Average Error: 0.1 → 0.1
Time: 6.5s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \left(2 \cdot \log \left(e^{\log y \cdot \frac{1}{3}}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \left(2 \cdot \log \left(e^{\log y \cdot \frac{1}{3}}\right)\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 r148280 = x;
        double r148281 = y;
        double r148282 = log(r148281);
        double r148283 = r148280 * r148282;
        double r148284 = r148283 - r148281;
        double r148285 = z;
        double r148286 = r148284 - r148285;
        double r148287 = t;
        double r148288 = log(r148287);
        double r148289 = r148286 + r148288;
        return r148289;
}
↓
double f(double x, double y, double z, double t) {
        double r148290 = x;
        double r148291 = 2.0;
        double r148292 = y;
        double r148293 = log(r148292);
        double r148294 = 0.3333333333333333;
        double r148295 = r148293 * r148294;
        double r148296 = exp(r148295);
        double r148297 = log(r148296);
        double r148298 = r148291 * r148297;
        double r148299 = r148290 * r148298;
        double r148300 = cbrt(r148292);
        double r148301 = log(r148300);
        double r148302 = r148290 * r148301;
        double r148303 = r148299 + r148302;
        double r148304 = r148303 - r148292;
        double r148305 = z;
        double r148306 = r148304 - r148305;
        double r148307 = t;
        double r148308 = log(r148307);
        double r148309 = r148306 + r148308;
        return r148309;
}

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 add-exp-log0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(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)))