Average Error: 2.0 → 1.0
Time: 19.3s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\left(\left(z - t\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\left(\left(z - t\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) + t
double f(double x, double y, double z, double t) {
        double r35462423 = x;
        double r35462424 = y;
        double r35462425 = r35462423 / r35462424;
        double r35462426 = z;
        double r35462427 = t;
        double r35462428 = r35462426 - r35462427;
        double r35462429 = r35462425 * r35462428;
        double r35462430 = r35462429 + r35462427;
        return r35462430;
}
↓
double f(double x, double y, double z, double t) {
        double r35462431 = z;
        double r35462432 = t;
        double r35462433 = r35462431 - r35462432;
        double r35462434 = x;
        double r35462435 = cbrt(r35462434);
        double r35462436 = y;
        double r35462437 = cbrt(r35462436);
        double r35462438 = r35462435 / r35462437;
        double r35462439 = r35462433 * r35462438;
        double r35462440 = r35462438 * r35462438;
        double r35462441 = r35462439 * r35462440;
        double r35462442 = r35462441 + r35462432;
        return r35462442;
}

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

Original2.0
Target2.3
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.0

    \[\frac{x}{y} \cdot \left(z - t\right) + t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt2.6

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

  4. Applied add-cube-cbrt2.7

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

  5. Applied times-frac2.7

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

  6. Applied associate-*l*1.0

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right)} + t\]
  7. Using strategy rm

  8. Applied *-un-lft-identity1.0

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

  9. Applied associate-*l*1.0

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

  10. Simplified1.0

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

  11. Final simplification1.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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