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

Average Error: 10.7 → 0.1

Time: 15.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -2.340030312805192606092491436342584165686 \cdot 10^{-4}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 16865043719047694:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r29083557 = x;
        double r29083558 = y;
        double r29083559 = z;
        double r29083560 = r29083558 - r29083559;
        double r29083561 = 1.0;
        double r29083562 = r29083560 + r29083561;
        double r29083563 = r29083557 * r29083562;
        double r29083564 = r29083563 / r29083559;
        return r29083564;
}

↓

double f(double x, double y, double z) {
        double r29083565 = z;
        double r29083566 = -0.00023400303128051926;
        bool r29083567 = r29083565 <= r29083566;
        double r29083568 = x;
        double r29083569 = y;
        double r29083570 = r29083569 - r29083565;
        double r29083571 = 1.0;
        double r29083572 = r29083570 + r29083571;
        double r29083573 = r29083565 / r29083572;
        double r29083574 = r29083568 / r29083573;
        double r29083575 = 16865043719047694.0;
        bool r29083576 = r29083565 <= r29083575;
        double r29083577 = r29083568 * r29083572;
        double r29083578 = r29083577 / r29083565;
        double r29083579 = r29083576 ? r29083578 : r29083574;
        double r29083580 = r29083567 ? r29083574 : r29083579;
        return r29083580;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	10.7
Target	0.5
Herbie	0.1

\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if z < -0.00023400303128051926 or 16865043719047694.0 < z

   1. Initial program 18.0

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

   3. Applied associate-/l* 0.1

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

   if -0.00023400303128051926 < z < 16865043719047694.0

   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 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.340030312805192606092491436342584165686 \cdot 10^{-4}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 16865043719047694:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))