Average Error: 11.9 → 2.6
Time: 2.8s
Precision: binary64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -6.060181816469218 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{elif}\;x \le -1.07880906454998636 \cdot 10^{-283}:\\ \;\;\;\;\frac{x \cdot y}{z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -6.060181816469218 \cdot 10^{-187}:\\
\;\;\;\;x \cdot \frac{y + z}{z}\\

\mathbf{elif}\;x \le -1.07880906454998636 \cdot 10^{-283}:\\
\;\;\;\;\frac{x \cdot y}{z} + x\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{y + z}}\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) (y + z)))) / z));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((x <= -6.060181816469218e-187)) {
		VAR = ((double) (x * ((double) (((double) (y + z)) / z))));
	} else {
		double VAR_1;
		if ((x <= -1.0788090645499864e-283)) {
			VAR_1 = ((double) (((double) (((double) (x * y)) / z)) + x));
		} else {
			VAR_1 = ((double) (x / ((double) (z / ((double) (y + z))))));
		}
		VAR = VAR_1;
	}
	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

Original11.9
Target2.7
Herbie2.6
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -6.060181816469218e-187

    1. Initial program 12.7

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

    3. Applied *-un-lft-identity12.7

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

    4. Applied times-frac1.9

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

    5. Simplified1.9

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

    if -6.060181816469218e-187 < x < -1.0788090645499864e-283

    1. Initial program 7.1

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

    2. Taylor expanded around 0 3.0

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

    if -1.0788090645499864e-283 < x

    1. Initial program 12.2

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

    3. Applied associate-/l*3.1

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.060181816469218 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{elif}\;x \le -1.07880906454998636 \cdot 10^{-283}:\\ \;\;\;\;\frac{x \cdot y}{z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020148 
(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))