Average Error: 0.0 → 0.0
Time: 15.4s
Precision: 64
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
↓
\[0.70711 \cdot \left(\frac{1}{\frac{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}{x \cdot 0.27061 + 2.30753}} - x\right)\]
0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)
↓
0.70711 \cdot \left(\frac{1}{\frac{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}{x \cdot 0.27061 + 2.30753}} - x\right)
double f(double x) {
        double r6971938 = 0.70711;
        double r6971939 = 2.30753;
        double r6971940 = x;
        double r6971941 = 0.27061;
        double r6971942 = r6971940 * r6971941;
        double r6971943 = r6971939 + r6971942;
        double r6971944 = 1.0;
        double r6971945 = 0.99229;
        double r6971946 = 0.04481;
        double r6971947 = r6971940 * r6971946;
        double r6971948 = r6971945 + r6971947;
        double r6971949 = r6971940 * r6971948;
        double r6971950 = r6971944 + r6971949;
        double r6971951 = r6971943 / r6971950;
        double r6971952 = r6971951 - r6971940;
        double r6971953 = r6971938 * r6971952;
        return r6971953;
}
↓
double f(double x) {
        double r6971954 = 0.70711;
        double r6971955 = 1.0;
        double r6971956 = x;
        double r6971957 = 0.04481;
        double r6971958 = r6971956 * r6971957;
        double r6971959 = 0.99229;
        double r6971960 = r6971958 + r6971959;
        double r6971961 = r6971956 * r6971960;
        double r6971962 = 1.0;
        double r6971963 = r6971961 + r6971962;
        double r6971964 = 0.27061;
        double r6971965 = r6971956 * r6971964;
        double r6971966 = 2.30753;
        double r6971967 = r6971965 + r6971966;
        double r6971968 = r6971963 / r6971967;
        double r6971969 = r6971955 / r6971968;
        double r6971970 = r6971969 - r6971956;
        double r6971971 = r6971954 * r6971970;
        return r6971971;
}

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

    \[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto 0.70711 \cdot \left(\color{blue}{\frac{1}{\frac{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}{2.30753 + x \cdot 0.27061}}} - x\right)\]

  4. Final simplification0.0

    \[\leadsto 0.70711 \cdot \left(\frac{1}{\frac{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}{x \cdot 0.27061 + 2.30753}} - x\right)\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))