Average Error: 0.0 → 0.0
Time: 29.7s
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 r96113 = 0.70711;
        double r96114 = 2.30753;
        double r96115 = x;
        double r96116 = 0.27061;
        double r96117 = r96115 * r96116;
        double r96118 = r96114 + r96117;
        double r96119 = 1.0;
        double r96120 = 0.99229;
        double r96121 = 0.04481;
        double r96122 = r96115 * r96121;
        double r96123 = r96120 + r96122;
        double r96124 = r96115 * r96123;
        double r96125 = r96119 + r96124;
        double r96126 = r96118 / r96125;
        double r96127 = r96126 - r96115;
        double r96128 = r96113 * r96127;
        return r96128;
}
↓
double f(double x) {
        double r96129 = 0.70711;
        double r96130 = 2.30753;
        double r96131 = x;
        double r96132 = 0.27061;
        double r96133 = r96131 * r96132;
        double r96134 = r96130 + r96133;
        double r96135 = 1.0;
        double r96136 = 1.0;
        double r96137 = 0.99229;
        double r96138 = 0.04481;
        double r96139 = r96131 * r96138;
        double r96140 = r96137 + r96139;
        double r96141 = r96131 * r96140;
        double r96142 = r96136 + r96141;
        double r96143 = 3.0;
        double r96144 = pow(r96142, r96143);
        double r96145 = r96135 / r96144;
        double r96146 = cbrt(r96145);
        double r96147 = r96134 * r96146;
        double r96148 = r96147 - r96131;
        double r96149 = r96129 * r96148;
        return r96149;
}

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)))