Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(x \cdot \left(2 \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(x \cdot \left(2 \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y
double f(double x, double y, double z) {
        double r30724 = x;
        double r30725 = y;
        double r30726 = log(r30725);
        double r30727 = r30724 * r30726;
        double r30728 = z;
        double r30729 = r30727 - r30728;
        double r30730 = r30729 - r30725;
        return r30730;
}
↓
double f(double x, double y, double z) {
        double r30731 = x;
        double r30732 = 2.0;
        double r30733 = 1.0;
        double r30734 = y;
        double r30735 = 0.3333333333333333;
        double r30736 = pow(r30734, r30735);
        double r30737 = r30733 * r30736;
        double r30738 = log(r30737);
        double r30739 = r30732 * r30738;
        double r30740 = r30731 * r30739;
        double r30741 = cbrt(r30734);
        double r30742 = log(r30741);
        double r30743 = r30731 * r30742;
        double r30744 = r30740 + r30743;
        double r30745 = z;
        double r30746 = r30744 - r30745;
        double r30747 = r30746 - r30734;
        return r30747;
}

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-lft-in0.1

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

  6. Simplified0.1

    \[\leadsto \left(\left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y\]
  7. Using strategy rm

  8. Applied *-un-lft-identity0.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{\color{blue}{1 \cdot y}}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y\]

  9. Applied cbrt-prod0.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{y}\right)}\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y\]

  10. Simplified0.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(\color{blue}{1} \cdot \sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y\]

  11. Simplified0.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(1 \cdot \color{blue}{{y}^{\frac{1}{3}}}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y\]

  12. Final simplification0.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y\]

Reproduce

herbie shell --seed 2020020 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))