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

Average Error: 7.0 → 3.8

Time: 19.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -2.648599861110283 \cdot 10^{+100}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \mathbf{elif}\;z \le 9.631568013141158 \cdot 10^{+215}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r36699008 = x;
        double r36699009 = y;
        double r36699010 = z;
        double r36699011 = r36699009 * r36699010;
        double r36699012 = r36699011 - r36699008;
        double r36699013 = t;
        double r36699014 = r36699013 * r36699010;
        double r36699015 = r36699014 - r36699008;
        double r36699016 = r36699012 / r36699015;
        double r36699017 = r36699008 + r36699016;
        double r36699018 = 1.0;
        double r36699019 = r36699008 + r36699018;
        double r36699020 = r36699017 / r36699019;
        return r36699020;
}

↓

double f(double x, double y, double z, double t) {
        double r36699021 = z;
        double r36699022 = -2.648599861110283e+100;
        bool r36699023 = r36699021 <= r36699022;
        double r36699024 = x;
        double r36699025 = y;
        double r36699026 = t;
        double r36699027 = r36699025 / r36699026;
        double r36699028 = r36699024 + r36699027;
        double r36699029 = 1.0;
        double r36699030 = r36699024 + r36699029;
        double r36699031 = r36699028 / r36699030;
        double r36699032 = 9.631568013141158e+215;
        bool r36699033 = r36699021 <= r36699032;
        double r36699034 = r36699025 * r36699021;
        double r36699035 = r36699034 - r36699024;
        double r36699036 = 1.0;
        double r36699037 = r36699026 * r36699021;
        double r36699038 = r36699037 - r36699024;
        double r36699039 = r36699036 / r36699038;
        double r36699040 = r36699035 * r36699039;
        double r36699041 = r36699024 + r36699040;
        double r36699042 = r36699041 / r36699030;
        double r36699043 = r36699033 ? r36699042 : r36699031;
        double r36699044 = r36699023 ? r36699031 : r36699043;
        return r36699044;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.0
Target	0.3
Herbie	3.8

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

Derivation

1. Split input into 2 regimes

2. if z < -2.648599861110283e+100 or 9.631568013141158e+215 < z

   1. Initial program 20.9

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

   2. Taylor expanded around inf 6.8

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

   if -2.648599861110283e+100 < z < 9.631568013141158e+215

   1. Initial program 2.9

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]
   2. Using strategy rm

   3. Applied div-inv 2.9

      \[\leadsto \frac{x + \color{blue}{\left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}}{x + 1.0}\]
3. Recombined 2 regimes into one program.

4. Final simplification 3.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.648599861110283 \cdot 10^{+100}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \mathbf{elif}\;z \le 9.631568013141158 \cdot 10^{+215}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(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)))