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

Average Error: 7.2 → 3.6

Time: 21.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.133110462800310208482394154224976883088 \cdot 10^{110}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 2.440341130353294724337390130573120009969 \cdot 10^{175}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{\frac{y \cdot z - x}{t \cdot z - x} + x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r32622011 = x;
        double r32622012 = y;
        double r32622013 = z;
        double r32622014 = r32622012 * r32622013;
        double r32622015 = r32622014 - r32622011;
        double r32622016 = t;
        double r32622017 = r32622016 * r32622013;
        double r32622018 = r32622017 - r32622011;
        double r32622019 = r32622015 / r32622018;
        double r32622020 = r32622011 + r32622019;
        double r32622021 = 1.0;
        double r32622022 = r32622011 + r32622021;
        double r32622023 = r32622020 / r32622022;
        return r32622023;
}

↓

double f(double x, double y, double z, double t) {
        double r32622024 = z;
        double r32622025 = -1.1331104628003102e+110;
        bool r32622026 = r32622024 <= r32622025;
        double r32622027 = x;
        double r32622028 = y;
        double r32622029 = t;
        double r32622030 = r32622028 / r32622029;
        double r32622031 = r32622027 + r32622030;
        double r32622032 = 1.0;
        double r32622033 = r32622027 + r32622032;
        double r32622034 = r32622031 / r32622033;
        double r32622035 = 2.4403411303532947e+175;
        bool r32622036 = r32622024 <= r32622035;
        double r32622037 = 1.0;
        double r32622038 = r32622028 * r32622024;
        double r32622039 = r32622038 - r32622027;
        double r32622040 = r32622029 * r32622024;
        double r32622041 = r32622040 - r32622027;
        double r32622042 = r32622039 / r32622041;
        double r32622043 = r32622042 + r32622027;
        double r32622044 = r32622033 / r32622043;
        double r32622045 = r32622037 / r32622044;
        double r32622046 = r32622036 ? r32622045 : r32622034;
        double r32622047 = r32622026 ? r32622034 : r32622046;
        return r32622047;
}

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 < -1.1331104628003102e+110 or 2.4403411303532947e+175 < z

   1. Initial program 21.0

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

   2. Taylor expanded around inf 7.0

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

   if -1.1331104628003102e+110 < z < 2.4403411303532947e+175

   1. Initial program 2.4

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

   3. Applied clear-num 2.4

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

4. Final simplification 3.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.133110462800310208482394154224976883088 \cdot 10^{110}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 2.440341130353294724337390130573120009969 \cdot 10^{175}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{\frac{y \cdot z - x}{t \cdot z - x} + x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(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)))