Average Error: 0.0 → 0.0
Time: 18.0s
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 r121265 = 0.70711;
        double r121266 = 2.30753;
        double r121267 = x;
        double r121268 = 0.27061;
        double r121269 = r121267 * r121268;
        double r121270 = r121266 + r121269;
        double r121271 = 1.0;
        double r121272 = 0.99229;
        double r121273 = 0.04481;
        double r121274 = r121267 * r121273;
        double r121275 = r121272 + r121274;
        double r121276 = r121267 * r121275;
        double r121277 = r121271 + r121276;
        double r121278 = r121270 / r121277;
        double r121279 = r121278 - r121267;
        double r121280 = r121265 * r121279;
        return r121280;
}
↓
double f(double x) {
        double r121281 = 0.70711;
        double r121282 = 2.30753;
        double r121283 = x;
        double r121284 = 0.27061;
        double r121285 = r121283 * r121284;
        double r121286 = r121282 + r121285;
        double r121287 = 1.0;
        double r121288 = 0.99229;
        double r121289 = 0.04481;
        double r121290 = r121283 * r121289;
        double r121291 = r121288 + r121290;
        double r121292 = r121283 * r121291;
        double r121293 = r121287 + r121292;
        double r121294 = r121286 / r121293;
        double r121295 = 3.0;
        double r121296 = pow(r121294, r121295);
        double r121297 = cbrt(r121296);
        double r121298 = r121297 - r121283;
        double r121299 = r121281 * r121298;
        return r121299;
}

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)))