Average Error: 2.2 → 2.2
Time: 6.3s
Precision: binary64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.65384692435384897 \cdot 10^{-31} \lor \neg \left(y \le 7.8552782891924364 \cdot 10^{-172}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.65384692435384897 \cdot 10^{-31} \lor \neg \left(y \le 7.8552782891924364 \cdot 10^{-172}\right):\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(x - y\right) \cdot 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 <= -4.653846924353849e-31) || !(y <= 7.855278289192436e-172))) {
		VAR = ((double) (((double) (((double) (x - y)) / ((double) (z - y)))) * t));
	} else {
		VAR = ((double) (((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

Original2.2
Target2.2
Herbie2.2
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.65384692435384897e-31 or 7.8552782891924364e-172 < y

    1. Initial program 1.0

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

    if -4.65384692435384897e-31 < y < 7.8552782891924364e-172

    1. Initial program 5.0

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

    3. Applied associate-*l/4.9

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.65384692435384897 \cdot 10^{-31} \lor \neg \left(y \le 7.8552782891924364 \cdot 10^{-172}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020163 
(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))