Average Error: 9.9 → 0.4
Time: 3.2s
Precision: binary64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -6905077904.134682 \lor \neg \left(z \leq 3.1075019531474167 \cdot 10^{-105}\right):\\ \;\;\;\;y + x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -6905077904.134682 \lor \neg \left(z \leq 3.1075019531474167 \cdot 10^{-105}\right):\\
\;\;\;\;y + x \cdot \frac{1 - y}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (+ x (* y (- z x))) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6905077904.134682) (not (<= z 3.1075019531474167e-105)))
   (+ y (* x (/ (- 1.0 y) z)))
   (/ (+ x (* y (- z x))) z)))
double code(double x, double y, double z) {
	return (((double) (x + ((double) (y * ((double) (z - x)))))) / z);
}
↓
double code(double x, double y, double z) {
	double tmp;
	if (((z <= -6905077904.134682) || !(z <= 3.1075019531474167e-105))) {
		tmp = ((double) (y + ((double) (x * (((double) (1.0 - y)) / z)))));
	} else {
		tmp = (((double) (x + ((double) (y * ((double) (z - x)))))) / z);
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.9
Target0.0
Herbie0.4
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6905077904.1346817 or 3.10750195314741666e-105 < z

    1. Initial program Error: 14.6 bits

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

    2. SimplifiedError: 0.5 bits

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

    if -6905077904.1346817 < z < 3.10750195314741666e-105

    1. Initial program Error: 0.1 bits

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

  4. Final simplificationError: 0.4 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6905077904.134682 \lor \neg \left(z \leq 3.1075019531474167 \cdot 10^{-105}\right):\\ \;\;\;\;y + x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

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

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