Average Error: 2.3 → 0.8
Time: 3.7s
Precision: binary64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.64977974968708 \cdot 10^{231} \lor \neg \left(\frac{x - y}{z - y} \le -1.075489859696683 \cdot 10^{-142} \lor \neg \left(\frac{x - y}{z - y} \le 0.0\right) \land \frac{x - y}{z - y} \le 3.62810592939642737 \cdot 10^{68}\right):\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le -1.64977974968708 \cdot 10^{231} \lor \neg \left(\frac{x - y}{z - y} \le -1.075489859696683 \cdot 10^{-142} \lor \neg \left(\frac{x - y}{z - y} \le 0.0\right) \land \frac{x - y}{z - y} \le 3.62810592939642737 \cdot 10^{68}\right):\\
\;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

\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)))) <= -1.64977974968708e+231) || !((((double) (((double) (x - y)) / ((double) (z - y)))) <= -1.075489859696683e-142) || (!(((double) (((double) (x - y)) / ((double) (z - y)))) <= 0.0) && (((double) (((double) (x - y)) / ((double) (z - y)))) <= 3.6281059293964274e+68))))) {
		VAR = ((double) (((double) (x - y)) / ((double) (((double) (z - y)) / t))));
	} else {
		VAR = ((double) (((double) (((double) (x - y)) / ((double) (z - y)))) * t));
	}
	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
Herbie0.8
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- x y) (- z y)) < -1.64977974968708e231 or -1.075489859696683e-142 < (/ (- x y) (- z y)) < 0.0 or 3.62810592939642737e68 < (/ (- x y) (- z y))

    1. Initial program 10.5

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

    3. Applied associate-*l/2.9

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

    5. Applied associate-/l*3.2

      \[\leadsto \color{blue}{\frac{x - y}{\frac{z - y}{t}}}\]

    if -1.64977974968708e231 < (/ (- x y) (- z y)) < -1.075489859696683e-142 or 0.0 < (/ (- x y) (- z y)) < 3.62810592939642737e68

    1. Initial program 0.2

      \[\frac{x - y}{z - y} \cdot t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.64977974968708 \cdot 10^{231} \lor \neg \left(\frac{x - y}{z - y} \le -1.075489859696683 \cdot 10^{-142} \lor \neg \left(\frac{x - y}{z - y} \le 0.0\right) \land \frac{x - y}{z - y} \le 3.62810592939642737 \cdot 10^{68}\right):\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(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))