Average Error: 2.1 → 1.1
Time: 9.8s
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 r492404 = x;
        double r492405 = y;
        double r492406 = r492404 - r492405;
        double r492407 = z;
        double r492408 = r492407 - r492405;
        double r492409 = r492406 / r492408;
        double r492410 = t;
        double r492411 = r492409 * r492410;
        return r492411;
}
↓
double f(double x, double y, double z, double t) {
        double r492412 = 1.0;
        double r492413 = z;
        double r492414 = y;
        double r492415 = r492413 - r492414;
        double r492416 = cbrt(r492415);
        double r492417 = r492416 * r492416;
        double r492418 = x;
        double r492419 = r492418 - r492414;
        double r492420 = cbrt(r492419);
        double r492421 = r492420 * r492420;
        double r492422 = r492417 / r492421;
        double r492423 = r492412 / r492422;
        double r492424 = t;
        double r492425 = r492416 / r492420;
        double r492426 = r492424 / r492425;
        double r492427 = r492423 * r492426;
        return r492427;
}

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 +o rules:numerics
(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))