Average Error: 0.2 → 0.3
Time: 12.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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]{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
double f(double x, double y, double z, double t, double a) {
        double r52638 = x;
        double r52639 = y;
        double r52640 = r52638 + r52639;
        double r52641 = log(r52640);
        double r52642 = z;
        double r52643 = log(r52642);
        double r52644 = r52641 + r52643;
        double r52645 = t;
        double r52646 = r52644 - r52645;
        double r52647 = a;
        double r52648 = 0.5;
        double r52649 = r52647 - r52648;
        double r52650 = log(r52645);
        double r52651 = r52649 * r52650;
        double r52652 = r52646 + r52651;
        return r52652;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r52653 = x;
        double r52654 = y;
        double r52655 = r52653 + r52654;
        double r52656 = cbrt(r52655);
        double r52657 = r52656 * r52656;
        double r52658 = log(r52657);
        double r52659 = log(r52656);
        double r52660 = z;
        double r52661 = log(r52660);
        double r52662 = r52659 + r52661;
        double r52663 = r52658 + r52662;
        double r52664 = t;
        double r52665 = r52663 - r52664;
        double r52666 = a;
        double r52667 = 0.5;
        double r52668 = r52666 - r52667;
        double r52669 = log(r52664);
        double r52670 = r52668 * r52669;
        double r52671 = r52665 + r52670;
        return r52671;
}

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 0.2

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.2

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

  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

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

Reproduce

herbie shell --seed 2019344 
(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))))