Average Error: 2.1 → 2.1
Time: 4.0s
Precision: binary64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1.9103146133462065 \cdot 10^{+82}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x - y\right) \cdot \frac{1}{z - y}\right)\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \leq -1.9103146133462065 \cdot 10^{+82}:\\
\;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\

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

\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 (((((double) (x - y)) / ((double) (z - y))) <= -1.9103146133462065e+82)) {
		VAR = ((double) (((double) (x - y)) * (t / ((double) (z - y)))));
	} else {
		VAR = ((double) (t * ((double) (((double) (x - y)) * (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
Herbie2.1
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- x y) (- z y)) < -1.9103146133462065e82

    1. Initial program 6.8

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

    2. Simplified4.8

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

    if -1.9103146133462065e82 < (/ (- x y) (- z y))

    1. Initial program 1.8

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

    3. Applied div-inv1.9

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1.9103146133462065 \cdot 10^{+82}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x - y\right) \cdot \frac{1}{z - y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(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))