Average Error: 0.1 → 0.1
Time: 22.7s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\log t + \left(\left(\log \left(\left(\sqrt[3]{{y}^{\frac{1}{3}}} \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot x - y\right) - z\right)\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\log t + \left(\left(\log \left(\left(\sqrt[3]{{y}^{\frac{1}{3}}} \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot x - y\right) - z\right)\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x
double f(double x, double y, double z, double t) {
        double r5612388 = x;
        double r5612389 = y;
        double r5612390 = log(r5612389);
        double r5612391 = r5612388 * r5612390;
        double r5612392 = r5612391 - r5612389;
        double r5612393 = z;
        double r5612394 = r5612392 - r5612393;
        double r5612395 = t;
        double r5612396 = log(r5612395);
        double r5612397 = r5612394 + r5612396;
        return r5612397;
}
↓
double f(double x, double y, double z, double t) {
        double r5612398 = t;
        double r5612399 = log(r5612398);
        double r5612400 = y;
        double r5612401 = 0.3333333333333333;
        double r5612402 = pow(r5612400, r5612401);
        double r5612403 = cbrt(r5612402);
        double r5612404 = r5612403 * r5612403;
        double r5612405 = r5612404 * r5612403;
        double r5612406 = log(r5612405);
        double r5612407 = x;
        double r5612408 = r5612406 * r5612407;
        double r5612409 = r5612408 - r5612400;
        double r5612410 = z;
        double r5612411 = r5612409 - r5612410;
        double r5612412 = r5612399 + r5612411;
        double r5612413 = cbrt(r5612400);
        double r5612414 = r5612413 * r5612413;
        double r5612415 = log(r5612414);
        double r5612416 = r5612415 * r5612407;
        double r5612417 = r5612412 + r5612416;
        return r5612417;
}

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. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  8. Applied associate-+l+0.1

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

  10. Applied pow1/30.1

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

  12. Applied add-cube-cbrt0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))