Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 18.6s

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 r14723228 = x;
        double r14723229 = y;
        double r14723230 = 0.5;
        double r14723231 = r14723229 + r14723230;
        double r14723232 = log(r14723229);
        double r14723233 = r14723231 * r14723232;
        double r14723234 = r14723228 - r14723233;
        double r14723235 = r14723234 + r14723229;
        double r14723236 = z;
        double r14723237 = r14723235 - r14723236;
        return r14723237;
}

↓

double f(double x, double y, double z) {
        double r14723238 = y;
        double r14723239 = x;
        double r14723240 = 0.5;
        double r14723241 = r14723238 + r14723240;
        double r14723242 = log(r14723238);
        double r14723243 = r14723241 * r14723242;
        double r14723244 = r14723239 - r14723243;
        double r14723245 = r14723238 + r14723244;
        double r14723246 = z;
        double r14723247 = r14723245 - r14723246;
        return r14723247;
}

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 2019192 
(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))