Average Error: 0.1 → 0.1
Time: 4.7s
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 r20661 = x;
        double r20662 = y;
        double r20663 = log(r20662);
        double r20664 = r20661 * r20663;
        double r20665 = z;
        double r20666 = r20664 - r20665;
        double r20667 = r20666 - r20662;
        return r20667;
}
↓
double f(double x, double y, double z) {
        double r20668 = y;
        double r20669 = cbrt(r20668);
        double r20670 = r20669 * r20669;
        double r20671 = log(r20670);
        double r20672 = x;
        double r20673 = r20671 * r20672;
        double r20674 = log(r20669);
        double r20675 = r20674 * r20672;
        double r20676 = z;
        double r20677 = r20675 - r20676;
        double r20678 = r20673 + r20677;
        double r20679 = r20678 - r20668;
        return r20679;
}

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