Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Average Error: 13.0 → 0.2

Time: 1.1m

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(y + z\right) \cdot x}{z} = -\infty:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le -4.14774853859052752082242347019496021536 \cdot 10^{-62}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot x}{z}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le 8.805228147539674220101537838741881415859 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le 1.284288781303400225636776173581348772622 \cdot 10^{300}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r20139020 = x;
        double r20139021 = y;
        double r20139022 = z;
        double r20139023 = r20139021 + r20139022;
        double r20139024 = r20139020 * r20139023;
        double r20139025 = r20139024 / r20139022;
        return r20139025;
}

↓

double f(double x, double y, double z) {
        double r20139026 = y;
        double r20139027 = z;
        double r20139028 = r20139026 + r20139027;
        double r20139029 = x;
        double r20139030 = r20139028 * r20139029;
        double r20139031 = r20139030 / r20139027;
        double r20139032 = -inf.0;
        bool r20139033 = r20139031 <= r20139032;
        double r20139034 = r20139027 / r20139028;
        double r20139035 = r20139029 / r20139034;
        double r20139036 = -4.1477485385905275e-62;
        bool r20139037 = r20139031 <= r20139036;
        double r20139038 = 8.805228147539674e-26;
        bool r20139039 = r20139031 <= r20139038;
        double r20139040 = 1.2842887813034002e+300;
        bool r20139041 = r20139031 <= r20139040;
        double r20139042 = r20139041 ? r20139031 : r20139035;
        double r20139043 = r20139039 ? r20139035 : r20139042;
        double r20139044 = r20139037 ? r20139031 : r20139043;
        double r20139045 = r20139033 ? r20139035 : r20139044;
        return r20139045;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	13.0
Target	3.1
Herbie	0.2

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

Derivation

1. Split input into 2 regimes

2. if (/ (* x (+ y z)) z) < -inf.0 or -4.1477485385905275e-62 < (/ (* x (+ y z)) z) < 8.805228147539674e-26 or 1.2842887813034002e+300 < (/ (* x (+ y z)) z)

   1. Initial program 25.5

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

   3. Applied associate-/l* 0.2

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

   if -inf.0 < (/ (* x (+ y z)) z) < -4.1477485385905275e-62 or 8.805228147539674e-26 < (/ (* x (+ y z)) z) < 1.2842887813034002e+300

   1. Initial program 0.2

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

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y + z\right) \cdot x}{z} = -\infty:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le -4.14774853859052752082242347019496021536 \cdot 10^{-62}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot x}{z}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le 8.805228147539674220101537838741881415859 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;\frac{\left(y + z\right) \cdot x}{z} \le 1.284288781303400225636776173581348772622 \cdot 10^{300}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019169 
(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))