Average Error: 2.1 → 1.5
Time: 3.4s
Precision: binary64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le 3.97599780479126807 \cdot 10^{218}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - y\right) \cdot t\right) \cdot \frac{1}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le 3.97599780479126807 \cdot 10^{218}:\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x - y\right) \cdot t\right) \cdot \frac{1}{z - y}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x - y)) / ((double) (z - y)))) * t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) (((double) (x - y)) / ((double) (z - y)))) <= 3.975997804791268e+218)) {
		VAR = ((double) (((double) (((double) (x - y)) / ((double) (z - y)))) * t));
	} else {
		VAR = ((double) (((double) (((double) (x - y)) * t)) * ((double) (1.0 / ((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

Original2.1
Target2.1
Herbie1.5
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- x y) (- z y)) < 3.97599780479126807e218

    1. Initial program 1.6

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

    if 3.97599780479126807e218 < (/ (- x y) (- z y))

    1. Initial program 26.4

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

    3. Applied div-inv26.4

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

    4. Applied associate-*l*0.9

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

    5. Simplified0.8

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

    7. Applied div-inv0.9

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

    8. Applied associate-*r*0.4

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le 3.97599780479126807 \cdot 10^{218}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - y\right) \cdot t\right) \cdot \frac{1}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020161 
(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))