Average Error: 0.3 → 0.3
Time: 12.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(1 \cdot {t}^{\frac{1}{3}}\right)\]
\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) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(1 \cdot {t}^{\frac{1}{3}}\right)
double f(double x, double y, double z, double t, double a) {
        double r48651 = x;
        double r48652 = y;
        double r48653 = r48651 + r48652;
        double r48654 = log(r48653);
        double r48655 = z;
        double r48656 = log(r48655);
        double r48657 = r48654 + r48656;
        double r48658 = t;
        double r48659 = r48657 - r48658;
        double r48660 = a;
        double r48661 = 0.5;
        double r48662 = r48660 - r48661;
        double r48663 = log(r48658);
        double r48664 = r48662 * r48663;
        double r48665 = r48659 + r48664;
        return r48665;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r48666 = x;
        double r48667 = y;
        double r48668 = r48666 + r48667;
        double r48669 = log(r48668);
        double r48670 = z;
        double r48671 = log(r48670);
        double r48672 = r48669 + r48671;
        double r48673 = t;
        double r48674 = r48672 - r48673;
        double r48675 = cbrt(r48673);
        double r48676 = r48675 * r48675;
        double r48677 = log(r48676);
        double r48678 = a;
        double r48679 = 0.5;
        double r48680 = r48678 - r48679;
        double r48681 = r48677 * r48680;
        double r48682 = r48674 + r48681;
        double r48683 = 1.0;
        double r48684 = 0.3333333333333333;
        double r48685 = pow(r48673, r48684);
        double r48686 = r48683 * r48685;
        double r48687 = log(r48686);
        double r48688 = r48680 * r48687;
        double r48689 = r48682 + r48688;
        return r48689;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Simplified0.3

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

  9. Applied *-un-lft-identity0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{\color{blue}{1 \cdot t}}\right)\]

  10. Applied cbrt-prod0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{t}\right)}\]

  11. Simplified0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(\color{blue}{1} \cdot \sqrt[3]{t}\right)\]

  12. Simplified0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(1 \cdot \color{blue}{{t}^{\frac{1}{3}}}\right)\]

  13. Final simplification0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(1 \cdot {t}^{\frac{1}{3}}\right)\]

Reproduce

herbie shell --seed 2020081 
(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))))