System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2

Average Error: 0.1 → 0.1

Time: 9.1s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

↓

\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

C

double f(double x, double y, double z) {
        double r296481 = x;
        double r296482 = 0.5;
        double r296483 = r296481 * r296482;
        double r296484 = y;
        double r296485 = 1.0;
        double r296486 = z;
        double r296487 = r296485 - r296486;
        double r296488 = log(r296486);
        double r296489 = r296487 + r296488;
        double r296490 = r296484 * r296489;
        double r296491 = r296483 + r296490;
        return r296491;
}

↓

double f(double x, double y, double z) {
        double r296492 = x;
        double r296493 = 0.5;
        double r296494 = r296492 * r296493;
        double r296495 = y;
        double r296496 = 1.0;
        double r296497 = z;
        double r296498 = r296496 - r296497;
        double r296499 = log(r296497);
        double r296500 = r296498 + r296499;
        double r296501 = r296495 * r296500;
        double r296502 = r296494 + r296501;
        return r296502;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.1
Target	0.1
Herbie	0.1

\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

1. Initial program 0.1

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

2. Final simplification 0.1

   \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1 z) (log z)))))