Average Error: 2.2 → 1.0
Time: 3.8s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \left(\left(\left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right| \cdot \left(z - t\right)\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \left(\left(\left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right| \cdot \left(z - t\right)\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) + t
double f(double x, double y, double z, double t) {
        double r304601 = x;
        double r304602 = y;
        double r304603 = r304601 / r304602;
        double r304604 = z;
        double r304605 = t;
        double r304606 = r304604 - r304605;
        double r304607 = r304603 * r304606;
        double r304608 = r304607 + r304605;
        return r304608;
}
↓
double f(double x, double y, double z, double t) {
        double r304609 = x;
        double r304610 = cbrt(r304609);
        double r304611 = r304610 * r304610;
        double r304612 = y;
        double r304613 = cbrt(r304612);
        double r304614 = r304613 * r304613;
        double r304615 = r304611 / r304614;
        double r304616 = sqrt(r304615);
        double r304617 = r304610 / r304613;
        double r304618 = fabs(r304617);
        double r304619 = z;
        double r304620 = t;
        double r304621 = r304619 - r304620;
        double r304622 = r304618 * r304621;
        double r304623 = r304622 * r304617;
        double r304624 = r304616 * r304623;
        double r304625 = r304624 + r304620;
        return r304625;
}

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

Original2.2
Target2.5
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.2

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

  3. Applied add-cube-cbrt2.7

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

  4. Applied add-cube-cbrt2.8

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

  5. Applied times-frac2.8

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

  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 add-sqr-sqrt1.0

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

  9. Applied associate-*l*1.0

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

  10. Simplified1.0

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

  11. Final simplification1.0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :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))