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

Average Error: 7.6 → 3.8

Time: 18.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.160115839689408068409085936108477411806 \cdot 10^{172}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 3.641116230673848176898687453531338972974 \cdot 10^{130}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r34503727 = x;
        double r34503728 = y;
        double r34503729 = z;
        double r34503730 = r34503728 * r34503729;
        double r34503731 = r34503730 - r34503727;
        double r34503732 = t;
        double r34503733 = r34503732 * r34503729;
        double r34503734 = r34503733 - r34503727;
        double r34503735 = r34503731 / r34503734;
        double r34503736 = r34503727 + r34503735;
        double r34503737 = 1.0;
        double r34503738 = r34503727 + r34503737;
        double r34503739 = r34503736 / r34503738;
        return r34503739;
}

↓

double f(double x, double y, double z, double t) {
        double r34503740 = z;
        double r34503741 = -1.160115839689408e+172;
        bool r34503742 = r34503740 <= r34503741;
        double r34503743 = x;
        double r34503744 = y;
        double r34503745 = t;
        double r34503746 = r34503744 / r34503745;
        double r34503747 = r34503743 + r34503746;
        double r34503748 = 1.0;
        double r34503749 = r34503743 + r34503748;
        double r34503750 = r34503747 / r34503749;
        double r34503751 = 3.641116230673848e+130;
        bool r34503752 = r34503740 <= r34503751;
        double r34503753 = r34503744 * r34503740;
        double r34503754 = r34503753 - r34503743;
        double r34503755 = r34503745 * r34503740;
        double r34503756 = r34503755 - r34503743;
        double r34503757 = r34503754 / r34503756;
        double r34503758 = r34503743 + r34503757;
        double r34503759 = r34503758 / r34503749;
        double r34503760 = r34503752 ? r34503759 : r34503750;
        double r34503761 = r34503742 ? r34503750 : r34503760;
        return r34503761;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.6
Target	0.4
Herbie	3.8

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

Derivation

1. Split input into 2 regimes

2. if z < -1.160115839689408e+172 or 3.641116230673848e+130 < z

   1. Initial program 22.4

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

   2. Taylor expanded around inf 7.4

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

   if -1.160115839689408e+172 < z < 3.641116230673848e+130

   1. Initial program 2.6

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

   2. Taylor expanded around 0 2.6

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

4. Final simplification 3.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.160115839689408068409085936108477411806 \cdot 10^{172}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 3.641116230673848176898687453531338972974 \cdot 10^{130}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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)))