Average Error: 0.0 → 0.0
Time: 16.0s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(-x\right) + 0.7071100000000000163069557856942992657423 \cdot \frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{1 + \left(x \cdot 0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot \left(x \cdot x\right)\right)}\]
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(-x\right) + 0.7071100000000000163069557856942992657423 \cdot \frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{1 + \left(x \cdot 0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot \left(x \cdot x\right)\right)}
double f(double x) {
        double r101375 = 0.70711;
        double r101376 = 2.30753;
        double r101377 = x;
        double r101378 = 0.27061;
        double r101379 = r101377 * r101378;
        double r101380 = r101376 + r101379;
        double r101381 = 1.0;
        double r101382 = 0.99229;
        double r101383 = 0.04481;
        double r101384 = r101377 * r101383;
        double r101385 = r101382 + r101384;
        double r101386 = r101377 * r101385;
        double r101387 = r101381 + r101386;
        double r101388 = r101380 / r101387;
        double r101389 = r101388 - r101377;
        double r101390 = r101375 * r101389;
        return r101390;
}
↓
double f(double x) {
        double r101391 = 0.70711;
        double r101392 = x;
        double r101393 = -r101392;
        double r101394 = r101391 * r101393;
        double r101395 = 2.30753;
        double r101396 = 0.27061;
        double r101397 = r101396 * r101392;
        double r101398 = r101395 + r101397;
        double r101399 = 1.0;
        double r101400 = 0.99229;
        double r101401 = r101392 * r101400;
        double r101402 = 0.04481;
        double r101403 = r101392 * r101392;
        double r101404 = r101402 * r101403;
        double r101405 = r101401 + r101404;
        double r101406 = r101399 + r101405;
        double r101407 = r101398 / r101406;
        double r101408 = r101391 * r101407;
        double r101409 = r101394 + r101408;
        return r101409;
}

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. Simplified0.0

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

  6. Simplified0.0

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

  8. Applied distribute-rgt-in0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(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)))