Average Error: 0.3 → 0.3
Time: 35.9s
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 r265603 = x;
        double r265604 = y;
        double r265605 = r265603 + r265604;
        double r265606 = log(r265605);
        double r265607 = z;
        double r265608 = log(r265607);
        double r265609 = r265606 + r265608;
        double r265610 = t;
        double r265611 = r265609 - r265610;
        double r265612 = a;
        double r265613 = 0.5;
        double r265614 = r265612 - r265613;
        double r265615 = log(r265610);
        double r265616 = r265614 * r265615;
        double r265617 = r265611 + r265616;
        return r265617;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r265618 = x;
        double r265619 = y;
        double r265620 = r265618 + r265619;
        double r265621 = log(r265620);
        double r265622 = z;
        double r265623 = log(r265622);
        double r265624 = t;
        double r265625 = r265623 - r265624;
        double r265626 = a;
        double r265627 = 0.5;
        double r265628 = r265626 - r265627;
        double r265629 = log(r265624);
        double r265630 = r265628 * r265629;
        double r265631 = r265625 + r265630;
        double r265632 = r265621 + r265631;
        return r265632;
}

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))))