Average Error: 11.5 → 1.4
Time: 9.8s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -9.693178357350792 \cdot 10^{+194}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.6781988869850722 \cdot 10^{+238}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -9.693178357350792 \cdot 10^{+194}:\\
\;\;\;\;x \cdot \frac{y - z}{t - z}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.6781988869850722 \cdot 10^{+238}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\

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

\end{array}
(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x (- y z)) (- t z)) -9.693178357350792e+194)
   (* x (/ (- y z) (- t z)))
   (if (<= (/ (* x (- y z)) (- t z)) 1.6781988869850722e+238)
     (/ (* x (- y z)) (- t z))
     (/ x (/ (- t z) (- y 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)) <= -9.693178357350792e+194) {
		tmp = x * ((y - z) / (t - z));
	} else if (((x * (y - z)) / (t - z)) <= 1.6781988869850722e+238) {
		tmp = (x * (y - z)) / (t - z);
	} else {
		tmp = x / ((t - z) / (y - 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

Original11.5
Target2.2
Herbie1.4
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -9.69317835735079163e194

    1. Initial program 46.3

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

    2. Simplified2.2

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

    if -9.69317835735079163e194 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.67819888698507223e238

    1. Initial program 1.3

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

    if 1.67819888698507223e238 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

    1. Initial program 53.3

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

    2. Simplified1.1

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -9.693178357350792 \cdot 10^{+194}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.6781988869850722 \cdot 10^{+238}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021176 
(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)))