Average Error: 0.3 → 0.3
Time: 19.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(\left(2 \cdot \left(a - 0.5\right)\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot \left(a - 0.5\right)\right)\right)\right)\]
\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]{t}\right)\right) + \left(\left(2 \cdot \left(a - 0.5\right)\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot \left(a - 0.5\right)\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r75556 = x;
        double r75557 = y;
        double r75558 = r75556 + r75557;
        double r75559 = log(r75558);
        double r75560 = z;
        double r75561 = log(r75560);
        double r75562 = r75559 + r75561;
        double r75563 = t;
        double r75564 = r75562 - r75563;
        double r75565 = a;
        double r75566 = 0.5;
        double r75567 = r75565 - r75566;
        double r75568 = log(r75563);
        double r75569 = r75567 * r75568;
        double r75570 = r75564 + r75569;
        return r75570;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r75571 = x;
        double r75572 = y;
        double r75573 = r75571 + r75572;
        double r75574 = log(r75573);
        double r75575 = z;
        double r75576 = log(r75575);
        double r75577 = t;
        double r75578 = r75576 - r75577;
        double r75579 = a;
        double r75580 = 0.5;
        double r75581 = r75579 - r75580;
        double r75582 = 2.0;
        double r75583 = cbrt(r75577);
        double r75584 = log(r75583);
        double r75585 = r75582 * r75584;
        double r75586 = r75581 * r75585;
        double r75587 = r75582 * r75581;
        double r75588 = cbrt(r75583);
        double r75589 = log(r75588);
        double r75590 = r75587 * r75589;
        double r75591 = r75589 * r75581;
        double r75592 = r75590 + r75591;
        double r75593 = r75586 + r75592;
        double r75594 = r75578 + r75593;
        double r75595 = r75574 + r75594;
        return r75595;
}

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

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

  12. Applied log-prod0.3

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

  13. Applied distribute-lft-in0.3

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

  14. Simplified0.3

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

  15. Simplified0.3

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

  16. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(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))))