Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(x \cdot \log \left(\sqrt{y}\right) + x \cdot \log \left(\sqrt{y}\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(x \cdot \log \left(\sqrt{y}\right) + x \cdot \log \left(\sqrt{y}\right)\right) - z\right) - y
double f(double x, double y, double z) {
        double r36384 = x;
        double r36385 = y;
        double r36386 = log(r36385);
        double r36387 = r36384 * r36386;
        double r36388 = z;
        double r36389 = r36387 - r36388;
        double r36390 = r36389 - r36385;
        return r36390;
}
↓
double f(double x, double y, double z) {
        double r36391 = x;
        double r36392 = y;
        double r36393 = sqrt(r36392);
        double r36394 = log(r36393);
        double r36395 = r36391 * r36394;
        double r36396 = r36395 + r36395;
        double r36397 = z;
        double r36398 = r36396 - r36397;
        double r36399 = r36398 - r36392;
        return r36399;
}

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

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))