Average Error: 0.3 → 0.3
Time: 10.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\frac{\left(\log \left(x + y\right) + \log \left({z}^{\frac{2}{3}}\right)\right) \cdot \left(\log \left(x + y\right) - \log \left({z}^{\frac{2}{3}}\right)\right)}{\log \left(x + y\right) - \log \left({z}^{\frac{2}{3}}\right)} + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\frac{\left(\log \left(x + y\right) + \log \left({z}^{\frac{2}{3}}\right)\right) \cdot \left(\log \left(x + y\right) - \log \left({z}^{\frac{2}{3}}\right)\right)}{\log \left(x + y\right) - \log \left({z}^{\frac{2}{3}}\right)} + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r65483 = x;
        double r65484 = y;
        double r65485 = r65483 + r65484;
        double r65486 = log(r65485);
        double r65487 = z;
        double r65488 = log(r65487);
        double r65489 = r65486 + r65488;
        double r65490 = t;
        double r65491 = r65489 - r65490;
        double r65492 = a;
        double r65493 = 0.5;
        double r65494 = r65492 - r65493;
        double r65495 = log(r65490);
        double r65496 = r65494 * r65495;
        double r65497 = r65491 + r65496;
        return r65497;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r65498 = x;
        double r65499 = y;
        double r65500 = r65498 + r65499;
        double r65501 = log(r65500);
        double r65502 = z;
        double r65503 = 0.6666666666666666;
        double r65504 = pow(r65502, r65503);
        double r65505 = log(r65504);
        double r65506 = r65501 + r65505;
        double r65507 = r65501 - r65505;
        double r65508 = r65506 * r65507;
        double r65509 = r65508 / r65507;
        double r65510 = cbrt(r65502);
        double r65511 = log(r65510);
        double r65512 = r65509 + r65511;
        double r65513 = t;
        double r65514 = r65512 - r65513;
        double r65515 = a;
        double r65516 = 0.5;
        double r65517 = r65515 - r65516;
        double r65518 = log(r65513);
        double r65519 = r65517 * r65518;
        double r65520 = r65514 + r65519;
        return r65520;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  7. Applied flip-+0.3

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

  8. Simplified0.3

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020057 
(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))))