Average Error: 0.3 → 0.3
Time: 21.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \left(\log \left(\sqrt{z}\right) - t\right)\right) + \log t \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \left(\log \left(\sqrt{z}\right) - t\right)\right) + \log t \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r385403 = x;
        double r385404 = y;
        double r385405 = r385403 + r385404;
        double r385406 = log(r385405);
        double r385407 = z;
        double r385408 = log(r385407);
        double r385409 = r385406 + r385408;
        double r385410 = t;
        double r385411 = r385409 - r385410;
        double r385412 = a;
        double r385413 = 0.5;
        double r385414 = r385412 - r385413;
        double r385415 = log(r385410);
        double r385416 = r385414 * r385415;
        double r385417 = r385411 + r385416;
        return r385417;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r385418 = x;
        double r385419 = y;
        double r385420 = r385418 + r385419;
        double r385421 = log(r385420);
        double r385422 = z;
        double r385423 = sqrt(r385422);
        double r385424 = log(r385423);
        double r385425 = r385421 + r385424;
        double r385426 = t;
        double r385427 = r385424 - r385426;
        double r385428 = r385425 + r385427;
        double r385429 = log(r385426);
        double r385430 = a;
        double r385431 = 0.5;
        double r385432 = r385430 - r385431;
        double r385433 = r385429 * r385432;
        double r385434 = r385428 + r385433;
        return r385434;
}

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 *-un-lft-identity0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left(1 \cdot t\right)}\]

  4. Applied log-prod0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \color{blue}{\left(\log 1 + \log t\right)}\]

  5. Applied distribute-rgt-in0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(\log 1 \cdot \left(a - 0.5\right) + \log t \cdot \left(a - 0.5\right)\right)}\]

  6. Applied associate-+r+0.3

    \[\leadsto \color{blue}{\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log 1 \cdot \left(a - 0.5\right)\right) + \log t \cdot \left(a - 0.5\right)}\]

  7. Simplified0.3

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

  9. Applied add-sqr-sqrt0.3

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

  10. Applied log-prod0.3

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

  11. Applied associate--l+0.3

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

  12. Applied associate-+r+0.3

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

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2020043 
(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))))