Average Error: 0.1 → 0.1
Time: 28.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left({y}^{\frac{1}{3}}\right) \cdot x\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left({y}^{\frac{1}{3}}\right) \cdot x\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r74650 = x;
        double r74651 = y;
        double r74652 = log(r74651);
        double r74653 = r74650 * r74652;
        double r74654 = r74653 - r74651;
        double r74655 = z;
        double r74656 = r74654 - r74655;
        double r74657 = t;
        double r74658 = log(r74657);
        double r74659 = r74656 + r74658;
        return r74659;
}
↓
double f(double x, double y, double z, double t) {
        double r74660 = 2.0;
        double r74661 = y;
        double r74662 = cbrt(r74661);
        double r74663 = log(r74662);
        double r74664 = r74660 * r74663;
        double r74665 = x;
        double r74666 = r74664 * r74665;
        double r74667 = 0.3333333333333333;
        double r74668 = pow(r74661, r74667);
        double r74669 = log(r74668);
        double r74670 = r74669 * r74665;
        double r74671 = r74666 + r74670;
        double r74672 = r74671 - r74661;
        double r74673 = z;
        double r74674 = r74672 - r74673;
        double r74675 = t;
        double r74676 = log(r74675);
        double r74677 = r74674 + r74676;
        return r74677;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  7. Simplified0.1

    \[\leadsto \left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \color{blue}{\log \left(\sqrt[3]{y}\right) \cdot x}\right) - y\right) - z\right) + \log t\]
  8. Using strategy rm

  9. Applied pow1/30.1

    \[\leadsto \left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \color{blue}{\left({y}^{\frac{1}{3}}\right)} \cdot x\right) - y\right) - z\right) + \log t\]

  10. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left({y}^{\frac{1}{3}}\right) \cdot x\right) - y\right) - z\right) + \log t\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))