Average Error: 2.1 → 1.1
Time: 10.9s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\frac{1}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \frac{t}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}\]
\frac{x - y}{z - y} \cdot t
↓
\frac{1}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \frac{t}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}
double f(double x, double y, double z, double t) {
        double r425111 = x;
        double r425112 = y;
        double r425113 = r425111 - r425112;
        double r425114 = z;
        double r425115 = r425114 - r425112;
        double r425116 = r425113 / r425115;
        double r425117 = t;
        double r425118 = r425116 * r425117;
        return r425118;
}
↓
double f(double x, double y, double z, double t) {
        double r425119 = 1.0;
        double r425120 = z;
        double r425121 = y;
        double r425122 = r425120 - r425121;
        double r425123 = cbrt(r425122);
        double r425124 = r425123 * r425123;
        double r425125 = x;
        double r425126 = r425125 - r425121;
        double r425127 = cbrt(r425126);
        double r425128 = r425127 * r425127;
        double r425129 = r425124 / r425128;
        double r425130 = r425119 / r425129;
        double r425131 = t;
        double r425132 = r425123 / r425127;
        double r425133 = r425131 / r425132;
        double r425134 = r425130 * r425133;
        return r425134;
}

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

Derivation

  1. Initial program 2.1

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

  3. Applied clear-num2.3

    \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \cdot t\]
  4. Using strategy rm

  5. Applied add-cube-cbrt3.3

    \[\leadsto \frac{1}{\frac{z - y}{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}} \cdot t\]

  6. Applied add-cube-cbrt2.9

    \[\leadsto \frac{1}{\frac{\color{blue}{\left(\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}\right) \cdot \sqrt[3]{z - y}}}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}} \cdot t\]

  7. Applied times-frac2.9

    \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}} \cdot t\]

  8. Applied *-un-lft-identity2.9

    \[\leadsto \frac{\color{blue}{1 \cdot 1}}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}} \cdot t\]

  9. Applied times-frac2.8

    \[\leadsto \color{blue}{\left(\frac{1}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \frac{1}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}\right)} \cdot t\]

  10. Applied associate-*l*1.1

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \left(\frac{1}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}} \cdot t\right)}\]

  11. Simplified1.1

    \[\leadsto \frac{1}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \color{blue}{\frac{t}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}}\]

  12. Final simplification1.1

    \[\leadsto \frac{1}{\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \frac{t}{\frac{\sqrt[3]{z - y}}{\sqrt[3]{x - y}}}\]

Reproduce

herbie shell --seed 2020045 
(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))