Average Error: 0.3 → 0.3
Time: 32.9s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(\log z - t\right)\right) + \log \left(y + x\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(\log z - t\right)\right) + \log \left(y + x\right)
double f(double x, double y, double z, double t, double a) {
        double r1597642 = x;
        double r1597643 = y;
        double r1597644 = r1597642 + r1597643;
        double r1597645 = log(r1597644);
        double r1597646 = z;
        double r1597647 = log(r1597646);
        double r1597648 = r1597645 + r1597647;
        double r1597649 = t;
        double r1597650 = r1597648 - r1597649;
        double r1597651 = a;
        double r1597652 = 0.5;
        double r1597653 = r1597651 - r1597652;
        double r1597654 = log(r1597649);
        double r1597655 = r1597653 * r1597654;
        double r1597656 = r1597650 + r1597655;
        return r1597656;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1597657 = a;
        double r1597658 = 0.5;
        double r1597659 = r1597657 - r1597658;
        double r1597660 = t;
        double r1597661 = cbrt(r1597660);
        double r1597662 = log(r1597661);
        double r1597663 = r1597659 * r1597662;
        double r1597664 = r1597661 * r1597661;
        double r1597665 = log(r1597664);
        double r1597666 = r1597665 * r1597659;
        double r1597667 = r1597663 + r1597666;
        double r1597668 = z;
        double r1597669 = log(r1597668);
        double r1597670 = r1597669 - r1597660;
        double r1597671 = r1597667 + r1597670;
        double r1597672 = y;
        double r1597673 = x;
        double r1597674 = r1597672 + r1597673;
        double r1597675 = log(r1597674);
        double r1597676 = r1597671 + r1597675;
        return r1597676;
}

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 associate--l+0.3

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

  4. Applied associate-+l+0.3

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

  6. Applied add-cube-cbrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied distribute-rgt-in0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019146 
(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))))