Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\log \left(\sqrt{y}\right) \cdot x + \left(\log \left(\sqrt{y}\right) \cdot x - z\right)\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\log \left(\sqrt{y}\right) \cdot x + \left(\log \left(\sqrt{y}\right) \cdot x - z\right)\right) - y
double f(double x, double y, double z) {
        double r26348 = x;
        double r26349 = y;
        double r26350 = log(r26349);
        double r26351 = r26348 * r26350;
        double r26352 = z;
        double r26353 = r26351 - r26352;
        double r26354 = r26353 - r26349;
        return r26354;
}
↓
double f(double x, double y, double z) {
        double r26355 = y;
        double r26356 = sqrt(r26355);
        double r26357 = log(r26356);
        double r26358 = x;
        double r26359 = r26357 * r26358;
        double r26360 = z;
        double r26361 = r26359 - r26360;
        double r26362 = r26359 + r26361;
        double r26363 = r26362 - r26355;
        return r26363;
}

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. Applied associate--l+0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020089 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))