Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\left(\mathsf{fma}\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right), y, x\right) + y \cdot \log \left(\sqrt[3]{y}\right)\right) - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\left(\mathsf{fma}\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right), y, x\right) + y \cdot \log \left(\sqrt[3]{y}\right)\right) - z}
double f(double x, double y, double z) {
        double r387263 = x;
        double r387264 = y;
        double r387265 = log(r387264);
        double r387266 = r387264 * r387265;
        double r387267 = r387263 + r387266;
        double r387268 = z;
        double r387269 = r387267 - r387268;
        double r387270 = exp(r387269);
        return r387270;
}
↓
double f(double x, double y, double z) {
        double r387271 = y;
        double r387272 = cbrt(r387271);
        double r387273 = r387272 * r387272;
        double r387274 = log(r387273);
        double r387275 = x;
        double r387276 = fma(r387274, r387271, r387275);
        double r387277 = log(r387272);
        double r387278 = r387271 * r387277;
        double r387279 = r387276 + r387278;
        double r387280 = z;
        double r387281 = r387279 - r387280;
        double r387282 = exp(r387281);
        return r387282;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[e^{\left(x - z\right) + \log y \cdot y}\]

Derivation

  1. Initial program 0.0

    \[e^{\left(x + y \cdot \log y\right) - z}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.0

    \[\leadsto e^{\left(x + y \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)}\right) - z}\]

  4. Applied log-prod0.0

    \[\leadsto e^{\left(x + y \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)}\right) - z}\]

  5. Applied distribute-lft-in0.0

    \[\leadsto e^{\left(x + \color{blue}{\left(y \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + y \cdot \log \left(\sqrt[3]{y}\right)\right)}\right) - z}\]

  6. Applied associate-+r+0.0

    \[\leadsto e^{\color{blue}{\left(\left(x + y \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) + y \cdot \log \left(\sqrt[3]{y}\right)\right)} - z}\]

  7. Simplified0.0

    \[\leadsto e^{\left(\color{blue}{\mathsf{fma}\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right), y, x\right)} + y \cdot \log \left(\sqrt[3]{y}\right)\right) - z}\]

  8. Final simplification0.0

    \[\leadsto e^{\left(\mathsf{fma}\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right), y, x\right) + y \cdot \log \left(\sqrt[3]{y}\right)\right) - z}\]

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

  (exp (- (+ x (* y (log y))) z)))