Average Error: 15.6 → 15.6
Time: 2.4s
Precision: binary64
\[\log \left(1 + x\right) - \frac{\left(1 + x\right) \cdot y}{2 \cdot {\left(1 + x\right)}^{3}}\]
↓
\[\log \left(1 + x\right) - \frac{\left(1 + x\right) \cdot y}{2 \cdot {\left(1 + x\right)}^{3}}\]
\log \left(1 + x\right) - \frac{\left(1 + x\right) \cdot y}{2 \cdot {\left(1 + x\right)}^{3}}
↓
\log \left(1 + x\right) - \frac{\left(1 + x\right) \cdot y}{2 \cdot {\left(1 + x\right)}^{3}}
double code(double x, double y) {
	return ((double) (((double) log(((double) (1.0 + x)))) - ((double) (((double) (((double) (1.0 + x)) * y)) / ((double) (2.0 * ((double) pow(((double) (1.0 + x)), 3.0))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) log(((double) (1.0 + x)))) - ((double) (((double) (((double) (1.0 + x)) * y)) / ((double) (2.0 * ((double) pow(((double) (1.0 + x)), 3.0))))))));
}

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 15.6

    \[\log \left(1 + x\right) - \frac{\left(1 + x\right) \cdot y}{2 \cdot {\left(1 + x\right)}^{3}}\]

  2. Final simplification15.6

    \[\leadsto \log \left(1 + x\right) - \frac{\left(1 + x\right) \cdot y}{2 \cdot {\left(1 + x\right)}^{3}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(- (log (+ 1 x)) (/ (* (+ 1 x) y) (* 2 (pow (+ 1 x) 3))))"
  :precision binary64
  (- (log (+ 1.0 x)) (/ (* (+ 1.0 x) y) (* 2.0 (pow (+ 1.0 x) 3.0)))))