Average Error: 0.1 → 0.1
Time: 6.5s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(0 + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(0 + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r128388 = x;
        double r128389 = y;
        double r128390 = log(r128389);
        double r128391 = r128388 * r128390;
        double r128392 = r128391 - r128389;
        double r128393 = z;
        double r128394 = r128392 - r128393;
        double r128395 = t;
        double r128396 = log(r128395);
        double r128397 = r128394 + r128396;
        return r128397;
}
↓
double f(double x, double y, double z, double t) {
        double r128398 = x;
        double r128399 = 2.0;
        double r128400 = y;
        double r128401 = cbrt(r128400);
        double r128402 = log(r128401);
        double r128403 = r128399 * r128402;
        double r128404 = r128398 * r128403;
        double r128405 = 0.0;
        double r128406 = 0.3333333333333333;
        double r128407 = pow(r128400, r128406);
        double r128408 = log(r128407);
        double r128409 = r128398 * r128408;
        double r128410 = r128405 + r128409;
        double r128411 = r128404 + r128410;
        double r128412 = r128411 - r128400;
        double r128413 = z;
        double r128414 = r128412 - r128413;
        double r128415 = t;
        double r128416 = log(r128415);
        double r128417 = r128414 + r128416;
        return r128417;
}

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

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

  8. Applied *-un-lft-identity0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Simplified0.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(\color{blue}{0} + x \cdot \log \left(\sqrt[3]{y}\right)\right)\right) - y\right) - z\right) + \log t\]

  13. Simplified0.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(0 + \color{blue}{x \cdot \log \left({y}^{\frac{1}{3}}\right)}\right)\right) - y\right) - z\right) + \log t\]

  14. Final simplification0.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(0 + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) - y\right) - z\right) + \log t\]

Reproduce

herbie shell --seed 2020065 
(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)))