Average Error: 0.1 → 0.1
Time: 2.8s
Precision: binary64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2 + \log \left(\sqrt[3]{{\left(\sqrt[3]{y}\right)}^{2}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2 + \log \left(\sqrt[3]{{\left(\sqrt[3]{y}\right)}^{2}}\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) (log (cbrt (pow (cbrt y) 2.0)))))
    (* x (log (cbrt (cbrt y)))))
   z)
  y))
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (x * ((double) log(y)))) - z)) - y));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (((double) (x * ((double) (((double) (((double) log(((double) cbrt(y)))) * 2.0)) + ((double) log(((double) cbrt(((double) pow(((double) cbrt(y)), 2.0)))))))))) + ((double) (x * ((double) log(((double) cbrt(((double) 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 Error: 0.1 bits

    \[\left(x \cdot \log y - z\right) - y\]
  2. Using strategy rm

  3. Applied add-cube-cbrtError: 0.1 bits

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

  4. Applied log-prodError: 0.1 bits

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

  5. Applied distribute-lft-inError: 0.1 bits

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

  6. SimplifiedError: 0.1 bits

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

  8. Applied add-cube-cbrtError: 0.1 bits

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

  9. Applied cbrt-prodError: 0.1 bits

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

  10. Applied log-prodError: 0.1 bits

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

  11. Applied distribute-lft-inError: 0.1 bits

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

  12. Applied associate-+r+Error: 0.1 bits

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

  13. SimplifiedError: 0.1 bits

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

  14. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020203 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))