Average Error: 0.1 → 0.1
Time: 1.9s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
double f(double x) {
        double r73084 = 1.0;
        double r73085 = x;
        double r73086 = 0.253;
        double r73087 = 0.12;
        double r73088 = r73085 * r73087;
        double r73089 = r73086 + r73088;
        double r73090 = r73085 * r73089;
        double r73091 = r73084 - r73090;
        return r73091;
}
↓
double f(double x) {
        double r73092 = 1.0;
        double r73093 = x;
        double r73094 = 0.253;
        double r73095 = 0.12;
        double r73096 = r73093 * r73095;
        double r73097 = r73094 + r73096;
        double r73098 = r73093 * r73097;
        double r73099 = r73092 - r73098;
        return r73099;
}

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

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

  5. Applied distribute-lft-out0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))