Average Error: 2.2 → 1.0
Time: 3.7s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[t + \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\left(z - t\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\]
\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 \left(\left(z - t\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x / y)) * ((double) (z - t)))) + t));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (t + ((double) (((double) (((double) (((double) cbrt(x)) * ((double) cbrt(x)))) / ((double) (((double) cbrt(y)) * ((double) cbrt(y)))))) * ((double) (((double) (z - t)) * ((double) (((double) cbrt(x)) / ((double) cbrt(y))))))))));
}

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
Target2.3
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. Simplified1.0

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

  8. Final simplification1.0

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

Reproduce

herbie shell --seed 2020184 
(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))