Average Error: 0.1 → 0.1
Time: 5.1s
Precision: binary64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\log y \cdot x - \left(y + z\right)\]
\left(x \cdot \log y - z\right) - y
↓
\log y \cdot x - \left(y + z\right)
(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))
↓
(FPCore (x y z) :precision binary64 (- (* (log y) x) (+ y z)))
double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}
↓
double code(double x, double y, double z) {
	return (log(y) * x) - (y + z);
}

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. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \log y \cdot x - \left(y + z\right)\]

Reproduce

herbie shell --seed 2021045 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))