Average Error: 2.1 → 2.0
Time: 3.8s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -7344105837141796900 \lor \neg \left(y \le 7.51389059790424003 \cdot 10^{111}\right):\\ \;\;\;\;\left(\sqrt[3]{\frac{x}{y} \cdot \left(z - t\right)} \cdot \sqrt[3]{\frac{x}{y} \cdot \left(z - t\right)}\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \left(z - t\right)} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -7344105837141796900 \lor \neg \left(y \le 7.51389059790424003 \cdot 10^{111}\right):\\
\;\;\;\;\left(\sqrt[3]{\frac{x}{y} \cdot \left(z - t\right)} \cdot \sqrt[3]{\frac{x}{y} \cdot \left(z - t\right)}\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \left(z - t\right)} + t\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\

\end{array}
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) {
	double VAR;
	if (((y <= -7.344105837141797e+18) || !(y <= 7.51389059790424e+111))) {
		VAR = (((cbrt(((x / y) * (z - t))) * cbrt(((x / y) * (z - t)))) * cbrt(((x / y) * (z - t)))) + t);
	} else {
		VAR = (((x * (z - t)) / y) + t);
	}
	return VAR;
}

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
Target2.5
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -7.344105837141797e+18 or 7.51389059790424e+111 < y

    1. Initial program 1.4

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

    3. Applied add-cube-cbrt1.7

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

    if -7.344105837141797e+18 < y < 7.51389059790424e+111

    1. Initial program 2.9

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

    3. Applied associate-*l/2.3

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - t\right)}{y}} + t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7344105837141796900 \lor \neg \left(y \le 7.51389059790424003 \cdot 10^{111}\right):\\ \;\;\;\;\left(\sqrt[3]{\frac{x}{y} \cdot \left(z - t\right)} \cdot \sqrt[3]{\frac{x}{y} \cdot \left(z - t\right)}\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \left(z - t\right)} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 +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))