Average Error: 12.8 → 2.2
Time: 2.6s
Precision: binary64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 1102539.5060136039 \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \leq 6.050063273952053 \cdot 10^{+226}\right):\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 1102539.5060136039 \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \leq 6.050063273952053 \cdot 10^{+226}\right):\\
\;\;\;\;x + x \cdot \frac{y}{z}\\

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

\end{array}
double code(double x, double y, double z) {
	return (((double) (x * ((double) (y + z)))) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((((((double) (x * ((double) (y + z)))) / z) <= 1102539.5060136039) || !((((double) (x * ((double) (y + z)))) / z) <= 6.050063273952053e+226))) {
		VAR = ((double) (x + ((double) (x * (y / z)))));
	} else {
		VAR = (((double) (x * ((double) (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

Original12.8
Target3.0
Herbie2.2
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (+ y z)) z) < 1102539.5060136039 or 6.0500632739520535e226 < (/ (* x (+ y z)) z)

    1. Initial program 15.2

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

    2. Simplified2.6

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

    if 1102539.5060136039 < (/ (* x (+ y z)) z) < 6.0500632739520535e226

    1. Initial program 0.2

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 1102539.5060136039 \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \leq 6.050063273952053 \cdot 10^{+226}\right):\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(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))