Average Error: 0.0 → 0.0
Time: 30.3s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}^{3}}} - x\right)\]
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(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}^{3}}} - x\right)
double f(double x) {
        double r83348 = 0.70711;
        double r83349 = 2.30753;
        double r83350 = x;
        double r83351 = 0.27061;
        double r83352 = r83350 * r83351;
        double r83353 = r83349 + r83352;
        double r83354 = 1.0;
        double r83355 = 0.99229;
        double r83356 = 0.04481;
        double r83357 = r83350 * r83356;
        double r83358 = r83355 + r83357;
        double r83359 = r83350 * r83358;
        double r83360 = r83354 + r83359;
        double r83361 = r83353 / r83360;
        double r83362 = r83361 - r83350;
        double r83363 = r83348 * r83362;
        return r83363;
}
↓
double f(double x) {
        double r83364 = 0.70711;
        double r83365 = 2.30753;
        double r83366 = x;
        double r83367 = 0.27061;
        double r83368 = r83366 * r83367;
        double r83369 = r83365 + r83368;
        double r83370 = 1.0;
        double r83371 = 1.0;
        double r83372 = 0.99229;
        double r83373 = 0.04481;
        double r83374 = r83366 * r83373;
        double r83375 = r83372 + r83374;
        double r83376 = r83366 * r83375;
        double r83377 = r83371 + r83376;
        double r83378 = 3.0;
        double r83379 = pow(r83377, r83378);
        double r83380 = r83370 / r83379;
        double r83381 = cbrt(r83380);
        double r83382 = r83369 * r83381;
        double r83383 = r83382 - r83366;
        double r83384 = r83364 * r83383;
        return r83384;
}

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 div-inv0.0

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

  5. Applied add-cbrt-cube0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{\color{blue}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}}} - x\right)\]

  6. Applied add-cbrt-cube0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{\color{blue}{\sqrt[3]{\left(1 \cdot 1\right) \cdot 1}}}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}} - x\right)\]

  7. Applied cbrt-undiv0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \color{blue}{\sqrt[3]{\frac{\left(1 \cdot 1\right) \cdot 1}{\left(\left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}}} - x\right)\]

  8. Simplified0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \sqrt[3]{\color{blue}{\frac{1}{{\left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}^{3}}}} - x\right)\]

  9. Final simplification0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}^{3}}} - x\right)\]

Reproduce

herbie shell --seed 2019303 
(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)))