Average Error: 0.3 → 0.3
Time: 36.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log t - t\right) + \left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(a - 0.5\right) \cdot \log t - t\right) + \left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r1797619 = x;
        double r1797620 = y;
        double r1797621 = r1797619 + r1797620;
        double r1797622 = log(r1797621);
        double r1797623 = z;
        double r1797624 = log(r1797623);
        double r1797625 = r1797622 + r1797624;
        double r1797626 = t;
        double r1797627 = r1797625 - r1797626;
        double r1797628 = a;
        double r1797629 = 0.5;
        double r1797630 = r1797628 - r1797629;
        double r1797631 = log(r1797626);
        double r1797632 = r1797630 * r1797631;
        double r1797633 = r1797627 + r1797632;
        return r1797633;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1797634 = a;
        double r1797635 = 0.5;
        double r1797636 = r1797634 - r1797635;
        double r1797637 = t;
        double r1797638 = log(r1797637);
        double r1797639 = r1797636 * r1797638;
        double r1797640 = r1797639 - r1797637;
        double r1797641 = y;
        double r1797642 = x;
        double r1797643 = r1797641 + r1797642;
        double r1797644 = cbrt(r1797643);
        double r1797645 = r1797644 * r1797644;
        double r1797646 = log(r1797645);
        double r1797647 = z;
        double r1797648 = log(r1797647);
        double r1797649 = log(r1797644);
        double r1797650 = r1797648 + r1797649;
        double r1797651 = r1797646 + r1797650;
        double r1797652 = r1797640 + r1797651;
        return r1797652;
}

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 sub-neg0.3

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

  4. Applied associate-+l+0.3

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

  5. Simplified0.3

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

  7. Applied add-cube-cbrt0.3

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

  8. Applied log-prod0.3

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

  9. Applied associate-+l+0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019144 
(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))))