Average Error: 0.1 → 0.1
Time: 13.8s
Precision: binary64
\[\left(x \cdot \log y - z\right) - y \]
↓
\[\left(\left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + x \cdot \log \left(\sqrt[3]{\sqrt{y} \cdot \sqrt[3]{\sqrt{y}}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right) - z\right) - y \]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + x \cdot \log \left(\sqrt[3]{\sqrt{y} \cdot \sqrt[3]{\sqrt{y}}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right) - z\right) - y

(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))
↓
(FPCore (x y z)
 :precision binary64
 (-
  (-
   (+
    (+
     (* x (* (log (cbrt y)) 2.0))
     (* x (log (cbrt (* (sqrt y) (cbrt (sqrt y)))))))
    (* x (log (cbrt (cbrt y)))))
   z)
  y))
double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}
↓
double code(double x, double y, double z) {
	return ((((x * (log(cbrt(y)) * 2.0)) + (x * log(cbrt(sqrt(y) * cbrt(sqrt(y)))))) + (x * log(cbrt(cbrt(y))))) - z) - y;
}

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. Applied add-cube-cbrt_binary640.1

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

  3. Applied log-prod_binary640.1

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

  4. Applied distribute-rgt-in_binary640.1

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  7. Applied add-cube-cbrt_binary640.1

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

  8. Applied cbrt-prod_binary640.1

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

  9. Applied log-prod_binary640.1

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

  10. Applied distribute-rgt-in_binary640.1

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

  11. Applied associate-+r+_binary640.1

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

  12. Applied add-sqr-sqrt_binary640.1

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

  13. Applied cbrt-prod_binary640.1

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

  14. Applied associate-*l*_binary640.1

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

  15. Simplified0.1

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

  16. Final simplification0.1

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

Reproduce

herbie shell --seed 2022068 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))