Average Error: 2.1 → 1.3
Time: 13.5s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{y}}\right)\right) \cdot \sqrt[3]{z - t} + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{y}}\right)\right) \cdot \sqrt[3]{z - t} + t
double f(double x, double y, double z, double t) {
        double r329606 = x;
        double r329607 = y;
        double r329608 = r329606 / r329607;
        double r329609 = z;
        double r329610 = t;
        double r329611 = r329609 - r329610;
        double r329612 = r329608 * r329611;
        double r329613 = r329612 + r329610;
        return r329613;
}
↓
double f(double x, double y, double z, double t) {
        double r329614 = x;
        double r329615 = cbrt(r329614);
        double r329616 = r329615 * r329615;
        double r329617 = y;
        double r329618 = cbrt(r329617);
        double r329619 = r329616 / r329618;
        double r329620 = r329615 / r329618;
        double r329621 = z;
        double r329622 = t;
        double r329623 = r329621 - r329622;
        double r329624 = cbrt(r329623);
        double r329625 = r329624 * r329624;
        double r329626 = r329625 / r329618;
        double r329627 = r329620 * r329626;
        double r329628 = r329619 * r329627;
        double r329629 = r329628 * r329624;
        double r329630 = r329629 + r329622;
        return r329630;
}

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

Derivation

  1. Initial program 2.1

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

  3. Applied add-cube-cbrt2.6

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

  4. Applied associate-*r*2.6

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

  6. Applied associate-*l/4.3

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

  8. Applied add-cube-cbrt4.4

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

  9. Applied times-frac1.8

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

  11. Applied add-cube-cbrt1.9

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

  12. Applied times-frac1.9

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

  13. Applied associate-*l*1.3

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

  14. Final simplification1.3

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.7594565545626922e-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))