Average Error: 0.1 → 0.1
Time: 4.2s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(\left(x \cdot \log \left(\sqrt{\sqrt{y}}\right) + x \cdot \log \left(\sqrt{\sqrt{y}}\right)\right) + x \cdot \log \left(\sqrt{y}\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(\left(x \cdot \log \left(\sqrt{\sqrt{y}}\right) + x \cdot \log \left(\sqrt{\sqrt{y}}\right)\right) + x \cdot \log \left(\sqrt{y}\right)\right) - z\right) - y
double f(double x, double y, double z) {
        double r24391 = x;
        double r24392 = y;
        double r24393 = log(r24392);
        double r24394 = r24391 * r24393;
        double r24395 = z;
        double r24396 = r24394 - r24395;
        double r24397 = r24396 - r24392;
        return r24397;
}
↓
double f(double x, double y, double z) {
        double r24398 = x;
        double r24399 = y;
        double r24400 = sqrt(r24399);
        double r24401 = sqrt(r24400);
        double r24402 = log(r24401);
        double r24403 = r24398 * r24402;
        double r24404 = r24403 + r24403;
        double r24405 = log(r24400);
        double r24406 = r24398 * r24405;
        double r24407 = r24404 + r24406;
        double r24408 = z;
        double r24409 = r24407 - r24408;
        double r24410 = r24409 - r24399;
        return r24410;
}

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. Using strategy rm

  7. Applied add-sqr-sqrt0.1

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

  8. Applied sqrt-prod0.1

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

  9. Applied log-prod0.1

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

  10. Applied distribute-lft-in0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 +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))