Average Error: 0.0 → 0.0
Time: 4.1m
Precision: 64
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
↓
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} - x\right)\]
0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)
↓
0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} - x\right)
double f(double x) {
        double r6784035 = 0.70711;
        double r6784036 = 2.30753;
        double r6784037 = x;
        double r6784038 = 0.27061;
        double r6784039 = r6784037 * r6784038;
        double r6784040 = r6784036 + r6784039;
        double r6784041 = 1.0;
        double r6784042 = 0.99229;
        double r6784043 = 0.04481;
        double r6784044 = r6784037 * r6784043;
        double r6784045 = r6784042 + r6784044;
        double r6784046 = r6784037 * r6784045;
        double r6784047 = r6784041 + r6784046;
        double r6784048 = r6784040 / r6784047;
        double r6784049 = r6784048 - r6784037;
        double r6784050 = r6784035 * r6784049;
        return r6784050;
}
↓
double f(double x) {
        double r6784051 = 0.70711;
        double r6784052 = 2.30753;
        double r6784053 = x;
        double r6784054 = 0.27061;
        double r6784055 = r6784053 * r6784054;
        double r6784056 = r6784052 + r6784055;
        double r6784057 = 1.0;
        double r6784058 = 0.04481;
        double r6784059 = r6784053 * r6784058;
        double r6784060 = 0.99229;
        double r6784061 = r6784059 + r6784060;
        double r6784062 = r6784053 * r6784061;
        double r6784063 = r6784057 + r6784062;
        double r6784064 = r6784056 / r6784063;
        double r6784065 = r6784064 - r6784053;
        double r6784066 = r6784051 * r6784065;
        return r6784066;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]

  2. Final simplification0.0

    \[\leadsto 0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} - x\right)\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))