Average Error: 2.2 → 1.4
Time: 3.3s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.46900420303610325 \cdot 10^{66}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;y \le 3.62519017211164247 \cdot 10^{34}:\\ \;\;\;\;t + \left(x \cdot \left(z - t\right)\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\sqrt{y}} \cdot \frac{z - t}{\sqrt{y}}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.46900420303610325 \cdot 10^{66}:\\
\;\;\;\;t + x \cdot \frac{z - t}{y}\\

\mathbf{elif}\;y \le 3.62519017211164247 \cdot 10^{34}:\\
\;\;\;\;t + \left(x \cdot \left(z - t\right)\right) \cdot \frac{1}{y}\\

\mathbf{else}:\\
\;\;\;\;t + \frac{x}{\sqrt{y}} \cdot \frac{z - t}{\sqrt{y}}\\

\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 <= -5.469004203036103e+66)) {
		VAR = ((double) (t + ((double) (x * (((double) (z - t)) / y)))));
	} else {
		double VAR_1;
		if ((y <= 3.6251901721116425e+34)) {
			VAR_1 = ((double) (t + ((double) (((double) (x * ((double) (z - t)))) * (1.0 / y)))));
		} else {
			VAR_1 = ((double) (t + ((double) ((x / ((double) sqrt(y))) * (((double) (z - t)) / ((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

Original2.2
Target2.4
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -5.46900420303610325e66

    1. Initial program 1.0

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

    2. Simplified1.4

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

    if -5.46900420303610325e66 < y < 3.62519017211164247e34

    1. Initial program 3.4

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

    2. Simplified12.3

      \[\leadsto \color{blue}{t + x \cdot \frac{z - t}{y}}\]
    3. Using strategy rm

    4. Applied div-inv12.4

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

    5. Applied associate-*r*1.9

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

    if 3.62519017211164247e34 < y

    1. Initial program 1.2

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

    2. Simplified1.1

      \[\leadsto \color{blue}{t + x \cdot \frac{z - t}{y}}\]
    3. Using strategy rm

    4. Applied add-sqr-sqrt1.2

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

    5. Applied *-un-lft-identity1.2

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

    6. Applied times-frac1.3

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

    7. Applied associate-*r*0.6

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

    8. Simplified0.6

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.46900420303610325 \cdot 10^{66}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;y \le 3.62519017211164247 \cdot 10^{34}:\\ \;\;\;\;t + \left(x \cdot \left(z - t\right)\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\sqrt{y}} \cdot \frac{z - t}{\sqrt{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))