Average Error: 12.5 → 0.7
Time: 2.0s
Precision: 64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \le -2.8024718099763744 \cdot 10^{284} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le -2.72792898397245706 \cdot 10^{55} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 1.6295824888591354 \cdot 10^{-81} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 2.06201301805685587 \cdot 10^{265}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \le -2.8024718099763744 \cdot 10^{284} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le -2.72792898397245706 \cdot 10^{55} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 1.6295824888591354 \cdot 10^{-81} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 2.06201301805685587 \cdot 10^{265}\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 temp;
	if (((((x * (y + z)) / z) <= -2.8024718099763744e+284) || !((((x * (y + z)) / z) <= -2.727928983972457e+55) || !((((x * (y + z)) / z) <= 1.6295824888591354e-81) || !(((x * (y + z)) / z) <= 2.062013018056856e+265))))) {
		temp = (x * ((y + z) / z));
	} else {
		temp = ((x * (y + z)) / z);
	}
	return temp;
}

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
Target3.2
Herbie0.7
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (+ y z)) z) < -2.8024718099763744e+284 or -2.727928983972457e+55 < (/ (* x (+ y z)) z) < 1.6295824888591354e-81 or 2.062013018056856e+265 < (/ (* x (+ y z)) z)

    1. Initial program 21.3

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

    3. Applied *-un-lft-identity21.3

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

    4. Applied times-frac1.0

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

    5. Simplified1.0

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

    if -2.8024718099763744e+284 < (/ (* x (+ y z)) z) < -2.727928983972457e+55 or 1.6295824888591354e-81 < (/ (* x (+ y z)) z) < 2.062013018056856e+265

    1. Initial program 0.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \le -2.8024718099763744 \cdot 10^{284} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le -2.72792898397245706 \cdot 10^{55} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 1.6295824888591354 \cdot 10^{-81} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 2.06201301805685587 \cdot 10^{265}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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))