Average Error: 0.3 → 0.3
Time: 32.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log t \cdot \left(a - 0.5\right) + \left(\left(\log \left(\sqrt{z}\right) - t\right) + \log \left(\sqrt{z}\right)\right)\right) + \log \left(y + x\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log t \cdot \left(a - 0.5\right) + \left(\left(\log \left(\sqrt{z}\right) - t\right) + \log \left(\sqrt{z}\right)\right)\right) + \log \left(y + x\right)
double f(double x, double y, double z, double t, double a) {
        double r17821556 = x;
        double r17821557 = y;
        double r17821558 = r17821556 + r17821557;
        double r17821559 = log(r17821558);
        double r17821560 = z;
        double r17821561 = log(r17821560);
        double r17821562 = r17821559 + r17821561;
        double r17821563 = t;
        double r17821564 = r17821562 - r17821563;
        double r17821565 = a;
        double r17821566 = 0.5;
        double r17821567 = r17821565 - r17821566;
        double r17821568 = log(r17821563);
        double r17821569 = r17821567 * r17821568;
        double r17821570 = r17821564 + r17821569;
        return r17821570;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r17821571 = t;
        double r17821572 = log(r17821571);
        double r17821573 = a;
        double r17821574 = 0.5;
        double r17821575 = r17821573 - r17821574;
        double r17821576 = r17821572 * r17821575;
        double r17821577 = z;
        double r17821578 = sqrt(r17821577);
        double r17821579 = log(r17821578);
        double r17821580 = r17821579 - r17821571;
        double r17821581 = r17821580 + r17821579;
        double r17821582 = r17821576 + r17821581;
        double r17821583 = y;
        double r17821584 = x;
        double r17821585 = r17821583 + r17821584;
        double r17821586 = log(r17821585);
        double r17821587 = r17821582 + r17821586;
        return r17821587;
}

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
Target0.2
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+0.2

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

  6. Applied add-sqr-sqrt0.2

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

  7. Applied log-prod0.2

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

  8. Applied associate--l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

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

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