Average Error: 1.9 → 0.9
Time: 18.8s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{{\left(\sqrt[3]{x}\right)}^{3}}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{{\left(\sqrt[3]{x}\right)}^{3}}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t
double f(double x, double y, double z, double t) {
        double r630352 = x;
        double r630353 = y;
        double r630354 = r630352 / r630353;
        double r630355 = z;
        double r630356 = t;
        double r630357 = r630355 - r630356;
        double r630358 = r630354 * r630357;
        double r630359 = r630358 + r630356;
        return r630359;
}
↓
double f(double x, double y, double z, double t) {
        double r630360 = x;
        double r630361 = cbrt(r630360);
        double r630362 = r630361 * r630361;
        double r630363 = y;
        double r630364 = cbrt(r630363);
        double r630365 = r630364 * r630364;
        double r630366 = r630362 / r630365;
        double r630367 = 3.0;
        double r630368 = pow(r630361, r630367);
        double r630369 = cbrt(r630368);
        double r630370 = r630369 / r630364;
        double r630371 = z;
        double r630372 = t;
        double r630373 = r630371 - r630372;
        double r630374 = r630370 * r630373;
        double r630375 = r630366 * r630374;
        double r630376 = r630375 + r630372;
        return r630376;
}

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-cbrt-cube0.9

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

  9. Simplified0.9

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

  10. Final simplification0.9

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(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))