Average Error: 0.1 → 0.1
Time: 25.3s
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 r29816 = x;
        double r29817 = y;
        double r29818 = log(r29817);
        double r29819 = r29816 * r29818;
        double r29820 = z;
        double r29821 = r29819 - r29820;
        double r29822 = r29821 - r29817;
        return r29822;
}
↓
double f(double x, double y, double z) {
        double r29823 = y;
        double r29824 = cbrt(r29823);
        double r29825 = r29824 * r29824;
        double r29826 = log(r29825);
        double r29827 = x;
        double r29828 = r29826 * r29827;
        double r29829 = log(r29824);
        double r29830 = r29829 * r29827;
        double r29831 = z;
        double r29832 = r29830 - r29831;
        double r29833 = r29828 + r29832;
        double r29834 = r29833 - r29823;
        return r29834;
}

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))