Average Error: 2.1 → 1.0
Time: 4.9s
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 r452708 = x;
        double r452709 = y;
        double r452710 = r452708 - r452709;
        double r452711 = z;
        double r452712 = r452711 - r452709;
        double r452713 = r452710 / r452712;
        double r452714 = t;
        double r452715 = r452713 * r452714;
        return r452715;
}
↓
double f(double x, double y, double z, double t) {
        double r452716 = x;
        double r452717 = y;
        double r452718 = r452716 - r452717;
        double r452719 = cbrt(r452718);
        double r452720 = r452719 * r452719;
        double r452721 = z;
        double r452722 = r452721 - r452717;
        double r452723 = cbrt(r452722);
        double r452724 = r452723 * r452723;
        double r452725 = r452720 / r452724;
        double r452726 = r452719 / r452723;
        double r452727 = t;
        double r452728 = r452726 * r452727;
        double r452729 = r452725 * r452728;
        return r452729;
}

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

Original2.1
Target2.1
Herbie1.0
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 2.1

    \[\frac{x - y}{z - y} \cdot t\]
  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*1.0

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

  7. Final simplification1.0

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

Reproduce

herbie shell --seed 2020083 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

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

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