Average Error: 12.5 → 0.8
Time: 2.4s
Precision: 64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \le -6.2559509423991317 \cdot 10^{293} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le -5.13924030840783878 \cdot 10^{59} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 1.4460188900352925 \cdot 10^{-198} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 2.35854138642000028 \cdot 10^{266}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \le -6.2559509423991317 \cdot 10^{293} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le -5.13924030840783878 \cdot 10^{59} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 1.4460188900352925 \cdot 10^{-198} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 2.35854138642000028 \cdot 10^{266}\right)\right)\right):\\
\;\;\;\;x \cdot \frac{y + z}{z}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((x * (y + z)) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((((x * (y + z)) / z) <= -6.255950942399132e+293) || !((((x * (y + z)) / z) <= -5.139240308407839e+59) || !((((x * (y + z)) / z) <= 1.4460188900352925e-198) || !(((x * (y + z)) / z) <= 2.3585413864200003e+266))))) {
		VAR = (x * ((y + z) / z));
	} else {
		VAR = ((x * (y + z)) / z);
	}
	return VAR;
}

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

Original12.5
Target2.7
Herbie0.8
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (+ y z)) z) < -6.255950942399132e+293 or -5.139240308407839e+59 < (/ (* x (+ y z)) z) < 1.4460188900352925e-198 or 2.3585413864200003e+266 < (/ (* x (+ y z)) z)

    1. Initial program 23.8

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

    3. Applied *-un-lft-identity23.8

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

    4. Applied times-frac1.2

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

    5. Simplified1.2

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

    if -6.255950942399132e+293 < (/ (* x (+ y z)) z) < -5.139240308407839e+59 or 1.4460188900352925e-198 < (/ (* x (+ y z)) z) < 2.3585413864200003e+266

    1. Initial program 0.3

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \le -6.2559509423991317 \cdot 10^{293} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le -5.13924030840783878 \cdot 10^{59} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 1.4460188900352925 \cdot 10^{-198} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 2.35854138642000028 \cdot 10^{266}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020092 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

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

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