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

Average Error: 9.8 → 0.7

Time: 6.1s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -8.34491040594951455 \cdot 10^{-75} \lor \neg \left(x \le 2.24523695161930029 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r778829 = x;
        double r778830 = y;
        double r778831 = z;
        double r778832 = r778830 - r778831;
        double r778833 = 1.0;
        double r778834 = r778832 + r778833;
        double r778835 = r778829 * r778834;
        double r778836 = r778835 / r778831;
        return r778836;
}

↓

double f(double x, double y, double z) {
        double r778837 = x;
        double r778838 = -8.344910405949515e-75;
        bool r778839 = r778837 <= r778838;
        double r778840 = 2.2452369516193003e-86;
        bool r778841 = r778837 <= r778840;
        double r778842 = !r778841;
        bool r778843 = r778839 || r778842;
        double r778844 = z;
        double r778845 = r778837 / r778844;
        double r778846 = y;
        double r778847 = r778846 - r778844;
        double r778848 = 1.0;
        double r778849 = r778847 + r778848;
        double r778850 = r778845 * r778849;
        double r778851 = r778837 * r778849;
        double r778852 = r778851 / r778844;
        double r778853 = r778843 ? r778850 : r778852;
        return r778853;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	9.8
Target	0.4
Herbie	0.7

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

Derivation

1. Split input into 2 regimes

2. if x < -8.344910405949515e-75 or 2.2452369516193003e-86 < x

   1. Initial program 17.9

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

   3. Applied associate-/l* 0.4

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
   4. Using strategy rm

   5. Applied associate-/r/ 1.2

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

   if -8.344910405949515e-75 < x < 2.2452369516193003e-86

   1. Initial program 0.2

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.34491040594951455 \cdot 10^{-75} \lor \neg \left(x \le 2.24523695161930029 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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))