Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} - x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} - x\right)
double f(double x) {
        double r4609092 = 0.70711;
        double r4609093 = 2.30753;
        double r4609094 = x;
        double r4609095 = 0.27061;
        double r4609096 = r4609094 * r4609095;
        double r4609097 = r4609093 + r4609096;
        double r4609098 = 1.0;
        double r4609099 = 0.99229;
        double r4609100 = 0.04481;
        double r4609101 = r4609094 * r4609100;
        double r4609102 = r4609099 + r4609101;
        double r4609103 = r4609094 * r4609102;
        double r4609104 = r4609098 + r4609103;
        double r4609105 = r4609097 / r4609104;
        double r4609106 = r4609105 - r4609094;
        double r4609107 = r4609092 * r4609106;
        return r4609107;
}
↓
double f(double x) {
        double r4609108 = 0.70711;
        double r4609109 = 2.30753;
        double r4609110 = x;
        double r4609111 = 0.27061;
        double r4609112 = r4609110 * r4609111;
        double r4609113 = r4609109 + r4609112;
        double r4609114 = 1.0;
        double r4609115 = 0.04481;
        double r4609116 = r4609110 * r4609115;
        double r4609117 = 0.99229;
        double r4609118 = r4609116 + r4609117;
        double r4609119 = r4609110 * r4609118;
        double r4609120 = r4609114 + r4609119;
        double r4609121 = r4609113 / r4609120;
        double r4609122 = r4609121 - r4609110;
        double r4609123 = r4609108 * r4609122;
        return r4609123;
}

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

    \[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]

  2. Final simplification0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} - x\right)\]

Reproduce

herbie shell --seed 2019172 
(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)))