Average Error: 0.1 → 0.1
Time: 18.9s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{y}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt{y}}\right)\right) + \left(\left(x \cdot \log \left(\sqrt{y}\right) - z\right) - y\right)\]
\left(x \cdot \log y - z\right) - y
↓
\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{y}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt{y}}\right)\right) + \left(\left(x \cdot \log \left(\sqrt{y}\right) - z\right) - y\right)
double f(double x, double y, double z) {
        double r34267 = x;
        double r34268 = y;
        double r34269 = log(r34268);
        double r34270 = r34267 * r34269;
        double r34271 = z;
        double r34272 = r34270 - r34271;
        double r34273 = r34272 - r34268;
        return r34273;
}
↓
double f(double x, double y, double z) {
        double r34274 = x;
        double r34275 = 2.0;
        double r34276 = y;
        double r34277 = sqrt(r34276);
        double r34278 = cbrt(r34277);
        double r34279 = log(r34278);
        double r34280 = r34275 * r34279;
        double r34281 = r34274 * r34280;
        double r34282 = r34274 * r34279;
        double r34283 = r34281 + r34282;
        double r34284 = log(r34277);
        double r34285 = r34274 * r34284;
        double r34286 = z;
        double r34287 = r34285 - r34286;
        double r34288 = r34287 - r34276;
        double r34289 = r34283 + r34288;
        return r34289;
}

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. Applied associate--l+0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  (- (- (* x (log y)) z) y))