Average Error: 1.9 → 2.0
Time: 3.5s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -1.5155016460348557 \cdot 10^{-124} \lor \neg \left(y \leq 1.2472961326844655 \cdot 10^{+29}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \left(z - t\right)\right) \cdot \frac{1}{y}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \leq -1.5155016460348557 \cdot 10^{-124} \lor \neg \left(y \leq 1.2472961326844655 \cdot 10^{+29}\right):\\
\;\;\;\;t + x \cdot \frac{z - t}{y}\\

\mathbf{else}:\\
\;\;\;\;t + \left(x \cdot \left(z - t\right)\right) \cdot \frac{1}{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 <= -1.5155016460348557e-124) || !(y <= 1.2472961326844655e+29))) {
		VAR = ((double) (t + ((double) (x * (((double) (z - t)) / y)))));
	} else {
		VAR = ((double) (t + ((double) (((double) (x * ((double) (z - t)))) * (1.0 / y)))));
	}
	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

Original1.9
Target2.3
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.51550164603485571e-124 or 1.2472961326844655e29 < y

    1. Initial program 1.1

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

    2. Simplified2.0

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

    if -1.51550164603485571e-124 < y < 1.2472961326844655e29

    1. Initial program 3.7

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

    3. Applied associate-*l/2.0

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

    5. Applied div-inv2.1

      \[\leadsto \color{blue}{\left(x \cdot \left(z - t\right)\right) \cdot \frac{1}{y}} + t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5155016460348557 \cdot 10^{-124} \lor \neg \left(y \leq 1.2472961326844655 \cdot 10^{+29}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \left(z - t\right)\right) \cdot \frac{1}{y}\\ \end{array}\]

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))