Average Error: 0.1 → 0.1
Time: 1.8s
Precision: binary64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
↓
\[1 - x \cdot \left(0.253 + \sqrt{0.12} \cdot \left(x \cdot \sqrt{0.12}\right)\right) \]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - x \cdot \left(0.253 + \sqrt{0.12} \cdot \left(x \cdot \sqrt{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 (* (sqrt 0.12) (* x (sqrt 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 + (sqrt(0.12) * (x * sqrt(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. Applied add-sqr-sqrt_binary640.1

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

  3. Applied associate-*r*_binary640.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2021313 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))