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

Average Error: 0.1 → 0.1

Time: 58.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r14419033 = x;
        double r14419034 = 0.5;
        double r14419035 = r14419033 * r14419034;
        double r14419036 = y;
        double r14419037 = 1.0;
        double r14419038 = z;
        double r14419039 = r14419037 - r14419038;
        double r14419040 = log(r14419038);
        double r14419041 = r14419039 + r14419040;
        double r14419042 = r14419036 * r14419041;
        double r14419043 = r14419035 + r14419042;
        return r14419043;
}

↓

double f(double x, double y, double z) {
        double r14419044 = z;
        double r14419045 = log(r14419044);
        double r14419046 = 1.0;
        double r14419047 = r14419045 + r14419046;
        double r14419048 = r14419047 - r14419044;
        double r14419049 = y;
        double r14419050 = r14419048 * r14419049;
        double r14419051 = 0.5;
        double r14419052 = x;
        double r14419053 = r14419051 * r14419052;
        double r14419054 = r14419050 + r14419053;
        return r14419054;
}

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. Taylor expanded around 0 0.1

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"

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

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))