Average Error: 19.8 → 19.8
Time: 2.3s
Precision: binary64
\[\log \left(1 + x\right) - \frac{x \cdot y}{\left(2 \cdot x\right) \cdot {\left(1 + x\right)}^{2}}\]
↓
\[\log \left(1 + x\right) - \frac{x \cdot y}{\left(2 \cdot x\right) \cdot {\left(1 + x\right)}^{2}}\]
\log \left(1 + x\right) - \frac{x \cdot y}{\left(2 \cdot x\right) \cdot {\left(1 + x\right)}^{2}}
↓
\log \left(1 + x\right) - \frac{x \cdot y}{\left(2 \cdot x\right) \cdot {\left(1 + x\right)}^{2}}
double code(double x, double y) {
	return ((double) (((double) log(((double) (1.0 + x)))) - ((double) (((double) (x * y)) / ((double) (((double) (2.0 * x)) * ((double) pow(((double) (1.0 + x)), 2.0))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) log(((double) (1.0 + x)))) - ((double) (((double) (x * y)) / ((double) (((double) (2.0 * x)) * ((double) pow(((double) (1.0 + x)), 2.0))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 19.8

    \[\log \left(1 + x\right) - \frac{x \cdot y}{\left(2 \cdot x\right) \cdot {\left(1 + x\right)}^{2}}\]

  2. Final simplification19.8

    \[\leadsto \log \left(1 + x\right) - \frac{x \cdot y}{\left(2 \cdot x\right) \cdot {\left(1 + x\right)}^{2}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(- (log (+ 1 x)) (/ (* x y) (* (* 2 x) (pow (+ 1 x) 2))))"
  :precision binary64
  (- (log (+ 1.0 x)) (/ (* x y) (* (* 2.0 x) (pow (+ 1.0 x) 2.0)))))