Average Error: 0.1 → 0.1
Time: 4.4s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(\left(x \cdot \left(2 \cdot \log \left({\left(\sqrt{y}\right)}^{\frac{1}{3}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt{y}}\right)\right) + x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{\sqrt{y}}\right)\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(\left(x \cdot \left(2 \cdot \log \left({\left(\sqrt{y}\right)}^{\frac{1}{3}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt{y}}\right)\right) + x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{\sqrt{y}}\right)\right)\right) - z\right) - y
double f(double x, double y, double z) {
        double r31716 = x;
        double r31717 = y;
        double r31718 = log(r31717);
        double r31719 = r31716 * r31718;
        double r31720 = z;
        double r31721 = r31719 - r31720;
        double r31722 = r31721 - r31717;
        return r31722;
}
↓
double f(double x, double y, double z) {
        double r31723 = x;
        double r31724 = 2.0;
        double r31725 = y;
        double r31726 = sqrt(r31725);
        double r31727 = 0.3333333333333333;
        double r31728 = pow(r31726, r31727);
        double r31729 = log(r31728);
        double r31730 = r31724 * r31729;
        double r31731 = r31723 * r31730;
        double r31732 = cbrt(r31726);
        double r31733 = log(r31732);
        double r31734 = r31723 * r31733;
        double r31735 = r31731 + r31734;
        double r31736 = sqrt(r31726);
        double r31737 = log(r31736);
        double r31738 = r31737 + r31737;
        double r31739 = r31723 * r31738;
        double r31740 = r31735 + r31739;
        double r31741 = z;
        double r31742 = r31740 - r31741;
        double r31743 = r31742 - r31725;
        return r31743;
}

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-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  7. Applied add-sqr-sqrt0.1

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

  8. Applied sqrt-prod0.1

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

  9. Applied log-prod0.1

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

  11. Applied add-cube-cbrt0.1

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

  12. Applied log-prod0.1

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

  13. Applied distribute-lft-in0.1

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

  14. Simplified0.1

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

  16. Applied pow1/30.1

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

  17. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))