Average Error: 0.1 → 0.1
Time: 22.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log t + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + \left(\left(2 \cdot x\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot 2\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot 2\right) \cdot x\right)\right) - y\right) - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log t + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + \left(\left(2 \cdot x\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot 2\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot 2\right) \cdot x\right)\right) - y\right) - z\right)
double f(double x, double y, double z, double t) {
        double r87371 = x;
        double r87372 = y;
        double r87373 = log(r87372);
        double r87374 = r87371 * r87373;
        double r87375 = r87374 - r87372;
        double r87376 = z;
        double r87377 = r87375 - r87376;
        double r87378 = t;
        double r87379 = log(r87378);
        double r87380 = r87377 + r87379;
        return r87380;
}
↓
double f(double x, double y, double z, double t) {
        double r87381 = t;
        double r87382 = log(r87381);
        double r87383 = y;
        double r87384 = cbrt(r87383);
        double r87385 = log(r87384);
        double r87386 = x;
        double r87387 = r87385 * r87386;
        double r87388 = 2.0;
        double r87389 = r87388 * r87386;
        double r87390 = cbrt(r87384);
        double r87391 = log(r87390);
        double r87392 = r87391 * r87388;
        double r87393 = r87389 * r87392;
        double r87394 = r87392 * r87386;
        double r87395 = r87393 + r87394;
        double r87396 = r87387 + r87395;
        double r87397 = r87396 - r87383;
        double r87398 = z;
        double r87399 = r87397 - r87398;
        double r87400 = r87382 + r87399;
        return r87400;
}

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. Taylor expanded around inf 0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Applied distribute-lft-in0.1

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

  13. Simplified0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))