Average Error: 12.4 → 2.5
Time: 1.5s
Precision: 64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.2437167390649342 \cdot 10^{138}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} + x\\ \mathbf{elif}\;y \le 6.42201996887575028 \cdot 10^{193}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;y \le 3.4762136697281315 \cdot 10^{266}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.2437167390649342 \cdot 10^{138}:\\
\;\;\;\;\frac{y}{\frac{z}{x}} + x\\

\mathbf{elif}\;y \le 6.42201996887575028 \cdot 10^{193}:\\
\;\;\;\;\frac{x}{\frac{z}{y + z}}\\

\mathbf{elif}\;y \le 3.4762136697281315 \cdot 10^{266}:\\
\;\;\;\;\frac{y}{\frac{z}{x}} + x\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{y + z}{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 ((y <= -3.243716739064934e+138)) {
		VAR = ((y / (z / x)) + x);
	} else {
		double VAR_1;
		if ((y <= 6.42201996887575e+193)) {
			VAR_1 = (x / (z / (y + z)));
		} else {
			double VAR_2;
			if ((y <= 3.4762136697281315e+266)) {
				VAR_2 = ((y / (z / x)) + x);
			} else {
				VAR_2 = (x * ((y + z) / z));
			}
			VAR_1 = VAR_2;
		}
		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

Original12.4
Target3.0
Herbie2.5
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -3.243716739064934e+138 or 6.42201996887575e+193 < y < 3.4762136697281315e+266

    1. Initial program 12.2

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

    2. Taylor expanded around 0 11.2

      \[\leadsto \color{blue}{\frac{x \cdot y}{z} + x}\]
    3. Using strategy rm

    4. Applied *-commutative11.2

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

    5. Applied associate-/l*7.3

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

    if -3.243716739064934e+138 < y < 6.42201996887575e+193

    1. Initial program 12.4

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

    3. Applied associate-/l*1.4

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

    if 3.4762136697281315e+266 < y

    1. Initial program 16.9

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

    3. Applied associate-/l*12.8

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + z}}}\]
    4. Using strategy rm

    5. Applied div-inv13.8

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

    6. Simplified13.7

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

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.2437167390649342 \cdot 10^{138}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} + x\\ \mathbf{elif}\;y \le 6.42201996887575028 \cdot 10^{193}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;y \le 3.4762136697281315 \cdot 10^{266}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(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))