Average Error: 0.1 → 0.1
Time: 4.7s
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 r39486 = x;
        double r39487 = y;
        double r39488 = log(r39487);
        double r39489 = r39486 * r39488;
        double r39490 = z;
        double r39491 = r39489 - r39490;
        double r39492 = r39491 - r39487;
        return r39492;
}
↓
double f(double x, double y, double z) {
        double r39493 = x;
        double r39494 = y;
        double r39495 = sqrt(r39494);
        double r39496 = log(r39495);
        double r39497 = r39493 * r39496;
        double r39498 = r39497 + r39497;
        double r39499 = z;
        double r39500 = r39498 - r39499;
        double r39501 = r39500 - r39494;
        return r39501;
}

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 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))