Average Error: 0.0 → 0.0
Time: 14.4s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\frac{6369080665019903}{9007199254740992} \cdot \left(\left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}^{3}}} - x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
\frac{6369080665019903}{9007199254740992} \cdot \left(\left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}^{3}}} - x\right)
double f(double x) {
        double r118139 = 0.70711;
        double r118140 = 2.30753;
        double r118141 = x;
        double r118142 = 0.27061;
        double r118143 = r118141 * r118142;
        double r118144 = r118140 + r118143;
        double r118145 = 1.0;
        double r118146 = 0.99229;
        double r118147 = 0.04481;
        double r118148 = r118141 * r118147;
        double r118149 = r118146 + r118148;
        double r118150 = r118141 * r118149;
        double r118151 = r118145 + r118150;
        double r118152 = r118144 / r118151;
        double r118153 = r118152 - r118141;
        double r118154 = r118139 * r118153;
        return r118154;
}
↓
double f(double x) {
        double r118155 = 6369080665019903.0;
        double r118156 = 9007199254740992.0;
        double r118157 = r118155 / r118156;
        double r118158 = 162377988252285.0;
        double r118159 = 70368744177664.0;
        double r118160 = r118158 / r118159;
        double r118161 = x;
        double r118162 = 609359547581365.0;
        double r118163 = 2251799813685248.0;
        double r118164 = r118162 / r118163;
        double r118165 = r118161 * r118164;
        double r118166 = r118160 + r118165;
        double r118167 = 1.0;
        double r118168 = 1.0;
        double r118169 = 8937753748486939.0;
        double r118170 = r118169 / r118156;
        double r118171 = 3228900788839551.0;
        double r118172 = 7.205759403792794e+16;
        double r118173 = r118171 / r118172;
        double r118174 = r118161 * r118173;
        double r118175 = r118170 + r118174;
        double r118176 = r118161 * r118175;
        double r118177 = r118168 + r118176;
        double r118178 = 3.0;
        double r118179 = pow(r118177, r118178);
        double r118180 = r118167 / r118179;
        double r118181 = cbrt(r118180);
        double r118182 = r118166 * r118181;
        double r118183 = r118182 - r118161;
        double r118184 = r118157 * r118183;
        return r118184;
}

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. Simplified0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \color{blue}{\frac{1}{1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)}} - x\right)\]
  5. Using strategy rm

  6. Applied add-cbrt-cube0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{\color{blue}{\sqrt[3]{\left(\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}}} - x\right)\]

  7. Applied add-cbrt-cube0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{\color{blue}{\sqrt[3]{\left(1 \cdot 1\right) \cdot 1}}}{\sqrt[3]{\left(\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}} - x\right)\]

  8. Applied cbrt-undiv0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \color{blue}{\sqrt[3]{\frac{\left(1 \cdot 1\right) \cdot 1}{\left(\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}}} - x\right)\]

  9. Simplified0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \sqrt[3]{\color{blue}{\frac{1}{{\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}^{3}}}} - x\right)\]

  10. Final simplification0.0

    \[\leadsto \frac{6369080665019903}{9007199254740992} \cdot \left(\left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}^{3}}} - x\right)\]

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)))