Average Error: 0.0 → 0.1
Time: 3.9s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot \sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\right)\]
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(\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot \sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\right)
double f(double x) {
        double r118233 = 0.70711;
        double r118234 = 2.30753;
        double r118235 = x;
        double r118236 = 0.27061;
        double r118237 = r118235 * r118236;
        double r118238 = r118234 + r118237;
        double r118239 = 1.0;
        double r118240 = 0.99229;
        double r118241 = 0.04481;
        double r118242 = r118235 * r118241;
        double r118243 = r118240 + r118242;
        double r118244 = r118235 * r118243;
        double r118245 = r118239 + r118244;
        double r118246 = r118238 / r118245;
        double r118247 = r118246 - r118235;
        double r118248 = r118233 * r118247;
        return r118248;
}
↓
double f(double x) {
        double r118249 = 0.70711;
        double r118250 = 2.30753;
        double r118251 = x;
        double r118252 = 0.27061;
        double r118253 = r118251 * r118252;
        double r118254 = r118250 + r118253;
        double r118255 = 1.0;
        double r118256 = 0.99229;
        double r118257 = 0.04481;
        double r118258 = r118251 * r118257;
        double r118259 = r118256 + r118258;
        double r118260 = r118251 * r118259;
        double r118261 = r118255 + r118260;
        double r118262 = cbrt(r118261);
        double r118263 = r118262 * r118262;
        double r118264 = r118254 / r118263;
        double r118265 = r118264 / r118262;
        double r118266 = r118265 - r118251;
        double r118267 = r118249 * r118266;
        return r118267;
}

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-cube-cbrt0.1

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

  4. Applied associate-/r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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)))