Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Average Error: 13.1 → 0.7

Time: 2.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} = -\infty \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le -1.24043934112551738 \cdot 10^{170} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 30542.5456077980816 \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 7.426458603776121 \cdot 10^{296}\right)\right)\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]

C

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 (((((double) (((double) (x * ((double) (y + z)))) / z)) <= -inf.0) || !((((double) (((double) (x * ((double) (y + z)))) / z)) <= -1.2404393411255174e+170) || !((((double) (((double) (x * ((double) (y + z)))) / z)) <= 30542.54560779808) || !(((double) (((double) (x * ((double) (y + z)))) / z)) <= 7.42645860377612e+296))))) {
		VAR = ((double) (x / ((double) (z / ((double) (y + z))))));
	} else {
		VAR = ((double) (((double) (x * ((double) (y + z)))) / z));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	13.1
Target	2.7
Herbie	0.7

\[\frac{x}{\frac{z}{y + z}}\]

Derivation

1. Split input into 2 regimes

2. if (/ (* x (+ y z)) z) < -inf.0 or -1.2404393411255174e+170 < (/ (* x (+ y z)) z) < 30542.54560779808 or 7.42645860377612e+296 < (/ (* x (+ y z)) z)

   1. Initial program 18.0

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

   3. Applied associate-/l* 0.8

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

   if -inf.0 < (/ (* x (+ y z)) z) < -1.2404393411255174e+170 or 30542.54560779808 < (/ (* x (+ y z)) z) < 7.42645860377612e+296

   1. Initial program 0.2

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} = -\infty \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le -1.24043934112551738 \cdot 10^{170} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 30542.5456077980816 \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 7.426458603776121 \cdot 10^{296}\right)\right)\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020120 
(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))