Average Error: 0.0 → 0.0
Time: 2.0s
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 r88395 = 0.70711;
        double r88396 = 2.30753;
        double r88397 = x;
        double r88398 = 0.27061;
        double r88399 = r88397 * r88398;
        double r88400 = r88396 + r88399;
        double r88401 = 1.0;
        double r88402 = 0.99229;
        double r88403 = 0.04481;
        double r88404 = r88397 * r88403;
        double r88405 = r88402 + r88404;
        double r88406 = r88397 * r88405;
        double r88407 = r88401 + r88406;
        double r88408 = r88400 / r88407;
        double r88409 = r88408 - r88397;
        double r88410 = r88395 * r88409;
        return r88410;
}
↓
double f(double x) {
        double r88411 = 0.70711;
        double r88412 = 2.30753;
        double r88413 = x;
        double r88414 = 0.27061;
        double r88415 = r88413 * r88414;
        double r88416 = r88412 + r88415;
        double r88417 = 1.0;
        double r88418 = 0.99229;
        double r88419 = 0.04481;
        double r88420 = r88413 * r88419;
        double r88421 = r88418 + r88420;
        double r88422 = r88413 * r88421;
        double r88423 = r88417 + r88422;
        double r88424 = r88416 / r88423;
        double r88425 = 3.0;
        double r88426 = pow(r88424, r88425);
        double r88427 = cbrt(r88426);
        double r88428 = r88427 - r88413;
        double r88429 = r88411 * r88428;
        return r88429;
}

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-cube21.3

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

  5. Applied cbrt-undiv21.3

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

  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 2020003 
(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)))