Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(\left(x \cdot \log \left(\sqrt{{y}^{\frac{1}{3}} \cdot {y}^{\frac{1}{3}}}\right) + x \cdot \log \left(\sqrt{\sqrt[3]{y}}\right)\right) + x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{\sqrt{y}}\right)\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(\left(x \cdot \log \left(\sqrt{{y}^{\frac{1}{3}} \cdot {y}^{\frac{1}{3}}}\right) + x \cdot \log \left(\sqrt{\sqrt[3]{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 r26096 = x;
        double r26097 = y;
        double r26098 = log(r26097);
        double r26099 = r26096 * r26098;
        double r26100 = z;
        double r26101 = r26099 - r26100;
        double r26102 = r26101 - r26097;
        return r26102;
}
↓
double f(double x, double y, double z) {
        double r26103 = x;
        double r26104 = y;
        double r26105 = 0.3333333333333333;
        double r26106 = pow(r26104, r26105);
        double r26107 = r26106 * r26106;
        double r26108 = sqrt(r26107);
        double r26109 = log(r26108);
        double r26110 = r26103 * r26109;
        double r26111 = cbrt(r26104);
        double r26112 = sqrt(r26111);
        double r26113 = log(r26112);
        double r26114 = r26103 * r26113;
        double r26115 = r26110 + r26114;
        double r26116 = sqrt(r26104);
        double r26117 = sqrt(r26116);
        double r26118 = log(r26117);
        double r26119 = r26118 + r26118;
        double r26120 = r26103 * r26119;
        double r26121 = r26115 + r26120;
        double r26122 = z;
        double r26123 = r26121 - r26122;
        double r26124 = r26123 - r26104;
        return r26124;
}

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

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

  12. Applied sqrt-prod0.1

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

  13. Applied log-prod0.1

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

  14. Applied distribute-lft-in0.1

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

  16. Applied add-sqr-sqrt0.1

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

  17. Applied add-sqr-sqrt0.1

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

  18. Applied swap-sqr0.1

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

  19. Simplified0.1

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

  20. Simplified0.1

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

  21. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 +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))