Average Error: 11.8 → 1.2
Time: 3.9s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -1.3739507758416665 \cdot 10^{+251} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq 7.074286107254158 \cdot 10^{+295}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -1.3739507758416665 \cdot 10^{+251} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq 7.074286107254158 \cdot 10^{+295}\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)) -1.3739507758416665e+251)
         (not (<= (/ (* x (- y z)) (- t z)) 7.074286107254158e+295)))
   (* x (/ (- y z) (- t z)))
   (/ (* x (- y z)) (- t z))))
double code(double x, double y, double z, double t) {
	return (((double) (x * ((double) (y - z)))) / ((double) (t - z)));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if ((((((double) (x * ((double) (y - z)))) / ((double) (t - z))) <= -1.3739507758416665e+251) || !((((double) (x * ((double) (y - z)))) / ((double) (t - z))) <= 7.074286107254158e+295))) {
		tmp = ((double) (x * (((double) (y - z)) / ((double) (t - z)))));
	} else {
		tmp = (((double) (x * ((double) (y - z)))) / ((double) (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

Original11.8
Target2.1
Herbie1.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) (- t z)) < -1.37395077584166649e251 or 7.0742861072541579e295 < (/ (* x (- y z)) (- t z))

    1. Initial program Error: 59.3 bits

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

    2. SimplifiedError: 0.6 bits

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

    if -1.37395077584166649e251 < (/ (* x (- y z)) (- t z)) < 7.0742861072541579e295

    1. Initial program Error: 1.3 bits

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

  4. Final simplificationError: 1.2 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -1.3739507758416665 \cdot 10^{+251} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq 7.074286107254158 \cdot 10^{+295}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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)))