Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Average Error: 7.2 → 3.6

Time: 1.1m

Precision: 64

Math

\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -8.287165386060872715453133833603909602049 \cdot 10^{86}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{1 + x}\\ \mathbf{elif}\;z \le 3.348305293084260034623912739354303673528 \cdot 10^{56}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{1 + x}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r37477616 = x;
        double r37477617 = y;
        double r37477618 = z;
        double r37477619 = r37477617 * r37477618;
        double r37477620 = r37477619 - r37477616;
        double r37477621 = t;
        double r37477622 = r37477621 * r37477618;
        double r37477623 = r37477622 - r37477616;
        double r37477624 = r37477620 / r37477623;
        double r37477625 = r37477616 + r37477624;
        double r37477626 = 1.0;
        double r37477627 = r37477616 + r37477626;
        double r37477628 = r37477625 / r37477627;
        return r37477628;
}

↓

double f(double x, double y, double z, double t) {
        double r37477629 = z;
        double r37477630 = -8.287165386060873e+86;
        bool r37477631 = r37477629 <= r37477630;
        double r37477632 = x;
        double r37477633 = y;
        double r37477634 = t;
        double r37477635 = r37477633 / r37477634;
        double r37477636 = r37477632 + r37477635;
        double r37477637 = 1.0;
        double r37477638 = r37477637 + r37477632;
        double r37477639 = r37477636 / r37477638;
        double r37477640 = 3.34830529308426e+56;
        bool r37477641 = r37477629 <= r37477640;
        double r37477642 = 1.0;
        double r37477643 = r37477634 * r37477629;
        double r37477644 = r37477643 - r37477632;
        double r37477645 = r37477633 * r37477629;
        double r37477646 = r37477645 - r37477632;
        double r37477647 = r37477644 / r37477646;
        double r37477648 = r37477642 / r37477647;
        double r37477649 = r37477632 + r37477648;
        double r37477650 = r37477649 / r37477638;
        double r37477651 = r37477641 ? r37477650 : r37477639;
        double r37477652 = r37477631 ? r37477639 : r37477651;
        return r37477652;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.2
Target	0.4
Herbie	3.6

\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

1. Split input into 2 regimes

2. if z < -8.287165386060873e+86 or 3.34830529308426e+56 < z

   1. Initial program 18.0

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]

   2. Taylor expanded around inf 8.3

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

   if -8.287165386060873e+86 < z < 3.34830529308426e+56

   1. Initial program 0.8

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
   2. Using strategy rm

   3. Applied clear-num 0.8

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}}{x + 1}\]
3. Recombined 2 regimes into one program.

4. Final simplification 3.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -8.287165386060872715453133833603909602049 \cdot 10^{86}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{1 + x}\\ \mathbf{elif}\;z \le 3.348305293084260034623912739354303673528 \cdot 10^{56}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{1 + x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))