Average Error: 0.1 → 0.1
Time: 854.0ms
Precision: binary64
\[1 + x \cdot \left(1 + x \cdot \left(1 + x\right)\right)\]
↓
\[1 + x \cdot \left(1 + x \cdot \left(1 + x\right)\right)\]
1 + x \cdot \left(1 + x \cdot \left(1 + x\right)\right)
↓
1 + x \cdot \left(1 + x \cdot \left(1 + x\right)\right)
double code(double x) {
	return ((double) (1.0 + ((double) (x * ((double) (1.0 + ((double) (x * ((double) (1.0 + x))))))))));
}
↓
double code(double x) {
	return ((double) (1.0 + ((double) (x * ((double) (1.0 + ((double) (x * ((double) (1.0 + 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

    \[1 + x \cdot \left(1 + x \cdot \left(1 + x\right)\right)\]

  2. Final simplification0.1

    \[\leadsto 1 + x \cdot \left(1 + x \cdot \left(1 + x\right)\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ 1 (* x (+ 1 (* x (+ 1 x)))))"
  :precision binary64
  (+ 1.0 (* x (+ 1.0 (* x (+ 1.0 x))))))