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

Average Error: 7.4 → 3.4

Time: 21.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -7.466575650945099720574707422047672473328 \cdot 10^{79}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 8.602497059991938743425250288839984899656 \cdot 10^{114}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r30203009 = x;
        double r30203010 = y;
        double r30203011 = z;
        double r30203012 = r30203010 * r30203011;
        double r30203013 = r30203012 - r30203009;
        double r30203014 = t;
        double r30203015 = r30203014 * r30203011;
        double r30203016 = r30203015 - r30203009;
        double r30203017 = r30203013 / r30203016;
        double r30203018 = r30203009 + r30203017;
        double r30203019 = 1.0;
        double r30203020 = r30203009 + r30203019;
        double r30203021 = r30203018 / r30203020;
        return r30203021;
}

↓

double f(double x, double y, double z, double t) {
        double r30203022 = z;
        double r30203023 = -7.4665756509451e+79;
        bool r30203024 = r30203022 <= r30203023;
        double r30203025 = x;
        double r30203026 = y;
        double r30203027 = t;
        double r30203028 = r30203026 / r30203027;
        double r30203029 = r30203025 + r30203028;
        double r30203030 = 1.0;
        double r30203031 = r30203025 + r30203030;
        double r30203032 = r30203029 / r30203031;
        double r30203033 = 8.602497059991939e+114;
        bool r30203034 = r30203022 <= r30203033;
        double r30203035 = 1.0;
        double r30203036 = r30203027 * r30203022;
        double r30203037 = r30203036 - r30203025;
        double r30203038 = r30203026 * r30203022;
        double r30203039 = r30203038 - r30203025;
        double r30203040 = r30203037 / r30203039;
        double r30203041 = r30203035 / r30203040;
        double r30203042 = r30203025 + r30203041;
        double r30203043 = r30203042 / r30203031;
        double r30203044 = r30203034 ? r30203043 : r30203032;
        double r30203045 = r30203024 ? r30203032 : r30203044;
        return r30203045;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.4
Target	0.3
Herbie	3.4

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

Derivation

1. Split input into 2 regimes

2. if z < -7.4665756509451e+79 or 8.602497059991939e+114 < z

   1. Initial program 19.4

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

   2. Taylor expanded around inf 7.5

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

   if -7.4665756509451e+79 < z < 8.602497059991939e+114

   1. Initial program 1.3

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

   3. Applied clear-num 1.3

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

4. Final simplification 3.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.466575650945099720574707422047672473328 \cdot 10^{79}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 8.602497059991938743425250288839984899656 \cdot 10^{114}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(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)))