Average Error: 0.0 → 0.0
Time: 16.1s
Precision: 64
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
↓
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} - x\right)\]
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{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} - x\right)
double f(double x) {
        double r6671046 = 0.70711;
        double r6671047 = 2.30753;
        double r6671048 = x;
        double r6671049 = 0.27061;
        double r6671050 = r6671048 * r6671049;
        double r6671051 = r6671047 + r6671050;
        double r6671052 = 1.0;
        double r6671053 = 0.99229;
        double r6671054 = 0.04481;
        double r6671055 = r6671048 * r6671054;
        double r6671056 = r6671053 + r6671055;
        double r6671057 = r6671048 * r6671056;
        double r6671058 = r6671052 + r6671057;
        double r6671059 = r6671051 / r6671058;
        double r6671060 = r6671059 - r6671048;
        double r6671061 = r6671046 * r6671060;
        return r6671061;
}
↓
double f(double x) {
        double r6671062 = 0.70711;
        double r6671063 = 2.30753;
        double r6671064 = x;
        double r6671065 = 0.27061;
        double r6671066 = r6671064 * r6671065;
        double r6671067 = r6671063 + r6671066;
        double r6671068 = 1.0;
        double r6671069 = 0.04481;
        double r6671070 = r6671064 * r6671069;
        double r6671071 = 0.99229;
        double r6671072 = r6671070 + r6671071;
        double r6671073 = r6671064 * r6671072;
        double r6671074 = r6671068 + r6671073;
        double r6671075 = r6671067 / r6671074;
        double r6671076 = r6671075 - r6671064;
        double r6671077 = r6671062 * r6671076;
        return r6671077;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 
(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)))