Average Error: 2.3 → 2.3
Time: 3.7s
Precision: binary64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8.72434399653163883 \cdot 10^{-74} \lor \neg \left(y \le 9.7809318527076706 \cdot 10^{-114}\right):\\ \;\;\;\;\left(\frac{x}{z - y} + \frac{-1}{\frac{z}{y} + -1}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -8.72434399653163883 \cdot 10^{-74} \lor \neg \left(y \le 9.7809318527076706 \cdot 10^{-114}\right):\\
\;\;\;\;\left(\frac{x}{z - y} + \frac{-1}{\frac{z}{y} + -1}\right) \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) (((double) (x - y)) / ((double) (z - y)))) * t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((y <= -8.724343996531639e-74) || !(y <= 9.78093185270767e-114))) {
		VAR = ((double) (((double) (((double) (x / ((double) (z - y)))) + ((double) (-1.0 / ((double) (((double) (z / y)) + -1.0)))))) * t));
	} else {
		VAR = ((double) (((double) (x - y)) * ((double) (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
Herbie2.3
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -8.72434399653163883e-74 or 9.7809318527076706e-114 < y

    1. Initial program 0.5

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

    3. Applied div-sub0.5

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

    5. Applied clear-num0.6

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

    6. Simplified0.6

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

    if -8.72434399653163883e-74 < y < 9.7809318527076706e-114

    1. Initial program 6.0

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

    2. Simplified5.9

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.72434399653163883 \cdot 10^{-74} \lor \neg \left(y \le 9.7809318527076706 \cdot 10^{-114}\right):\\ \;\;\;\;\left(\frac{x}{z - y} + \frac{-1}{\frac{z}{y} + -1}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))