Average Error: 0.1 → 0.1
Time: 4.3s
Precision: binary64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log \left(\sqrt{y}\right) \cdot x + \left(\log \left(\sqrt{y}\right) \cdot x + \left(\left(\log t - z\right) - y\right)\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log \left(\sqrt{y}\right) \cdot x + \left(\log \left(\sqrt{y}\right) \cdot x + \left(\left(\log t - z\right) - y\right)\right)
(FPCore (x y z t) :precision binary64 (+ (- (- (* x (log y)) y) z) (log t)))
↓
(FPCore (x y z t)
 :precision binary64
 (+ (* (log (sqrt y)) x) (+ (* (log (sqrt y)) x) (- (- (log t) z) y))))
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 (log(sqrt(y)) * x) + ((log(sqrt(y)) * x) + ((log(t) - z) - y));
}

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-sqr-sqrt_binary64_24570.1

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

  4. Applied log-prod_binary64_25190.1

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

  5. Applied distribute-rgt-in_binary64_23880.1

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

  6. Applied associate--l+_binary64_23750.1

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

  7. Applied associate--l+_binary64_23750.1

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

  8. Applied associate-+l+_binary64_23710.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020280 
(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)))