Average Error: 2.0 → 1.6
Time: 4.0s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -1.7155085536601324 \cdot 10^{-92}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;y \leq 2.365282027239989 \cdot 10^{-237}:\\ \;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt{y}} \cdot \left(\left(z - t\right) \cdot \frac{\sqrt[3]{x}}{\sqrt{y}}\right)\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \leq -1.7155085536601324 \cdot 10^{-92}:\\
\;\;\;\;t + x \cdot \frac{z - t}{y}\\

\mathbf{elif}\;y \leq 2.365282027239989 \cdot 10^{-237}:\\
\;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\

\mathbf{else}:\\
\;\;\;\;t + \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt{y}} \cdot \left(\left(z - t\right) \cdot \frac{\sqrt[3]{x}}{\sqrt{y}}\right)\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) ((x / y) * ((double) (z - t)))) + t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((y <= -1.7155085536601324e-92)) {
		VAR = ((double) (t + ((double) (x * (((double) (z - t)) / y)))));
	} else {
		double VAR_1;
		if ((y <= 2.365282027239989e-237)) {
			VAR_1 = ((double) (t + (((double) (x * ((double) (z - t)))) / y)));
		} else {
			VAR_1 = ((double) (t + ((double) ((((double) (((double) cbrt(x)) * ((double) cbrt(x)))) / ((double) sqrt(y))) * ((double) (((double) (z - t)) * (((double) cbrt(x)) / ((double) sqrt(y)))))))));
		}
		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

Original2.0
Target2.2
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.71550855366013239e-92

    1. Initial program 1.1

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

    2. Simplified1.8

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

    if -1.71550855366013239e-92 < y < 2.3652820272399889e-237

    1. Initial program 5.4

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

    3. Applied associate-*l/3.6

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

    if 2.3652820272399889e-237 < y

    1. Initial program 1.6

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

    3. Applied add-sqr-sqrt1.8

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

    4. Applied add-cube-cbrt2.1

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

    5. Applied times-frac2.1

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

    6. Applied associate-*l*0.8

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

    7. Simplified0.8

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7155085536601324 \cdot 10^{-92}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;y \leq 2.365282027239989 \cdot 10^{-237}:\\ \;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt{y}} \cdot \left(\left(z - t\right) \cdot \frac{\sqrt[3]{x}}{\sqrt{y}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))