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

Average Error: 7.3 → 2.1

Time: 11.3s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} = -\infty \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 8.3183219701519654 \cdot 10^{263}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r878619 = x;
        double r878620 = y;
        double r878621 = z;
        double r878622 = r878620 * r878621;
        double r878623 = r878622 - r878619;
        double r878624 = t;
        double r878625 = r878624 * r878621;
        double r878626 = r878625 - r878619;
        double r878627 = r878623 / r878626;
        double r878628 = r878619 + r878627;
        double r878629 = 1.0;
        double r878630 = r878619 + r878629;
        double r878631 = r878628 / r878630;
        return r878631;
}

↓

double f(double x, double y, double z, double t) {
        double r878632 = x;
        double r878633 = y;
        double r878634 = z;
        double r878635 = r878633 * r878634;
        double r878636 = r878635 - r878632;
        double r878637 = t;
        double r878638 = r878637 * r878634;
        double r878639 = r878638 - r878632;
        double r878640 = r878636 / r878639;
        double r878641 = r878632 + r878640;
        double r878642 = 1.0;
        double r878643 = r878632 + r878642;
        double r878644 = r878641 / r878643;
        double r878645 = -inf.0;
        bool r878646 = r878644 <= r878645;
        double r878647 = 8.318321970151965e+263;
        bool r878648 = r878644 <= r878647;
        double r878649 = !r878648;
        bool r878650 = r878646 || r878649;
        double r878651 = r878633 / r878637;
        double r878652 = r878632 + r878651;
        double r878653 = r878652 / r878643;
        double r878654 = r878650 ? r878653 : r878644;
        return r878654;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.3
Target	0.4
Herbie	2.1

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

Derivation

1. Split input into 2 regimes

2. if (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) < -inf.0 or 8.318321970151965e+263 < (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))

   1. Initial program 61.3

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

   2. Taylor expanded around inf 14.0

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

   if -inf.0 < (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) < 8.318321970151965e+263

   1. Initial program 0.7

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

4. Final simplification 2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} = -\infty \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 8.3183219701519654 \cdot 10^{263}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))