Average Error: 0.3 → 0.3
Time: 40.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\left(\left(\log z + \log \left(\sqrt[3]{y + x}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\left(\left(\log z + \log \left(\sqrt[3]{y + x}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r3320576 = x;
        double r3320577 = y;
        double r3320578 = r3320576 + r3320577;
        double r3320579 = log(r3320578);
        double r3320580 = z;
        double r3320581 = log(r3320580);
        double r3320582 = r3320579 + r3320581;
        double r3320583 = t;
        double r3320584 = r3320582 - r3320583;
        double r3320585 = a;
        double r3320586 = 0.5;
        double r3320587 = r3320585 - r3320586;
        double r3320588 = log(r3320583);
        double r3320589 = r3320587 * r3320588;
        double r3320590 = r3320584 + r3320589;
        return r3320590;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r3320591 = y;
        double r3320592 = x;
        double r3320593 = r3320591 + r3320592;
        double r3320594 = cbrt(r3320593);
        double r3320595 = r3320594 * r3320594;
        double r3320596 = log(r3320595);
        double r3320597 = z;
        double r3320598 = log(r3320597);
        double r3320599 = log(r3320594);
        double r3320600 = r3320598 + r3320599;
        double r3320601 = t;
        double r3320602 = r3320600 - r3320601;
        double r3320603 = log(r3320601);
        double r3320604 = a;
        double r3320605 = 0.5;
        double r3320606 = r3320604 - r3320605;
        double r3320607 = r3320603 * r3320606;
        double r3320608 = r3320602 + r3320607;
        double r3320609 = r3320596 + r3320608;
        return r3320609;
}

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. Applied associate--l+0.3

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

  7. Applied associate-+l+0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019158 
(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))))