Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 16.3s

Precision: 64

Math

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

↓

\[\mathsf{fma}\left(\log t, a - 0.5, \left(\log \left(x + y\right) + \log z\right) - t\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r356250 = x;
        double r356251 = y;
        double r356252 = r356250 + r356251;
        double r356253 = log(r356252);
        double r356254 = z;
        double r356255 = log(r356254);
        double r356256 = r356253 + r356255;
        double r356257 = t;
        double r356258 = r356256 - r356257;
        double r356259 = a;
        double r356260 = 0.5;
        double r356261 = r356259 - r356260;
        double r356262 = log(r356257);
        double r356263 = r356261 * r356262;
        double r356264 = r356258 + r356263;
        return r356264;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r356265 = t;
        double r356266 = log(r356265);
        double r356267 = a;
        double r356268 = 0.5;
        double r356269 = r356267 - r356268;
        double r356270 = x;
        double r356271 = y;
        double r356272 = r356270 + r356271;
        double r356273 = log(r356272);
        double r356274 = z;
        double r356275 = log(r356274);
        double r356276 = r356273 + r356275;
        double r356277 = r356276 - r356265;
        double r356278 = fma(r356266, r356269, r356277);
        return r356278;
}

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. Simplified 0.3

   \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - 0.5, \left(\log \left(x + y\right) + \log z\right) - t\right)}\]
3. Using strategy rm

4. Applied *-un-lft-identity 0.3

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

5. Final simplification 0.3

   \[\leadsto \mathsf{fma}\left(\log t, a - 0.5, \left(\log \left(x + y\right) + \log z\right) - t\right)\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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