Average Error: 0.1 → 0.1
Time: 13.5s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\log \left(\sqrt{y}\right) \cdot \left(x + x\right) - \left(z + y\right)\]
\left(x \cdot \log y - z\right) - y
↓
\log \left(\sqrt{y}\right) \cdot \left(x + x\right) - \left(z + y\right)
double f(double x, double y, double z) {
        double r32770 = x;
        double r32771 = y;
        double r32772 = log(r32771);
        double r32773 = r32770 * r32772;
        double r32774 = z;
        double r32775 = r32773 - r32774;
        double r32776 = r32775 - r32771;
        return r32776;
}
↓
double f(double x, double y, double z) {
        double r32777 = y;
        double r32778 = sqrt(r32777);
        double r32779 = log(r32778);
        double r32780 = x;
        double r32781 = r32780 + r32780;
        double r32782 = r32779 * r32781;
        double r32783 = z;
        double r32784 = r32783 + r32777;
        double r32785 = r32782 - r32784;
        return r32785;
}

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-rgt-in0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))