Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 46.1s

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 r17226165 = x;
        double r17226166 = y;
        double r17226167 = 0.5;
        double r17226168 = r17226166 + r17226167;
        double r17226169 = log(r17226166);
        double r17226170 = r17226168 * r17226169;
        double r17226171 = r17226165 - r17226170;
        double r17226172 = r17226171 + r17226166;
        double r17226173 = z;
        double r17226174 = r17226172 - r17226173;
        return r17226174;
}

↓

double f(double x, double y, double z) {
        double r17226175 = y;
        double r17226176 = x;
        double r17226177 = 0.5;
        double r17226178 = r17226175 + r17226177;
        double r17226179 = log(r17226175);
        double r17226180 = r17226178 * r17226179;
        double r17226181 = r17226176 - r17226180;
        double r17226182 = r17226175 + r17226181;
        double r17226183 = z;
        double r17226184 = r17226182 - r17226183;
        return r17226184;
}

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 2019168 
(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))