Average Error: 0.1 → 0.1
Time: 15.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(\frac{-2}{3} \cdot \left(\left(-\log y\right) \cdot x\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(\frac{-2}{3} \cdot \left(\left(-\log y\right) \cdot x\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r116346 = x;
        double r116347 = y;
        double r116348 = log(r116347);
        double r116349 = r116346 * r116348;
        double r116350 = r116349 - r116347;
        double r116351 = z;
        double r116352 = r116350 - r116351;
        double r116353 = t;
        double r116354 = log(r116353);
        double r116355 = r116352 + r116354;
        return r116355;
}
↓
double f(double x, double y, double z, double t) {
        double r116356 = -0.6666666666666666;
        double r116357 = y;
        double r116358 = log(r116357);
        double r116359 = -r116358;
        double r116360 = x;
        double r116361 = r116359 * r116360;
        double r116362 = r116356 * r116361;
        double r116363 = cbrt(r116357);
        double r116364 = log(r116363);
        double r116365 = r116360 * r116364;
        double r116366 = r116362 + r116365;
        double r116367 = r116366 - r116357;
        double r116368 = z;
        double r116369 = r116367 - r116368;
        double r116370 = t;
        double r116371 = log(r116370);
        double r116372 = r116369 + r116371;
        return r116372;
}

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. Taylor expanded around inf 0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(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)))