Average Error: 0.3 → 0.3
Time: 38.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r225435 = x;
        double r225436 = y;
        double r225437 = r225435 + r225436;
        double r225438 = log(r225437);
        double r225439 = z;
        double r225440 = log(r225439);
        double r225441 = r225438 + r225440;
        double r225442 = t;
        double r225443 = r225441 - r225442;
        double r225444 = a;
        double r225445 = 0.5;
        double r225446 = r225444 - r225445;
        double r225447 = log(r225442);
        double r225448 = r225446 * r225447;
        double r225449 = r225443 + r225448;
        return r225449;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r225450 = x;
        double r225451 = y;
        double r225452 = r225450 + r225451;
        double r225453 = log(r225452);
        double r225454 = z;
        double r225455 = log(r225454);
        double r225456 = t;
        double r225457 = r225455 - r225456;
        double r225458 = a;
        double r225459 = 0.5;
        double r225460 = r225458 - r225459;
        double r225461 = log(r225456);
        double r225462 = r225460 * r225461;
        double r225463 = r225457 + r225462;
        double r225464 = r225453 + r225463;
        return r225464;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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. Applied associate-+l+0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 
(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))))