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

Average Error: 10.0 → 0.1

Time: 2.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -0.00681634526194420994 \lor \neg \left(z \le 52.414166203019263\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r639565 = x;
        double r639566 = y;
        double r639567 = z;
        double r639568 = r639566 - r639567;
        double r639569 = 1.0;
        double r639570 = r639568 + r639569;
        double r639571 = r639565 * r639570;
        double r639572 = r639571 / r639567;
        return r639572;
}

↓

double f(double x, double y, double z) {
        double r639573 = z;
        double r639574 = -0.00681634526194421;
        bool r639575 = r639573 <= r639574;
        double r639576 = 52.41416620301926;
        bool r639577 = r639573 <= r639576;
        double r639578 = !r639577;
        bool r639579 = r639575 || r639578;
        double r639580 = x;
        double r639581 = y;
        double r639582 = r639581 - r639573;
        double r639583 = 1.0;
        double r639584 = r639582 + r639583;
        double r639585 = r639573 / r639584;
        double r639586 = r639580 / r639585;
        double r639587 = r639580 / r639573;
        double r639588 = r639587 * r639584;
        double r639589 = r639579 ? r639586 : r639588;
        return r639589;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	10.0
Target	0.4
Herbie	0.1

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

Derivation

1. Split input into 2 regimes

2. if z < -0.00681634526194421 or 52.41416620301926 < z

   1. Initial program 16.4

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

   3. Applied associate-/l* 0.1

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

   if -0.00681634526194421 < z < 52.41416620301926

   1. Initial program 0.1

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

   3. Applied associate-/l* 7.9

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

   5. Applied associate-/r/ 0.1

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

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -0.00681634526194420994 \lor \neg \left(z \le 52.414166203019263\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(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))