Average Error: 0.3 → 0.3
Time: 26.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(a - 0.5\right) \cdot \log t + \left(\left(\log \left(x + y\right) + \log z\right) - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(a - 0.5\right) \cdot \log t + \left(\left(\log \left(x + y\right) + \log z\right) - t\right)
double f(double x, double y, double z, double t, double a) {
        double r254474 = x;
        double r254475 = y;
        double r254476 = r254474 + r254475;
        double r254477 = log(r254476);
        double r254478 = z;
        double r254479 = log(r254478);
        double r254480 = r254477 + r254479;
        double r254481 = t;
        double r254482 = r254480 - r254481;
        double r254483 = a;
        double r254484 = 0.5;
        double r254485 = r254483 - r254484;
        double r254486 = log(r254481);
        double r254487 = r254485 * r254486;
        double r254488 = r254482 + r254487;
        return r254488;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r254489 = a;
        double r254490 = 0.5;
        double r254491 = r254489 - r254490;
        double r254492 = t;
        double r254493 = log(r254492);
        double r254494 = r254491 * r254493;
        double r254495 = x;
        double r254496 = y;
        double r254497 = r254495 + r254496;
        double r254498 = log(r254497);
        double r254499 = z;
        double r254500 = log(r254499);
        double r254501 = r254498 + r254500;
        double r254502 = r254501 - r254492;
        double r254503 = r254494 + r254502;
        return r254503;
}

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 sub-neg0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019297 
(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))))