Average Error: 0.0 → 0.1
Time: 5.2s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\frac{1}{\sqrt[3]{{\left(\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\right)\]
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{1}{\sqrt[3]{{\left(\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\right)
double f(double x) {
        double r97320 = 0.70711;
        double r97321 = 2.30753;
        double r97322 = x;
        double r97323 = 0.27061;
        double r97324 = r97322 * r97323;
        double r97325 = r97321 + r97324;
        double r97326 = 1.0;
        double r97327 = 0.99229;
        double r97328 = 0.04481;
        double r97329 = r97322 * r97328;
        double r97330 = r97327 + r97329;
        double r97331 = r97322 * r97330;
        double r97332 = r97326 + r97331;
        double r97333 = r97325 / r97332;
        double r97334 = r97333 - r97322;
        double r97335 = r97320 * r97334;
        return r97335;
}
↓
double f(double x) {
        double r97336 = 0.70711;
        double r97337 = 1.0;
        double r97338 = 1.0;
        double r97339 = x;
        double r97340 = 0.99229;
        double r97341 = 0.04481;
        double r97342 = r97339 * r97341;
        double r97343 = r97340 + r97342;
        double r97344 = r97339 * r97343;
        double r97345 = r97338 + r97344;
        double r97346 = sqrt(r97345);
        double r97347 = 3.0;
        double r97348 = pow(r97346, r97347);
        double r97349 = cbrt(r97348);
        double r97350 = r97337 / r97349;
        double r97351 = 2.30753;
        double r97352 = 0.27061;
        double r97353 = r97339 * r97352;
        double r97354 = r97351 + r97353;
        double r97355 = r97354 / r97346;
        double r97356 = r97350 * r97355;
        double r97357 = r97356 - r97339;
        double r97358 = r97336 * r97357;
        return r97358;
}

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-sqr-sqrt0.1

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

  4. Applied *-un-lft-identity0.1

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

  5. Applied times-frac0.1

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

  7. Applied add-cbrt-cube0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020100 
(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)))