Average Error: 0.1 → 0.1
Time: 3.5s
Precision: binary64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \left(2 \cdot \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \left(2 \cdot \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right) - y\right) - z\right) + \log t
(FPCore (x y z t) :precision binary64 (+ (- (- (* x (log y)) y) z) (log t)))
↓
(FPCore (x y z t)
 :precision binary64
 (+
  (-
   (-
    (+
     (* x (* 2.0 (+ (log (cbrt y)) (log (cbrt (cbrt y))))))
     (* x (log (cbrt (cbrt y)))))
    y)
   z)
  (log t)))
double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(t);
}
↓
double code(double x, double y, double z, double t) {
	return ((((x * (2.0 * (log(cbrt(y)) + log(cbrt(cbrt(y)))))) + (x * log(cbrt(cbrt(y))))) - y) - z) + log(t);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt_binary640.1

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

  4. Applied log-prod_binary640.1

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

  5. Applied distribute-rgt-in_binary640.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  9. Applied add-cube-cbrt_binary640.1

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

  10. Applied log-prod_binary640.1

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

  11. Applied distribute-rgt-in_binary640.1

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

  12. Applied associate-+r+_binary640.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020233 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))