Average Error: 0.1 → 0.1
Time: 1.7s
Precision: binary64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - \left(x \cdot 0.253 + x \cdot \left(x \cdot 0.12\right)\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - \left(x \cdot 0.253 + x \cdot \left(x \cdot 0.12\right)\right)
(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))
↓
(FPCore (x) :precision binary64 (- 1.0 (+ (* x 0.253) (* x (* x 0.12)))))
double code(double x) {
	return ((double) (1.0 - ((double) (x * ((double) (0.253 + ((double) (x * 0.12))))))));
}
↓
double code(double x) {
	return ((double) (1.0 - ((double) (((double) (x * 0.253)) + ((double) (x * ((double) (x * 0.12))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 0.1 bits

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-inError: 0.1 bits

    \[\leadsto 1 - \color{blue}{\left(x \cdot 0.253 + x \cdot \left(x \cdot 0.12\right)\right)}\]

  4. Final simplificationError: 0.1 bits

    \[\leadsto 1 - \left(x \cdot 0.253 + x \cdot \left(x \cdot 0.12\right)\right)\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))