Average Error: 0.0 → 0.0
Time: 6.7s
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 r5112301 = 0.70711;
        double r5112302 = 2.30753;
        double r5112303 = x;
        double r5112304 = 0.27061;
        double r5112305 = r5112303 * r5112304;
        double r5112306 = r5112302 + r5112305;
        double r5112307 = 1.0;
        double r5112308 = 0.99229;
        double r5112309 = 0.04481;
        double r5112310 = r5112303 * r5112309;
        double r5112311 = r5112308 + r5112310;
        double r5112312 = r5112303 * r5112311;
        double r5112313 = r5112307 + r5112312;
        double r5112314 = r5112306 / r5112313;
        double r5112315 = r5112314 - r5112303;
        double r5112316 = r5112301 * r5112315;
        return r5112316;
}
↓
double f(double x) {
        double r5112317 = 0.70711;
        double r5112318 = 2.30753;
        double r5112319 = x;
        double r5112320 = 0.27061;
        double r5112321 = r5112319 * r5112320;
        double r5112322 = r5112318 + r5112321;
        double r5112323 = 1.0;
        double r5112324 = 0.04481;
        double r5112325 = r5112319 * r5112324;
        double r5112326 = 0.99229;
        double r5112327 = r5112325 + r5112326;
        double r5112328 = r5112319 * r5112327;
        double r5112329 = r5112323 + r5112328;
        double r5112330 = r5112322 / r5112329;
        double r5112331 = r5112330 - r5112319;
        double r5112332 = r5112317 * r5112331;
        return r5112332;
}

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 2019171 
(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)))