Average Error: 0.1 → 0.1
Time: 31.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log t + \left(\left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot \left(x + x\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log t + \left(\left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot \left(x + x\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right)
double f(double x, double y, double z, double t) {
        double r4514572 = x;
        double r4514573 = y;
        double r4514574 = log(r4514573);
        double r4514575 = r4514572 * r4514574;
        double r4514576 = r4514575 - r4514573;
        double r4514577 = z;
        double r4514578 = r4514576 - r4514577;
        double r4514579 = t;
        double r4514580 = log(r4514579);
        double r4514581 = r4514578 + r4514580;
        return r4514581;
}
↓
double f(double x, double y, double z, double t) {
        double r4514582 = t;
        double r4514583 = log(r4514582);
        double r4514584 = y;
        double r4514585 = 0.3333333333333333;
        double r4514586 = pow(r4514584, r4514585);
        double r4514587 = log(r4514586);
        double r4514588 = x;
        double r4514589 = r4514588 + r4514588;
        double r4514590 = r4514587 * r4514589;
        double r4514591 = cbrt(r4514584);
        double r4514592 = log(r4514591);
        double r4514593 = r4514588 * r4514592;
        double r4514594 = r4514590 + r4514593;
        double r4514595 = r4514594 - r4514584;
        double r4514596 = z;
        double r4514597 = r4514595 - r4514596;
        double r4514598 = r4514583 + r4514597;
        return r4514598;
}

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-rgt-in0.1

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

  6. Simplified0.1

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

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))