Average Error: 0.3 → 0.3
Time: 37.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + 2 \cdot \log \left(\sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + 2 \cdot \log \left(\sqrt[3]{z}\right)\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 r61601 = x;
        double r61602 = y;
        double r61603 = r61601 + r61602;
        double r61604 = log(r61603);
        double r61605 = z;
        double r61606 = log(r61605);
        double r61607 = r61604 + r61606;
        double r61608 = t;
        double r61609 = r61607 - r61608;
        double r61610 = a;
        double r61611 = 0.5;
        double r61612 = r61610 - r61611;
        double r61613 = log(r61608);
        double r61614 = r61612 * r61613;
        double r61615 = r61609 + r61614;
        return r61615;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r61616 = x;
        double r61617 = y;
        double r61618 = r61616 + r61617;
        double r61619 = log(r61618);
        double r61620 = 2.0;
        double r61621 = z;
        double r61622 = cbrt(r61621);
        double r61623 = log(r61622);
        double r61624 = r61620 * r61623;
        double r61625 = r61619 + r61624;
        double r61626 = r61625 + r61623;
        double r61627 = t;
        double r61628 = r61626 - r61627;
        double r61629 = a;
        double r61630 = 0.5;
        double r61631 = r61629 - r61630;
        double r61632 = log(r61627);
        double r61633 = r61631 * r61632;
        double r61634 = r61628 + r61633;
        return r61634;
}

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. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019325 
(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))))