Average Error: 0.1 → 0.1
Time: 21.4s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(\log \left(\sqrt[3]{\sqrt{y}}\right) \cdot x - z\right) + \left(\log \left(\sqrt{y}\right) + \log \left(\sqrt[3]{\sqrt{y}} \cdot \sqrt[3]{\sqrt{y}}\right)\right) \cdot x\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(\log \left(\sqrt[3]{\sqrt{y}}\right) \cdot x - z\right) + \left(\log \left(\sqrt{y}\right) + \log \left(\sqrt[3]{\sqrt{y}} \cdot \sqrt[3]{\sqrt{y}}\right)\right) \cdot x\right) - y
double f(double x, double y, double z) {
        double r1071237 = x;
        double r1071238 = y;
        double r1071239 = log(r1071238);
        double r1071240 = r1071237 * r1071239;
        double r1071241 = z;
        double r1071242 = r1071240 - r1071241;
        double r1071243 = r1071242 - r1071238;
        return r1071243;
}
↓
double f(double x, double y, double z) {
        double r1071244 = y;
        double r1071245 = sqrt(r1071244);
        double r1071246 = cbrt(r1071245);
        double r1071247 = log(r1071246);
        double r1071248 = x;
        double r1071249 = r1071247 * r1071248;
        double r1071250 = z;
        double r1071251 = r1071249 - r1071250;
        double r1071252 = log(r1071245);
        double r1071253 = r1071246 * r1071246;
        double r1071254 = log(r1071253);
        double r1071255 = r1071252 + r1071254;
        double r1071256 = r1071255 * r1071248;
        double r1071257 = r1071251 + r1071256;
        double r1071258 = r1071257 - r1071244;
        return r1071258;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x \cdot \log y - z\right) - y\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--l+0.1

    \[\leadsto \color{blue}{\left(x \cdot \log \left(\sqrt{y}\right) + \left(x \cdot \log \left(\sqrt{y}\right) - z\right)\right)} - y\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.1

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

  9. Applied log-prod0.1

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

  10. Applied distribute-rgt-in0.1

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

  11. Applied associate--l+0.1

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

  12. Applied associate-+r+0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  (- (- (* x (log y)) z) y))