Average Error: 1.9 → 1.5
Time: 3.1s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.54076295773237828 \cdot 10^{26} \lor \neg \left(y \le 3.6542658473411332 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.54076295773237828 \cdot 10^{26} \lor \neg \left(y \le 3.6542658473411332 \cdot 10^{-81}\right):\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + 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 <= -1.5407629577323783e+26) || !(y <= 3.654265847341133e-81))) {
		VAR = ((x * ((z - t) / y)) + t);
	} else {
		VAR = (((x * (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

Original1.9
Target2.0
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.5407629577323783e+26 or 3.654265847341133e-81 < y

    1. Initial program 1.0

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

    3. Applied div-inv1.1

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

    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 -1.5407629577323783e+26 < y < 3.654265847341133e-81

    1. Initial program 3.5

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

    3. Applied associate-*l/1.7

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.54076295773237828 \cdot 10^{26} \lor \neg \left(y \le 3.6542658473411332 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020102 +o rules:numerics
(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))