Average Error: 0.3 → 0.3
Time: 11.9s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(\log \left(\sqrt[3]{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot 2\right) \cdot \left(a - 0.5\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2 + \log \left(\sqrt[3]{t}\right)\right)\right)\]
\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 z\right) - t\right) + \left(\left(\log \left(\sqrt[3]{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot 2\right) \cdot \left(a - 0.5\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)
double f(double x, double y, double z, double t, double a) {
        double r49447 = x;
        double r49448 = y;
        double r49449 = r49447 + r49448;
        double r49450 = log(r49449);
        double r49451 = z;
        double r49452 = log(r49451);
        double r49453 = r49450 + r49452;
        double r49454 = t;
        double r49455 = r49453 - r49454;
        double r49456 = a;
        double r49457 = 0.5;
        double r49458 = r49456 - r49457;
        double r49459 = log(r49454);
        double r49460 = r49458 * r49459;
        double r49461 = r49455 + r49460;
        return r49461;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r49462 = x;
        double r49463 = y;
        double r49464 = r49462 + r49463;
        double r49465 = log(r49464);
        double r49466 = z;
        double r49467 = log(r49466);
        double r49468 = r49465 + r49467;
        double r49469 = t;
        double r49470 = r49468 - r49469;
        double r49471 = cbrt(r49469);
        double r49472 = r49471 * r49471;
        double r49473 = cbrt(r49472);
        double r49474 = log(r49473);
        double r49475 = 2.0;
        double r49476 = r49474 * r49475;
        double r49477 = a;
        double r49478 = 0.5;
        double r49479 = r49477 - r49478;
        double r49480 = r49476 * r49479;
        double r49481 = cbrt(r49471);
        double r49482 = log(r49481);
        double r49483 = r49482 * r49475;
        double r49484 = log(r49471);
        double r49485 = r49483 + r49484;
        double r49486 = r49479 * r49485;
        double r49487 = r49480 + r49486;
        double r49488 = r49470 + r49487;
        return r49488;
}

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 add-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Simplified0.3

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

  8. Applied add-cube-cbrt0.3

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

  9. Applied cbrt-prod0.3

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

  10. Applied log-prod0.3

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

  11. Applied distribute-rgt-in0.3

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

  12. Applied distribute-rgt-in0.3

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

  13. Applied associate-+l+0.3

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

  14. Simplified0.3

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

  15. Final simplification0.3

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

Reproduce

herbie shell --seed 2020001 
(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))))