Average Error: 0.0 → 0.0
Time: 19.3s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{0.7071100000000000163069557856942992657423}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{0.7071100000000000163069557856942992657423}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)
double f(double x) {
        double r86322 = 0.70711;
        double r86323 = 2.30753;
        double r86324 = x;
        double r86325 = 0.27061;
        double r86326 = r86324 * r86325;
        double r86327 = r86323 + r86326;
        double r86328 = 1.0;
        double r86329 = 0.99229;
        double r86330 = 0.04481;
        double r86331 = r86324 * r86330;
        double r86332 = r86329 + r86331;
        double r86333 = r86324 * r86332;
        double r86334 = r86328 + r86333;
        double r86335 = r86327 / r86334;
        double r86336 = r86335 - r86324;
        double r86337 = r86322 * r86336;
        return r86337;
}
↓
double f(double x) {
        double r86338 = 2.30753;
        double r86339 = x;
        double r86340 = 0.27061;
        double r86341 = r86339 * r86340;
        double r86342 = r86338 + r86341;
        double r86343 = 0.70711;
        double r86344 = 1.0;
        double r86345 = 0.99229;
        double r86346 = 0.04481;
        double r86347 = r86339 * r86346;
        double r86348 = r86345 + r86347;
        double r86349 = r86339 * r86348;
        double r86350 = r86344 + r86349;
        double r86351 = r86343 / r86350;
        double r86352 = r86342 * r86351;
        double r86353 = -r86339;
        double r86354 = r86343 * r86353;
        double r86355 = r86352 + r86354;
        return r86355;
}

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

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

  7. Applied div-inv0.0

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

  8. Applied associate-*l*0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.707110000000000016 (- (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* x (+ 0.992290000000000005 (* x 0.044810000000000003))))) x)))