Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Average Error: 11.7 → 0.5

Time: 1.1m

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(y + z\right) \cdot x}{z} = -\infty:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le -3.0719468564861416 \cdot 10^{-106}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot x}{z}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le 2.739367360965913 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le 1.597998240181167 \cdot 10^{+270}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r20731294 = x;
        double r20731295 = y;
        double r20731296 = z;
        double r20731297 = r20731295 + r20731296;
        double r20731298 = r20731294 * r20731297;
        double r20731299 = r20731298 / r20731296;
        return r20731299;
}

↓

double f(double x, double y, double z) {
        double r20731300 = y;
        double r20731301 = z;
        double r20731302 = r20731300 + r20731301;
        double r20731303 = x;
        double r20731304 = r20731302 * r20731303;
        double r20731305 = r20731304 / r20731301;
        double r20731306 = -inf.0;
        bool r20731307 = r20731305 <= r20731306;
        double r20731308 = r20731302 / r20731301;
        double r20731309 = r20731303 * r20731308;
        double r20731310 = -3.0719468564861416e-106;
        bool r20731311 = r20731305 <= r20731310;
        double r20731312 = 2.739367360965913e+16;
        bool r20731313 = r20731305 <= r20731312;
        double r20731314 = 1.597998240181167e+270;
        bool r20731315 = r20731305 <= r20731314;
        double r20731316 = r20731315 ? r20731305 : r20731309;
        double r20731317 = r20731313 ? r20731309 : r20731316;
        double r20731318 = r20731311 ? r20731305 : r20731317;
        double r20731319 = r20731307 ? r20731309 : r20731318;
        return r20731319;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	11.7
Target	2.9
Herbie	0.5

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

Derivation

1. Split input into 2 regimes

2. if (/ (* x (+ y z)) z) < -inf.0 or -3.0719468564861416e-106 < (/ (* x (+ y z)) z) < 2.739367360965913e+16 or 1.597998240181167e+270 < (/ (* x (+ y z)) z)

   1. Initial program 22.3

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

   3. Applied *-un-lft-identity 22.3

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

   4. Applied times-frac 0.7

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

   5. Simplified 0.7

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

   if -inf.0 < (/ (* x (+ y z)) z) < -3.0719468564861416e-106 or 2.739367360965913e+16 < (/ (* x (+ y z)) z) < 1.597998240181167e+270

   1. Initial program 0.2

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

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y + z\right) \cdot x}{z} = -\infty:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le -3.0719468564861416 \cdot 10^{-106}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot x}{z}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le 2.739367360965913 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le 1.597998240181167 \cdot 10^{+270}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))