Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 11.3s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r356416 = x;
        double r356417 = y;
        double r356418 = r356416 + r356417;
        double r356419 = log(r356418);
        double r356420 = z;
        double r356421 = log(r356420);
        double r356422 = r356419 + r356421;
        double r356423 = t;
        double r356424 = r356422 - r356423;
        double r356425 = a;
        double r356426 = 0.5;
        double r356427 = r356425 - r356426;
        double r356428 = log(r356423);
        double r356429 = r356427 * r356428;
        double r356430 = r356424 + r356429;
        return r356430;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r356431 = x;
        double r356432 = y;
        double r356433 = r356431 + r356432;
        double r356434 = log(r356433);
        double r356435 = z;
        double r356436 = log(r356435);
        double r356437 = t;
        double r356438 = r356436 - r356437;
        double r356439 = r356434 + r356438;
        double r356440 = a;
        double r356441 = 0.5;
        double r356442 = r356440 - r356441;
        double r356443 = log(r356437);
        double r356444 = r356442 * r356443;
        double r356445 = r356439 + r356444;
        return r356445;
}

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 associate--l+ 0.3

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

4. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020060 
(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))))