Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3

Average Error: 10.6 → 0.6

Time: 13.4s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -3.9021083944700275 \cdot 10^{-239} \lor \neg \left(x \le 1.5249655170051624 \cdot 10^{-193}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(\left(y - z\right) + 1\right)}}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r710850 = x;
        double r710851 = y;
        double r710852 = z;
        double r710853 = r710851 - r710852;
        double r710854 = 1.0;
        double r710855 = r710853 + r710854;
        double r710856 = r710850 * r710855;
        double r710857 = r710856 / r710852;
        return r710857;
}

↓

double f(double x, double y, double z) {
        double r710858 = x;
        double r710859 = -3.9021083944700275e-239;
        bool r710860 = r710858 <= r710859;
        double r710861 = 1.5249655170051624e-193;
        bool r710862 = r710858 <= r710861;
        double r710863 = !r710862;
        bool r710864 = r710860 || r710863;
        double r710865 = z;
        double r710866 = r710858 / r710865;
        double r710867 = 1.0;
        double r710868 = y;
        double r710869 = r710867 + r710868;
        double r710870 = r710866 * r710869;
        double r710871 = r710870 - r710858;
        double r710872 = 1.0;
        double r710873 = r710868 - r710865;
        double r710874 = r710873 + r710867;
        double r710875 = r710858 * r710874;
        double r710876 = r710865 / r710875;
        double r710877 = r710872 / r710876;
        double r710878 = r710864 ? r710871 : r710877;
        return r710878;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	10.6
Target	0.4
Herbie	0.6

\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if x < -3.9021083944700275e-239 or 1.5249655170051624e-193 < x

   1. Initial program 12.9

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

   2. Taylor expanded around 0 4.3

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

   3. Simplified 0.6

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

   if -3.9021083944700275e-239 < x < 1.5249655170051624e-193

   1. Initial program 0.2

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
   2. Using strategy rm

   3. Applied clear-num 0.3

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

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.9021083944700275 \cdot 10^{-239} \lor \neg \left(x \le 1.5249655170051624 \cdot 10^{-193}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(\left(y - z\right) + 1\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1)) z))