Average Error: 2.3 → 2.4
Time: 3.3min
Precision: binary64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le 9.0572447404066833 \cdot 10^{-289} \lor \neg \left(y \le 7.1873917266292553 \cdot 10^{-201}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le 9.0572447404066833 \cdot 10^{-289} \lor \neg \left(y \le 7.1873917266292553 \cdot 10^{-201}\right):\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) ((((double) (x - y)) / ((double) (z - y))) * t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((y <= 9.057244740406683e-289) || !(y <= 7.187391726629255e-201))) {
		VAR = ((double) ((((double) (x - y)) / ((double) (z - y))) * t));
	} else {
		VAR = ((double) (((double) (x - y)) * (t / ((double) (z - 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

Original2.3
Target2.3
Herbie2.4
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < 9.0572447404066833e-289 or 7.1873917266292553e-201 < y

    1. Initial program 2.0

      \[\frac{x - y}{z - y} \cdot t\]

    if 9.0572447404066833e-289 < y < 7.1873917266292553e-201

    1. Initial program 6.0

      \[\frac{x - y}{z - y} \cdot t\]
    2. Using strategy rm

    3. Applied div-inv6.1

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

    4. Applied associate-*l*7.8

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

    5. Simplified7.8

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 9.0572447404066833 \cdot 10^{-289} \lor \neg \left(y \le 7.1873917266292553 \cdot 10^{-201}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))