Average Error: 11.3 → 1.2
Time: 6.8s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -5.952252119762416 \cdot 10^{+264} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.3347842911496855 \cdot 10^{+300}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -5.952252119762416 \cdot 10^{+264} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.3347842911496855 \cdot 10^{+300}\right):\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

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

\end{array}
(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ (* x (- y z)) (- t z)) -5.952252119762416e+264)
         (not (<= (/ (* x (- y z)) (- t z)) 1.3347842911496855e+300)))
   (* x (/ (- y z) (- t z)))
   (/ (* x (- y z)) (- t z))))
double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x * (y - z)) / (t - z)) <= -5.952252119762416e+264) || !(((x * (y - z)) / (t - z)) <= 1.3347842911496855e+300)) {
		tmp = x * ((y - z) / (t - z));
	} else {
		tmp = (x * (y - z)) / (t - z);
	}
	return tmp;
}

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

Original11.3
Target2.1
Herbie1.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -5.95225211976241631e264 or 1.33478429114968551e300 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

    1. Initial program 59.6

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

    3. Applied *-un-lft-identity_binary64_1508259.6

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

    4. Applied times-frac_binary64_150880.8

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

    if -5.95225211976241631e264 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.33478429114968551e300

    1. Initial program 1.3

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -5.952252119762416 \cdot 10^{+264} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.3347842911496855 \cdot 10^{+300}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2021043 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))