Average Error: 0.0 → 0.0
Time: 7.9s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} - x\right)\]
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 r3788388 = 0.70711;
        double r3788389 = 2.30753;
        double r3788390 = x;
        double r3788391 = 0.27061;
        double r3788392 = r3788390 * r3788391;
        double r3788393 = r3788389 + r3788392;
        double r3788394 = 1.0;
        double r3788395 = 0.99229;
        double r3788396 = 0.04481;
        double r3788397 = r3788390 * r3788396;
        double r3788398 = r3788395 + r3788397;
        double r3788399 = r3788390 * r3788398;
        double r3788400 = r3788394 + r3788399;
        double r3788401 = r3788393 / r3788400;
        double r3788402 = r3788401 - r3788390;
        double r3788403 = r3788388 * r3788402;
        return r3788403;
}
↓
double f(double x) {
        double r3788404 = 0.70711;
        double r3788405 = 2.30753;
        double r3788406 = x;
        double r3788407 = 0.27061;
        double r3788408 = r3788406 * r3788407;
        double r3788409 = r3788405 + r3788408;
        double r3788410 = 1.0;
        double r3788411 = 0.04481;
        double r3788412 = r3788406 * r3788411;
        double r3788413 = 0.99229;
        double r3788414 = r3788412 + r3788413;
        double r3788415 = r3788406 * r3788414;
        double r3788416 = r3788410 + r3788415;
        double r3788417 = r3788409 / r3788416;
        double r3788418 = r3788417 - r3788406;
        double r3788419 = r3788404 * r3788418;
        return r3788419;
}

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)))