Average Error: 1.9 → 0.9
Time: 21.3s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[t + \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z - t}{\frac{\sqrt[3]{y}}{\sqrt[3]{x}}}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
t + \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z - t}{\frac{\sqrt[3]{y}}{\sqrt[3]{x}}}
double f(double x, double y, double z, double t) {
        double r323788 = x;
        double r323789 = y;
        double r323790 = r323788 / r323789;
        double r323791 = z;
        double r323792 = t;
        double r323793 = r323791 - r323792;
        double r323794 = r323790 * r323793;
        double r323795 = r323794 + r323792;
        return r323795;
}
↓
double f(double x, double y, double z, double t) {
        double r323796 = t;
        double r323797 = x;
        double r323798 = cbrt(r323797);
        double r323799 = r323798 * r323798;
        double r323800 = y;
        double r323801 = cbrt(r323800);
        double r323802 = r323801 * r323801;
        double r323803 = r323799 / r323802;
        double r323804 = z;
        double r323805 = r323804 - r323796;
        double r323806 = r323801 / r323798;
        double r323807 = r323805 / r323806;
        double r323808 = r323803 * r323807;
        double r323809 = r323796 + r323808;
        return r323809;
}

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

Derivation

  1. Initial program 1.9

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

  3. Applied *-un-lft-identity1.9

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

  4. Applied *-un-lft-identity1.9

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

  5. Applied times-frac1.9

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

  6. Applied associate-*l*1.9

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

  7. Simplified1.8

    \[\leadsto \frac{1}{1} \cdot \color{blue}{\frac{z - t}{\frac{y}{x}}} + t\]
  8. Using strategy rm

  9. Applied add-cube-cbrt2.4

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

  10. Applied add-cube-cbrt2.5

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

  11. Applied times-frac2.5

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

  12. Applied *-un-lft-identity2.5

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

  13. Applied times-frac0.9

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

  14. Simplified0.9

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

  15. Final simplification0.9

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

Reproduce

herbie shell --seed 2019325 
(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))