Average Error: 0.1 → 0.1
Time: 12.2s
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 r30240 = x;
        double r30241 = y;
        double r30242 = log(r30241);
        double r30243 = r30240 * r30242;
        double r30244 = z;
        double r30245 = r30243 - r30244;
        double r30246 = r30245 - r30241;
        return r30246;
}
↓
double f(double x, double y, double z) {
        double r30247 = y;
        double r30248 = sqrt(r30247);
        double r30249 = log(r30248);
        double r30250 = x;
        double r30251 = r30250 + r30250;
        double r30252 = r30249 * r30251;
        double r30253 = z;
        double r30254 = r30253 + r30247;
        double r30255 = r30252 - r30254;
        return r30255;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019294 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))