Average Error: 0.0 → 0.0
Time: 22.1s
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 r6990109 = 0.70711;
        double r6990110 = 2.30753;
        double r6990111 = x;
        double r6990112 = 0.27061;
        double r6990113 = r6990111 * r6990112;
        double r6990114 = r6990110 + r6990113;
        double r6990115 = 1.0;
        double r6990116 = 0.99229;
        double r6990117 = 0.04481;
        double r6990118 = r6990111 * r6990117;
        double r6990119 = r6990116 + r6990118;
        double r6990120 = r6990111 * r6990119;
        double r6990121 = r6990115 + r6990120;
        double r6990122 = r6990114 / r6990121;
        double r6990123 = r6990122 - r6990111;
        double r6990124 = r6990109 * r6990123;
        return r6990124;
}
↓
double f(double x) {
        double r6990125 = 0.70711;
        double r6990126 = 2.30753;
        double r6990127 = x;
        double r6990128 = 0.27061;
        double r6990129 = r6990127 * r6990128;
        double r6990130 = r6990126 + r6990129;
        double r6990131 = 1.0;
        double r6990132 = 0.04481;
        double r6990133 = r6990127 * r6990132;
        double r6990134 = 0.99229;
        double r6990135 = r6990133 + r6990134;
        double r6990136 = r6990127 * r6990135;
        double r6990137 = r6990131 + r6990136;
        double r6990138 = r6990130 / r6990137;
        double r6990139 = r6990138 - r6990127;
        double r6990140 = r6990125 * r6990139;
        return r6990140;
}

Error

Bits error versus x

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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. 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 2019158 
(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)))