Average Error: 0.3 → 0.3
Time: 40.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left({\left(y + x\right)}^{\frac{2}{3}}\right) + \left(\log z + \log \left({\left(y + x\right)}^{\frac{1}{3}}\right)\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left({\left(y + x\right)}^{\frac{2}{3}}\right) + \left(\log z + \log \left({\left(y + x\right)}^{\frac{1}{3}}\right)\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r2449591 = x;
        double r2449592 = y;
        double r2449593 = r2449591 + r2449592;
        double r2449594 = log(r2449593);
        double r2449595 = z;
        double r2449596 = log(r2449595);
        double r2449597 = r2449594 + r2449596;
        double r2449598 = t;
        double r2449599 = r2449597 - r2449598;
        double r2449600 = a;
        double r2449601 = 0.5;
        double r2449602 = r2449600 - r2449601;
        double r2449603 = log(r2449598);
        double r2449604 = r2449602 * r2449603;
        double r2449605 = r2449599 + r2449604;
        return r2449605;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2449606 = y;
        double r2449607 = x;
        double r2449608 = r2449606 + r2449607;
        double r2449609 = 0.6666666666666666;
        double r2449610 = pow(r2449608, r2449609);
        double r2449611 = log(r2449610);
        double r2449612 = z;
        double r2449613 = log(r2449612);
        double r2449614 = 0.3333333333333333;
        double r2449615 = pow(r2449608, r2449614);
        double r2449616 = log(r2449615);
        double r2449617 = r2449613 + r2449616;
        double r2449618 = r2449611 + r2449617;
        double r2449619 = t;
        double r2449620 = r2449618 - r2449619;
        double r2449621 = log(r2449619);
        double r2449622 = a;
        double r2449623 = 0.5;
        double r2449624 = r2449622 - r2449623;
        double r2449625 = r2449621 * r2449624;
        double r2449626 = r2449620 + r2449625;
        return r2449626;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  7. Applied pow1/30.3

    \[\leadsto \left(\left(\log \left(\sqrt[3]{x + y} \cdot \color{blue}{{\left(x + y\right)}^{\frac{1}{3}}}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  8. Applied pow1/30.3

    \[\leadsto \left(\left(\log \left(\color{blue}{{\left(x + y\right)}^{\frac{1}{3}}} \cdot {\left(x + y\right)}^{\frac{1}{3}}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  9. Applied pow-sqr0.3

    \[\leadsto \left(\left(\log \color{blue}{\left({\left(x + y\right)}^{\left(2 \cdot \frac{1}{3}\right)}\right)} + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  10. Simplified0.3

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

  12. Applied pow1/30.3

    \[\leadsto \left(\left(\log \left({\left(x + y\right)}^{\frac{2}{3}}\right) + \left(\log \color{blue}{\left({\left(x + y\right)}^{\frac{1}{3}}\right)} + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  13. Final simplification0.3

    \[\leadsto \left(\left(\log \left({\left(y + x\right)}^{\frac{2}{3}}\right) + \left(\log z + \log \left({\left(y + x\right)}^{\frac{1}{3}}\right)\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(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))))