Average Error: 0.2 → 0.2
Time: 57.3s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r112930133 = a;
        double r112930134 = r112930133 * r112930133;
        double r112930135 = b;
        double r112930136 = r112930135 * r112930135;
        double r112930137 = r112930134 + r112930136;
        double r112930138 = 2.0;
        double r112930139 = pow(r112930137, r112930138);
        double r112930140 = 4.0;
        double r112930141 = 1.0;
        double r112930142 = r112930141 + r112930133;
        double r112930143 = r112930134 * r112930142;
        double r112930144 = 3.0;
        double r112930145 = r112930144 * r112930133;
        double r112930146 = r112930141 - r112930145;
        double r112930147 = r112930136 * r112930146;
        double r112930148 = r112930143 + r112930147;
        double r112930149 = r112930140 * r112930148;
        double r112930150 = r112930139 + r112930149;
        double r112930151 = r112930150 - r112930141;
        return r112930151;
}
↓
double f(double a, double b) {
        double r112930152 = a;
        double r112930153 = r112930152 * r112930152;
        double r112930154 = b;
        double r112930155 = r112930154 * r112930154;
        double r112930156 = r112930153 + r112930155;
        double r112930157 = 2.0;
        double r112930158 = pow(r112930156, r112930157);
        double r112930159 = 1.0;
        double r112930160 = r112930152 + r112930159;
        double r112930161 = r112930153 * r112930160;
        double r112930162 = 3.0;
        double r112930163 = r112930162 * r112930152;
        double r112930164 = r112930159 - r112930163;
        double r112930165 = r112930155 * r112930164;
        double r112930166 = r112930161 + r112930165;
        double r112930167 = 4.0;
        double r112930168 = r112930166 * r112930167;
        double r112930169 = r112930158 + r112930168;
        double r112930170 = r112930169 - r112930159;
        return r112930170;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]

  2. Final simplification0.2

    \[\leadsto \left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1\]

Reproduce

herbie shell --seed 2019128 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))