Average Error: 0.1 → 0.1
Time: 1.4s
Precision: binary64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[\left(1 - x \cdot 0.253\right) - \left(x \cdot x\right) \cdot 0.12\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
\left(1 - x \cdot 0.253\right) - \left(x \cdot x\right) \cdot 0.12
(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) (((double) (1.0 - ((double) (x * 0.253)))) - ((double) (((double) (x * x)) * 0.12))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied distribute-lft-in0.1

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

  4. Applied associate--r+0.1

    \[\leadsto \color{blue}{\left(1 - x \cdot 0.253\right) - x \cdot \left(x \cdot 0.12\right)}\]
  5. Using strategy rm

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020198 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))