Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Average Error: 12.9 → 0.5

Time: 3.9min

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \le -7.52835981644123167 \cdot 10^{304}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \le -2.59558062994810634 \cdot 10^{26}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \le 3.0413648196648165 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \le 3.60838654474187404 \cdot 10^{290}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + z\right)\\ \end{array}\]

C

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) <= -7.528359816441232e+304)) {
		VAR = (x / (z / ((double) (y + z))));
	} else {
		double VAR_1;
		if (((((double) (x * ((double) (y + z)))) / z) <= -2.5955806299481063e+26)) {
			VAR_1 = (((double) (x * ((double) (y + z)))) / z);
		} else {
			double VAR_2;
			if (((((double) (x * ((double) (y + z)))) / z) <= 3.0413648196648165e-53)) {
				VAR_2 = (x / (z / ((double) (y + z))));
			} else {
				double VAR_3;
				if (((((double) (x * ((double) (y + z)))) / z) <= 3.608386544741874e+290)) {
					VAR_3 = (((double) (x * ((double) (y + z)))) / z);
				} else {
					VAR_3 = ((double) ((x / z) * ((double) (y + z))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	12.9
Target	2.9
Herbie	0.5

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

Derivation

1. Split input into 3 regimes

2. if (/ (* x (+ y z)) z) < -7.52835981644123167e304 or -2.59558062994810634e26 < (/ (* x (+ y z)) z) < 3.0413648196648165e-53

   1. Initial program 16.0

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

   3. Applied associate-/l* 0.1

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

   if -7.52835981644123167e304 < (/ (* x (+ y z)) z) < -2.59558062994810634e26 or 3.0413648196648165e-53 < (/ (* x (+ y z)) z) < 3.60838654474187404e290

   1. Initial program 0.2

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

   if 3.60838654474187404e290 < (/ (* x (+ y z)) z)

   1. Initial program 57.4

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

   3. Applied associate-/l* 1.5

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

   5. Applied associate-/r/ 3.4

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

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \le -7.52835981644123167 \cdot 10^{304}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \le -2.59558062994810634 \cdot 10^{26}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \le 3.0413648196648165 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \le 3.60838654474187404 \cdot 10^{290}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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))