Average Error: 10.3 → 10.3
Time: 2.1s
Precision: binary64
\[\log \left(1 + x\right) - \frac{y}{{\left(1 + x\right)}^{2}}\]
↓
\[\log \left(1 + x\right) - \frac{y}{{\left(1 + x\right)}^{2}}\]
\log \left(1 + x\right) - \frac{y}{{\left(1 + x\right)}^{2}}
↓
\log \left(1 + x\right) - \frac{y}{{\left(1 + x\right)}^{2}}
double code(double x, double y) {
	return ((double) (((double) log(((double) (1.0 + x)))) - ((double) (y / ((double) pow(((double) (1.0 + x)), 2.0))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) log(((double) (1.0 + x)))) - ((double) (y / ((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 10.3

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

  2. Final simplification10.3

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

Reproduce

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