Average Error: 0.3 → 0.3
Time: 52.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\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 r3589647 = x;
        double r3589648 = y;
        double r3589649 = r3589647 + r3589648;
        double r3589650 = log(r3589649);
        double r3589651 = z;
        double r3589652 = log(r3589651);
        double r3589653 = r3589650 + r3589652;
        double r3589654 = t;
        double r3589655 = r3589653 - r3589654;
        double r3589656 = a;
        double r3589657 = 0.5;
        double r3589658 = r3589656 - r3589657;
        double r3589659 = log(r3589654);
        double r3589660 = r3589658 * r3589659;
        double r3589661 = r3589655 + r3589660;
        return r3589661;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r3589662 = y;
        double r3589663 = x;
        double r3589664 = r3589662 + r3589663;
        double r3589665 = cbrt(r3589664);
        double r3589666 = r3589665 * r3589665;
        double r3589667 = log(r3589666);
        double r3589668 = z;
        double r3589669 = log(r3589668);
        double r3589670 = log(r3589665);
        double r3589671 = r3589669 + r3589670;
        double r3589672 = r3589667 + r3589671;
        double r3589673 = t;
        double r3589674 = r3589672 - r3589673;
        double r3589675 = a;
        double r3589676 = 0.5;
        double r3589677 = r3589675 - r3589676;
        double r3589678 = log(r3589673);
        double r3589679 = r3589677 * r3589678;
        double r3589680 = r3589674 + r3589679;
        return r3589680;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019112 
(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))))