Average Error: 0.1 → 0.1
Time: 12.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y}\right) \cdot \left(3 \cdot x\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\log \left(\sqrt[3]{y}\right) \cdot \left(3 \cdot x\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r101468 = x;
        double r101469 = y;
        double r101470 = log(r101469);
        double r101471 = r101468 * r101470;
        double r101472 = r101471 - r101469;
        double r101473 = z;
        double r101474 = r101472 - r101473;
        double r101475 = t;
        double r101476 = log(r101475);
        double r101477 = r101474 + r101476;
        return r101477;
}
↓
double f(double x, double y, double z, double t) {
        double r101478 = y;
        double r101479 = cbrt(r101478);
        double r101480 = log(r101479);
        double r101481 = 3.0;
        double r101482 = x;
        double r101483 = r101481 * r101482;
        double r101484 = r101480 * r101483;
        double r101485 = r101484 - r101478;
        double r101486 = z;
        double r101487 = r101485 - r101486;
        double r101488 = t;
        double r101489 = log(r101488);
        double r101490 = r101487 + r101489;
        return r101490;
}

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 0 0.2

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(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)))