Average Error: 0.1 → 0.1
Time: 15.6s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(\log \left(\sqrt{y}\right) \cdot x + \log \left(\sqrt{y}\right) \cdot x\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(\log \left(\sqrt{y}\right) \cdot x + \log \left(\sqrt{y}\right) \cdot x\right) - z\right) - y
double f(double x, double y, double z) {
        double r39162 = x;
        double r39163 = y;
        double r39164 = log(r39163);
        double r39165 = r39162 * r39164;
        double r39166 = z;
        double r39167 = r39165 - r39166;
        double r39168 = r39167 - r39163;
        return r39168;
}
↓
double f(double x, double y, double z) {
        double r39169 = y;
        double r39170 = sqrt(r39169);
        double r39171 = log(r39170);
        double r39172 = x;
        double r39173 = r39171 * r39172;
        double r39174 = r39173 + r39173;
        double r39175 = z;
        double r39176 = r39174 - r39175;
        double r39177 = r39176 - r39169;
        return r39177;
}

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. Simplified0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  (- (- (* x (log y)) z) y))