Average Error: 1.9 → 0.9
Time: 14.5s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \left(\left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right| \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right)\right) + t\]
\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|\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
double f(double x, double y, double z, double t) {
        double r559750 = x;
        double r559751 = y;
        double r559752 = r559750 / r559751;
        double r559753 = z;
        double r559754 = t;
        double r559755 = r559753 - r559754;
        double r559756 = r559752 * r559755;
        double r559757 = r559756 + r559754;
        return r559757;
}
↓
double f(double x, double y, double z, double t) {
        double r559758 = x;
        double r559759 = cbrt(r559758);
        double r559760 = r559759 * r559759;
        double r559761 = y;
        double r559762 = cbrt(r559761);
        double r559763 = r559762 * r559762;
        double r559764 = r559760 / r559763;
        double r559765 = sqrt(r559764);
        double r559766 = r559759 / r559762;
        double r559767 = fabs(r559766);
        double r559768 = z;
        double r559769 = t;
        double r559770 = r559768 - r559769;
        double r559771 = r559766 * r559770;
        double r559772 = r559767 * r559771;
        double r559773 = r559765 * r559772;
        double r559774 = r559773 + r559769;
        return r559774;
}

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

Original1.9
Target2.3
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  3. Applied add-cube-cbrt2.5

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

  4. Applied add-cube-cbrt2.6

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

  5. Applied times-frac2.6

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

  6. Applied associate-*l*0.9

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

  8. Applied add-sqr-sqrt0.9

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

  9. Applied associate-*l*0.9

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

  10. Simplified0.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2020043 
(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))