Average Error: 0.1 → 0.1
Time: 20.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r105283 = x;
        double r105284 = y;
        double r105285 = log(r105284);
        double r105286 = r105283 * r105285;
        double r105287 = r105286 - r105284;
        double r105288 = z;
        double r105289 = r105287 - r105288;
        double r105290 = t;
        double r105291 = log(r105290);
        double r105292 = r105289 + r105291;
        return r105292;
}
↓
double f(double x, double y, double z, double t) {
        double r105293 = 2.0;
        double r105294 = y;
        double r105295 = cbrt(r105294);
        double r105296 = log(r105295);
        double r105297 = r105293 * r105296;
        double r105298 = x;
        double r105299 = r105297 * r105298;
        double r105300 = 0.3333333333333333;
        double r105301 = pow(r105294, r105300);
        double r105302 = log(r105301);
        double r105303 = r105298 * r105302;
        double r105304 = r105299 + r105303;
        double r105305 = r105304 - r105294;
        double r105306 = z;
        double r105307 = r105305 - r105306;
        double r105308 = t;
        double r105309 = log(r105308);
        double r105310 = r105307 + r105309;
        return r105310;
}

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. Using strategy rm

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(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)))