Average Error: 0.0 → 0.0
Time: 18.1s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
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(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
double f(double x) {
        double r96467 = 0.70711;
        double r96468 = 2.30753;
        double r96469 = x;
        double r96470 = 0.27061;
        double r96471 = r96469 * r96470;
        double r96472 = r96468 + r96471;
        double r96473 = 1.0;
        double r96474 = 0.99229;
        double r96475 = 0.04481;
        double r96476 = r96469 * r96475;
        double r96477 = r96474 + r96476;
        double r96478 = r96469 * r96477;
        double r96479 = r96473 + r96478;
        double r96480 = r96472 / r96479;
        double r96481 = r96480 - r96469;
        double r96482 = r96467 * r96481;
        return r96482;
}
↓
double f(double x) {
        double r96483 = 0.70711;
        double r96484 = 2.30753;
        double r96485 = x;
        double r96486 = 0.27061;
        double r96487 = r96485 * r96486;
        double r96488 = r96484 + r96487;
        double r96489 = 1.0;
        double r96490 = 0.99229;
        double r96491 = 0.04481;
        double r96492 = r96485 * r96491;
        double r96493 = r96490 + r96492;
        double r96494 = r96485 * r96493;
        double r96495 = r96489 + r96494;
        double r96496 = r96488 / r96495;
        double r96497 = r96496 - r96485;
        double r96498 = r96483 * r96497;
        return r96498;
}

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

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x)))