Average Error: 0.0 → 0.0
Time: 28.9s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(-x\right) \cdot 0.7071100000000000163069557856942992657423 + \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} \cdot 0.7071100000000000163069557856942992657423\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
\left(-x\right) \cdot 0.7071100000000000163069557856942992657423 + \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} \cdot 0.7071100000000000163069557856942992657423
double f(double x) {
        double r5093125 = 0.70711;
        double r5093126 = 2.30753;
        double r5093127 = x;
        double r5093128 = 0.27061;
        double r5093129 = r5093127 * r5093128;
        double r5093130 = r5093126 + r5093129;
        double r5093131 = 1.0;
        double r5093132 = 0.99229;
        double r5093133 = 0.04481;
        double r5093134 = r5093127 * r5093133;
        double r5093135 = r5093132 + r5093134;
        double r5093136 = r5093127 * r5093135;
        double r5093137 = r5093131 + r5093136;
        double r5093138 = r5093130 / r5093137;
        double r5093139 = r5093138 - r5093127;
        double r5093140 = r5093125 * r5093139;
        return r5093140;
}
↓
double f(double x) {
        double r5093141 = x;
        double r5093142 = -r5093141;
        double r5093143 = 0.70711;
        double r5093144 = r5093142 * r5093143;
        double r5093145 = 2.30753;
        double r5093146 = 0.27061;
        double r5093147 = r5093141 * r5093146;
        double r5093148 = r5093145 + r5093147;
        double r5093149 = 1.0;
        double r5093150 = 0.04481;
        double r5093151 = r5093141 * r5093150;
        double r5093152 = 0.99229;
        double r5093153 = r5093151 + r5093152;
        double r5093154 = r5093141 * r5093153;
        double r5093155 = r5093149 + r5093154;
        double r5093156 = r5093148 / r5093155;
        double r5093157 = r5093156 * r5093143;
        double r5093158 = r5093144 + r5093157;
        return r5093158;
}

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. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(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)))