Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 16.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r16504931 = x;
        double r16504932 = y;
        double r16504933 = 0.5;
        double r16504934 = r16504932 + r16504933;
        double r16504935 = log(r16504932);
        double r16504936 = r16504934 * r16504935;
        double r16504937 = r16504931 - r16504936;
        double r16504938 = r16504937 + r16504932;
        double r16504939 = z;
        double r16504940 = r16504938 - r16504939;
        return r16504940;
}

↓

double f(double x, double y, double z) {
        double r16504941 = y;
        double r16504942 = x;
        double r16504943 = 0.5;
        double r16504944 = r16504941 + r16504943;
        double r16504945 = log(r16504941);
        double r16504946 = r16504944 * r16504945;
        double r16504947 = r16504942 - r16504946;
        double r16504948 = r16504941 + r16504947;
        double r16504949 = z;
        double r16504950 = r16504948 - r16504949;
        return r16504950;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

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

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