Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 52.1s

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 r21575932 = x;
        double r21575933 = y;
        double r21575934 = 0.5;
        double r21575935 = r21575933 + r21575934;
        double r21575936 = log(r21575933);
        double r21575937 = r21575935 * r21575936;
        double r21575938 = r21575932 - r21575937;
        double r21575939 = r21575938 + r21575933;
        double r21575940 = z;
        double r21575941 = r21575939 - r21575940;
        return r21575941;
}

↓

double f(double x, double y, double z) {
        double r21575942 = y;
        double r21575943 = x;
        double r21575944 = 0.5;
        double r21575945 = r21575942 + r21575944;
        double r21575946 = log(r21575942);
        double r21575947 = r21575945 * r21575946;
        double r21575948 = r21575943 - r21575947;
        double r21575949 = r21575942 + r21575948;
        double r21575950 = z;
        double r21575951 = r21575949 - r21575950;
        return r21575951;
}

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))