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

Average Error: 6.8 → 3.4

Time: 19.7s

Precision: 64

Math

\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.705982485713477 \cdot 10^{+79}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \mathbf{elif}\;z \le 2.2939420975234537 \cdot 10^{+108}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r33352565 = x;
        double r33352566 = y;
        double r33352567 = z;
        double r33352568 = r33352566 * r33352567;
        double r33352569 = r33352568 - r33352565;
        double r33352570 = t;
        double r33352571 = r33352570 * r33352567;
        double r33352572 = r33352571 - r33352565;
        double r33352573 = r33352569 / r33352572;
        double r33352574 = r33352565 + r33352573;
        double r33352575 = 1.0;
        double r33352576 = r33352565 + r33352575;
        double r33352577 = r33352574 / r33352576;
        return r33352577;
}

↓

double f(double x, double y, double z, double t) {
        double r33352578 = z;
        double r33352579 = -1.705982485713477e+79;
        bool r33352580 = r33352578 <= r33352579;
        double r33352581 = x;
        double r33352582 = y;
        double r33352583 = t;
        double r33352584 = r33352582 / r33352583;
        double r33352585 = r33352581 + r33352584;
        double r33352586 = 1.0;
        double r33352587 = r33352581 + r33352586;
        double r33352588 = r33352585 / r33352587;
        double r33352589 = 2.2939420975234537e+108;
        bool r33352590 = r33352578 <= r33352589;
        double r33352591 = r33352582 * r33352578;
        double r33352592 = r33352591 - r33352581;
        double r33352593 = r33352583 * r33352578;
        double r33352594 = r33352593 - r33352581;
        double r33352595 = r33352592 / r33352594;
        double r33352596 = r33352581 + r33352595;
        double r33352597 = r33352596 / r33352587;
        double r33352598 = r33352590 ? r33352597 : r33352588;
        double r33352599 = r33352580 ? r33352588 : r33352598;
        return r33352599;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.8
Target	0.4
Herbie	3.4

\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]

Derivation

1. Split input into 2 regimes

2. if z < -1.705982485713477e+79 or 2.2939420975234537e+108 < z

   1. Initial program 18.5

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]

   2. Taylor expanded around inf 8.1

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1.0}\]

   if -1.705982485713477e+79 < z < 2.2939420975234537e+108

   1. Initial program 1.0

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]

   2. Taylor expanded around 0 1.0

      \[\leadsto \frac{x + \frac{\color{blue}{z \cdot y - x}}{t \cdot z - x}}{x + 1.0}\]
3. Recombined 2 regimes into one program.

4. Final simplification 3.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.705982485713477 \cdot 10^{+79}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \mathbf{elif}\;z \le 2.2939420975234537 \cdot 10^{+108}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(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)))