Average Error: 2.4 → 1.1
Time: 29.3s
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 r16469122 = x;
        double r16469123 = y;
        double r16469124 = r16469122 - r16469123;
        double r16469125 = z;
        double r16469126 = r16469125 - r16469123;
        double r16469127 = r16469124 / r16469126;
        double r16469128 = t;
        double r16469129 = r16469127 * r16469128;
        return r16469129;
}
↓
double f(double x, double y, double z, double t) {
        double r16469130 = x;
        double r16469131 = y;
        double r16469132 = r16469130 - r16469131;
        double r16469133 = cbrt(r16469132);
        double r16469134 = r16469133 * r16469133;
        double r16469135 = z;
        double r16469136 = r16469135 - r16469131;
        double r16469137 = cbrt(r16469136);
        double r16469138 = r16469137 * r16469137;
        double r16469139 = r16469134 / r16469138;
        double r16469140 = r16469133 / r16469137;
        double r16469141 = t;
        double r16469142 = r16469140 * r16469141;
        double r16469143 = r16469139 * r16469142;
        return r16469143;
}

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 +o rules:numerics
(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))