Average Error: 0.0 → 0.0
Time: 4.0s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}} - x\right)\]
0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
↓
0.707110000000000016 \cdot \left(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}} - x\right)
double f(double x) {
        double r125162 = 0.70711;
        double r125163 = 2.30753;
        double r125164 = x;
        double r125165 = 0.27061;
        double r125166 = r125164 * r125165;
        double r125167 = r125163 + r125166;
        double r125168 = 1.0;
        double r125169 = 0.99229;
        double r125170 = 0.04481;
        double r125171 = r125164 * r125170;
        double r125172 = r125169 + r125171;
        double r125173 = r125164 * r125172;
        double r125174 = r125168 + r125173;
        double r125175 = r125167 / r125174;
        double r125176 = r125175 - r125164;
        double r125177 = r125162 * r125176;
        return r125177;
}
↓
double f(double x) {
        double r125178 = 0.70711;
        double r125179 = 2.30753;
        double r125180 = x;
        double r125181 = 0.27061;
        double r125182 = r125180 * r125181;
        double r125183 = r125179 + r125182;
        double r125184 = 1.0;
        double r125185 = 0.99229;
        double r125186 = 0.04481;
        double r125187 = r125180 * r125186;
        double r125188 = r125185 + r125187;
        double r125189 = r125180 * r125188;
        double r125190 = r125184 + r125189;
        double r125191 = r125183 / r125190;
        double r125192 = 3.0;
        double r125193 = pow(r125191, r125192);
        double r125194 = cbrt(r125193);
        double r125195 = r125194 - r125180;
        double r125196 = r125178 * r125195;
        return r125196;
}

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

    \[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto 0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{\color{blue}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}}} - x\right)\]

  4. Applied add-cbrt-cube21.7

    \[\leadsto 0.707110000000000016 \cdot \left(\frac{\color{blue}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}} - x\right)\]

  5. Applied cbrt-undiv21.7

    \[\leadsto 0.707110000000000016 \cdot \left(\color{blue}{\sqrt[3]{\frac{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}}} - x\right)\]

  6. Simplified0.0

    \[\leadsto 0.707110000000000016 \cdot \left(\sqrt[3]{\color{blue}{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}}} - x\right)\]

  7. Final simplification0.0

    \[\leadsto 0.707110000000000016 \cdot \left(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}} - x\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x)))