Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Average Error: 12.3 → 0.9

Time: 12.7s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} = -\infty \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le -6.314719169796707913625869261166949931185 \cdot 10^{133} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 260817532774.372833251953125\right) \land \frac{x \cdot \left(y + z\right)}{z} \le 5.286185397003034641152716277040577167977 \cdot 10^{280}\right):\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r321490 = x;
        double r321491 = y;
        double r321492 = z;
        double r321493 = r321491 + r321492;
        double r321494 = r321490 * r321493;
        double r321495 = r321494 / r321492;
        return r321495;
}

↓

double f(double x, double y, double z) {
        double r321496 = x;
        double r321497 = y;
        double r321498 = z;
        double r321499 = r321497 + r321498;
        double r321500 = r321496 * r321499;
        double r321501 = r321500 / r321498;
        double r321502 = -inf.0;
        bool r321503 = r321501 <= r321502;
        double r321504 = -6.314719169796708e+133;
        bool r321505 = r321501 <= r321504;
        double r321506 = 260817532774.37283;
        bool r321507 = r321501 <= r321506;
        double r321508 = !r321507;
        double r321509 = 5.286185397003035e+280;
        bool r321510 = r321501 <= r321509;
        bool r321511 = r321508 && r321510;
        bool r321512 = r321505 || r321511;
        double r321513 = !r321512;
        bool r321514 = r321503 || r321513;
        double r321515 = r321499 / r321498;
        double r321516 = r321496 * r321515;
        double r321517 = r321514 ? r321516 : r321501;
        return r321517;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	12.3
Target	3.2
Herbie	0.9

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

Derivation

1. Split input into 2 regimes

2. if (/ (* x (+ y z)) z) < -inf.0 or -6.314719169796708e+133 < (/ (* x (+ y z)) z) < 260817532774.37283 or 5.286185397003035e+280 < (/ (* x (+ y z)) z)

   1. Initial program 17.4

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

   3. Applied *-un-lft-identity 17.4

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

   4. Applied times-frac 1.2

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

   5. Simplified 1.2

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

   if -inf.0 < (/ (* x (+ y z)) z) < -6.314719169796708e+133 or 260817532774.37283 < (/ (* x (+ y z)) z) < 5.286185397003035e+280

   1. Initial program 0.2

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

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} = -\infty \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le -6.314719169796707913625869261166949931185 \cdot 10^{133} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \le 260817532774.372833251953125\right) \land \frac{x \cdot \left(y + z\right)}{z} \le 5.286185397003034641152716277040577167977 \cdot 10^{280}\right):\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))