Average Error: 0.3 → 0.3
Time: 36.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log \left(y + x\right) + \left(\log \left(\sqrt[3]{\sqrt{t}}\right) \cdot \left(a - 0.5\right) + \left(\left(\log z + \left(\log \left(\sqrt[3]{\sqrt{t}}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{\sqrt{t}}\right) \cdot \left(a - 0.5\right)\right)\right) - t\right)\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log \left(y + x\right) + \left(\log \left(\sqrt[3]{\sqrt{t}}\right) \cdot \left(a - 0.5\right) + \left(\left(\log z + \left(\log \left(\sqrt[3]{\sqrt{t}}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{\sqrt{t}}\right) \cdot \left(a - 0.5\right)\right)\right) - t\right)\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)
double f(double x, double y, double z, double t, double a) {
        double r1679580 = x;
        double r1679581 = y;
        double r1679582 = r1679580 + r1679581;
        double r1679583 = log(r1679582);
        double r1679584 = z;
        double r1679585 = log(r1679584);
        double r1679586 = r1679583 + r1679585;
        double r1679587 = t;
        double r1679588 = r1679586 - r1679587;
        double r1679589 = a;
        double r1679590 = 0.5;
        double r1679591 = r1679589 - r1679590;
        double r1679592 = log(r1679587);
        double r1679593 = r1679591 * r1679592;
        double r1679594 = r1679588 + r1679593;
        return r1679594;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1679595 = y;
        double r1679596 = x;
        double r1679597 = r1679595 + r1679596;
        double r1679598 = log(r1679597);
        double r1679599 = t;
        double r1679600 = sqrt(r1679599);
        double r1679601 = cbrt(r1679600);
        double r1679602 = log(r1679601);
        double r1679603 = a;
        double r1679604 = 0.5;
        double r1679605 = r1679603 - r1679604;
        double r1679606 = r1679602 * r1679605;
        double r1679607 = z;
        double r1679608 = log(r1679607);
        double r1679609 = r1679606 + r1679606;
        double r1679610 = r1679608 + r1679609;
        double r1679611 = r1679610 - r1679599;
        double r1679612 = r1679606 + r1679611;
        double r1679613 = r1679598 + r1679612;
        double r1679614 = log(r1679600);
        double r1679615 = r1679605 * r1679614;
        double r1679616 = r1679613 + r1679615;
        return r1679616;
}

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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Applied associate-+r+0.3

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

  8. Applied associate--l+0.3

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

  9. Applied associate-+l+0.3

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

  11. Applied add-cube-cbrt0.3

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

  12. Applied log-prod0.3

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

  13. Applied distribute-rgt-in0.3

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

  14. Applied associate-+r+0.3

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

  15. Simplified0.3

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

  16. Final simplification0.3

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

Reproduce

herbie shell --seed 2019143 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))