Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 45.0s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r198077 = x;
        double r198078 = y;
        double r198079 = r198077 + r198078;
        double r198080 = log(r198079);
        double r198081 = z;
        double r198082 = log(r198081);
        double r198083 = r198080 + r198082;
        double r198084 = t;
        double r198085 = r198083 - r198084;
        double r198086 = a;
        double r198087 = 0.5;
        double r198088 = r198086 - r198087;
        double r198089 = log(r198084);
        double r198090 = r198088 * r198089;
        double r198091 = r198085 + r198090;
        return r198091;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r198092 = x;
        double r198093 = y;
        double r198094 = r198092 + r198093;
        double r198095 = log(r198094);
        double r198096 = z;
        double r198097 = log(r198096);
        double r198098 = r198095 + r198097;
        double r198099 = t;
        double r198100 = r198098 - r198099;
        double r198101 = a;
        double r198102 = 0.5;
        double r198103 = r198101 - r198102;
        double r198104 = log(r198099);
        double r198105 = r198103 * r198104;
        double r198106 = r198100 + r198105;
        return r198106;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	0.3
Target	0.3
Herbie	0.3

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

Derivation

1. Initial program 0.3

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
2. Using strategy rm

3. Applied pow1 0.3

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

4. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

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

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