Average Error: 0.1 → 0.1
Time: 1.0s
Precision: binary64
\[1 + \left(0.278393 + \left(0.23038900000000001 + \left(9.7199999999999999 \cdot 10^{-4} + 0.0781079999999999969 \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\]
↓
\[1 + \left(0.278393 + \left(0.23038900000000001 + \left(9.7199999999999999 \cdot 10^{-4} + 0.0781079999999999969 \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\]
1 + \left(0.278393 + \left(0.23038900000000001 + \left(9.7199999999999999 \cdot 10^{-4} + 0.0781079999999999969 \cdot x\right) \cdot x\right) \cdot x\right) \cdot x
↓
1 + \left(0.278393 + \left(0.23038900000000001 + \left(9.7199999999999999 \cdot 10^{-4} + 0.0781079999999999969 \cdot x\right) \cdot x\right) \cdot x\right) \cdot x
double code(double x) {
	return ((double) (1.0 + ((double) (((double) (0.278393 + ((double) (((double) (0.230389 + ((double) (((double) (0.000972 + ((double) (0.078108 * x)))) * x)))) * x)))) * x))));
}
↓
double code(double x) {
	return ((double) (1.0 + ((double) (((double) (0.278393 + ((double) (((double) (0.230389 + ((double) (((double) (0.000972 + ((double) (0.078108 * x)))) * x)))) * x)))) * x))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[1 + \left(0.278393 + \left(0.23038900000000001 + \left(9.7199999999999999 \cdot 10^{-4} + 0.0781079999999999969 \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\]

  2. Final simplification0.1

    \[\leadsto 1 + \left(0.278393 + \left(0.23038900000000001 + \left(9.7199999999999999 \cdot 10^{-4} + 0.0781079999999999969 \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ 1.0 (* (+ 0.278393 (* (+ 0.230389 (* (+ 0.000972 (* 0.078108 x)) x)) x)) x))"
  :precision binary64
  (+ 1.0 (* (+ 0.278393 (* (+ 0.230389 (* (+ 0.000972 (* 0.078108 x)) x)) x)) x)))