Average Error: 2.0 → 2.6
Time: 5.1s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.398221560293491 \cdot 10^{-111} \lor \neg \left(z \le 9.8776861560231574 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{y} \cdot z + \left(t - t \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.398221560293491 \cdot 10^{-111} \lor \neg \left(z \le 9.8776861560231574 \cdot 10^{-45}\right):\\
\;\;\;\;\frac{x}{y} \cdot z + \left(t - t \cdot \frac{x}{y}\right)\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x / y)) * ((double) (z - t)))) + t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((z <= -1.3982215602934908e-111) || !(z <= 9.877686156023157e-45))) {
		VAR = ((double) (((double) (((double) (x / y)) * z)) + ((double) (t - ((double) (t * ((double) (x / y))))))));
	} else {
		VAR = ((double) (((double) (((double) (x * ((double) (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

Original2.0
Target2.3
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.398221560293491e-111 or 9.8776861560231574e-45 < z

    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

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

    5. Applied associate-+l+1.4

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

    6. Simplified1.4

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

    if -1.398221560293491e-111 < z < 9.8776861560231574e-45

    1. Initial program 2.9

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

    3. Applied associate-*l/4.3

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.398221560293491 \cdot 10^{-111} \lor \neg \left(z \le 9.8776861560231574 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{y} \cdot z + \left(t - t \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020171 
(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))