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

Average Error: 10.6 → 0.6

Time: 8.4s

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 r809524 = x;
        double r809525 = y;
        double r809526 = z;
        double r809527 = r809525 - r809526;
        double r809528 = 1.0;
        double r809529 = r809527 + r809528;
        double r809530 = r809524 * r809529;
        double r809531 = r809530 / r809526;
        return r809531;
}

↓

double f(double x, double y, double z) {
        double r809532 = x;
        double r809533 = -3.9021083944700275e-239;
        bool r809534 = r809532 <= r809533;
        double r809535 = 1.5249655170051624e-193;
        bool r809536 = r809532 <= r809535;
        double r809537 = !r809536;
        bool r809538 = r809534 || r809537;
        double r809539 = z;
        double r809540 = r809532 / r809539;
        double r809541 = 1.0;
        double r809542 = y;
        double r809543 = r809541 + r809542;
        double r809544 = r809540 * r809543;
        double r809545 = r809544 - r809532;
        double r809546 = 1.0;
        double r809547 = r809542 - r809539;
        double r809548 = r809547 + r809541;
        double r809549 = r809532 * r809548;
        double r809550 = r809539 / r809549;
        double r809551 = r809546 / r809550;
        double r809552 = r809538 ? r809545 : r809551;
        return r809552;
}

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))