Average Error: 0.1 → 0.1
Time: 18.2s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(\left(\log \left(\sqrt[3]{{y}^{\frac{2}{3}}}\right) \cdot \left(x \cdot 2\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot 2\right) \cdot x\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(\left(\log \left(\sqrt[3]{{y}^{\frac{2}{3}}}\right) \cdot \left(x \cdot 2\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot 2\right) \cdot x\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y
double f(double x, double y, double z) {
        double r28639 = x;
        double r28640 = y;
        double r28641 = log(r28640);
        double r28642 = r28639 * r28641;
        double r28643 = z;
        double r28644 = r28642 - r28643;
        double r28645 = r28644 - r28640;
        return r28645;
}
↓
double f(double x, double y, double z) {
        double r28646 = y;
        double r28647 = 0.6666666666666666;
        double r28648 = pow(r28646, r28647);
        double r28649 = cbrt(r28648);
        double r28650 = log(r28649);
        double r28651 = x;
        double r28652 = 2.0;
        double r28653 = r28651 * r28652;
        double r28654 = r28650 * r28653;
        double r28655 = cbrt(r28646);
        double r28656 = cbrt(r28655);
        double r28657 = log(r28656);
        double r28658 = r28657 * r28652;
        double r28659 = r28658 * r28651;
        double r28660 = r28654 + r28659;
        double r28661 = log(r28655);
        double r28662 = r28651 * r28661;
        double r28663 = r28660 + r28662;
        double r28664 = z;
        double r28665 = r28663 - r28664;
        double r28666 = r28665 - r28646;
        return r28666;
}

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 add-cube-cbrt0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Applied distribute-lft-in0.1

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

  13. Simplified0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 +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))