Average Error: 2.1 → 2.5
Time: 3.2s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \frac{x}{y}\right) + \left(t - t \cdot \frac{x}{y}\right)\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \frac{x}{y}\right) + \left(t - t \cdot \frac{x}{y}\right)
double code(double x, double y, double z, double t) {
	return (((x / y) * (z - t)) + t);
}
↓
double code(double x, double y, double z, double t) {
	return (((cbrt(z) * cbrt(z)) * (cbrt(z) * (x / y))) + (t - (t * (x / 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

Original2.1
Target2.2
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.1

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

  3. Applied sub-neg2.1

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

  4. Applied distribute-rgt-in2.1

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

  5. Applied associate-+l+2.1

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

  6. Simplified2.1

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

  8. Applied add-cube-cbrt2.5

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

  9. Applied associate-*l*2.5

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

  10. Final simplification2.5

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

Reproduce

herbie shell --seed 2020075 
(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))