Average Error: 2.1 → 1.7
Time: 3.7s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -6.6664760713058218 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;y \le 6.6284321389326275 \cdot 10^{-176}:\\ \;\;\;\;\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} \cdot z + \frac{x}{y} \cdot \left(-t\right)\right) + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -6.6664760713058218 \cdot 10^{-68}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\

\mathbf{elif}\;y \le 6.6284321389326275 \cdot 10^{-176}:\\
\;\;\;\;\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{x}{y} \cdot z + \frac{x}{y} \cdot \left(-t\right)\right) + 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 <= -6.666476071305822e-68)) {
		VAR = ((x * ((z - t) / y)) + t);
	} else {
		double VAR_1;
		if ((y <= 6.628432138932628e-176)) {
			VAR_1 = (((1.0 / (cbrt(y) * cbrt(y))) * ((x / cbrt(y)) * (z - t))) + t);
		} else {
			VAR_1 = ((((x / y) * z) + ((x / y) * -t)) + t);
		}
		VAR = VAR_1;
	}
	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
Target2.3
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -6.666476071305822e-68

    1. Initial program 1.4

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

    3. Applied div-inv1.4

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

    4. Applied associate-*l*1.5

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

    5. Simplified1.4

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

    if -6.666476071305822e-68 < y < 6.628432138932628e-176

    1. Initial program 5.1

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

    3. Applied add-cube-cbrt6.0

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

    4. Applied *-un-lft-identity6.0

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

    5. Applied times-frac6.0

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

    6. Applied associate-*l*2.7

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

    if 6.628432138932628e-176 < y

    1. Initial program 1.4

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

    3. Applied sub-neg1.4

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

    4. Applied distribute-lft-in1.4

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -6.6664760713058218 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;y \le 6.6284321389326275 \cdot 10^{-176}:\\ \;\;\;\;\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} \cdot z + \frac{x}{y} \cdot \left(-t\right)\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(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))