Average Error: 0.1 → 0.1
Time: 2.2s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[\left(1 - 0.253 \cdot x\right) - \left(x \cdot 0.12\right) \cdot x\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
\left(1 - 0.253 \cdot x\right) - \left(x \cdot 0.12\right) \cdot x
double f(double x) {
        double r71995 = 1.0;
        double r71996 = x;
        double r71997 = 0.253;
        double r71998 = 0.12;
        double r71999 = r71996 * r71998;
        double r72000 = r71997 + r71999;
        double r72001 = r71996 * r72000;
        double r72002 = r71995 - r72001;
        return r72002;
}
↓
double f(double x) {
        double r72003 = 1.0;
        double r72004 = 0.253;
        double r72005 = x;
        double r72006 = r72004 * r72005;
        double r72007 = r72003 - r72006;
        double r72008 = 0.12;
        double r72009 = r72005 * r72008;
        double r72010 = r72009 * r72005;
        double r72011 = r72007 - r72010;
        return r72011;
}

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-rgt-in0.1

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

  4. Applied associate--r+0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))