Average Error: 0.1 → 0.1
Time: 3.2s
Precision: binary64
Cost: 704
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - \left(x \cdot 0.253 + x \cdot \left(x \cdot 0.12\right)\right)\]
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 1.0 - (x * (0.253 + (x * 0.12)));
}
↓
double code(double x) {
	return 1.0 - ((x * 0.253) + (x * (x * 0.12)));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.1
Cost576
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
Alternative 2
Error1.9
Cost448
\[1 - x \cdot \left(x \cdot 0.12\right)\]
Alternative 3
Error21.7
Cost320
\[1 - x \cdot 0.253\]
Alternative 4
Error22.7
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

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

  3. Applied distribute-rgt-in_binary64_24150.1

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

  4. Simplified0.1

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))