Average Error: 0.3 → 0.3
Time: 10.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2 + \log \left(\sqrt[3]{t}\right)\right)\right)\right)\]
\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(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2 + \log \left(\sqrt[3]{t}\right)\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r62484 = x;
        double r62485 = y;
        double r62486 = r62484 + r62485;
        double r62487 = log(r62486);
        double r62488 = z;
        double r62489 = log(r62488);
        double r62490 = r62487 + r62489;
        double r62491 = t;
        double r62492 = r62490 - r62491;
        double r62493 = a;
        double r62494 = 0.5;
        double r62495 = r62493 - r62494;
        double r62496 = log(r62491);
        double r62497 = r62495 * r62496;
        double r62498 = r62492 + r62497;
        return r62498;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r62499 = x;
        double r62500 = y;
        double r62501 = r62499 + r62500;
        double r62502 = log(r62501);
        double r62503 = z;
        double r62504 = log(r62503);
        double r62505 = t;
        double r62506 = r62504 - r62505;
        double r62507 = a;
        double r62508 = 0.5;
        double r62509 = r62507 - r62508;
        double r62510 = 2.0;
        double r62511 = cbrt(r62505);
        double r62512 = cbrt(r62511);
        double r62513 = r62512 * r62512;
        double r62514 = log(r62513);
        double r62515 = r62510 * r62514;
        double r62516 = r62509 * r62515;
        double r62517 = log(r62512);
        double r62518 = r62517 * r62510;
        double r62519 = log(r62511);
        double r62520 = r62518 + r62519;
        double r62521 = r62509 * r62520;
        double r62522 = r62516 + r62521;
        double r62523 = r62506 + r62522;
        double r62524 = r62502 + r62523;
        return r62524;
}

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

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. Using strategy rm

  6. Applied add-cube-cbrt0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\right)\]

  7. Applied log-prod0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\right)\]

  8. Applied distribute-lft-in0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \color{blue}{\left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)}\right)\]

  9. Simplified0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\color{blue}{\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\]
  10. Using strategy rm

  11. Applied add-cube-cbrt0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \sqrt[3]{\sqrt[3]{t}}\right)}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\]

  12. Applied log-prod0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right)}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\]

  13. Applied distribute-lft-in0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\left(a - 0.5\right) \cdot \color{blue}{\left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) + 2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\]

  14. Applied distribute-lft-in0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\color{blue}{\left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right)\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\]

  15. Applied associate-+l+0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \color{blue}{\left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right)}\right)\]

  16. Simplified0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2 + \log \left(\sqrt[3]{t}\right)\right)}\right)\right)\]

  17. Final simplification0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2 + \log \left(\sqrt[3]{t}\right)\right)\right)\right)\]

Reproduce

herbie shell --seed 2020020 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))