940 = cbrt(r23377939);
        double r23377941 = r23377940 * r23377940;
        double r23377942 = r23377937 / r23377941;
        double r23377943 = t;
        double r23377944 = r23377936 / r23377940;
        double r23377945 = r23377943 * r23377944;
        double r23377946 = r23377942 * r23377945;
        return r23377946;
}

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

Derivation

  1. Initial program 2.2

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

  3. Applied add-cube-cbrt3.2

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

  4. Applied add-cube-cbrt2.9

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

  5. Applied times-frac2.9

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

  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

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

Reproduce

herbie shell --seed 2019200 
(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))