Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - z\right)\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - z\right)\right) - y
double f(double x, double y, double z) {
        double r21309 = x;
        double r21310 = y;
        double r21311 = log(r21310);
        double r21312 = r21309 * r21311;
        double r21313 = z;
        double r21314 = r21312 - r21313;
        double r21315 = r21314 - r21310;
        return r21315;
}
↓
double f(double x, double y, double z) {
        double r21316 = y;
        double r21317 = cbrt(r21316);
        double r21318 = r21317 * r21317;
        double r21319 = log(r21318);
        double r21320 = x;
        double r21321 = r21319 * r21320;
        double r21322 = log(r21317);
        double r21323 = r21322 * r21320;
        double r21324 = z;
        double r21325 = r21323 - r21324;
        double r21326 = r21321 + r21325;
        double r21327 = r21326 - r21316;
        return r21327;
}

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-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Applied associate--l+0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +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))