Average Error: 0.2 → 0.2
Time: 15.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1\]
\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(3 + a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r222129 = a;
        double r222130 = r222129 * r222129;
        double r222131 = b;
        double r222132 = r222131 * r222131;
        double r222133 = r222130 + r222132;
        double r222134 = 2.0;
        double r222135 = pow(r222133, r222134);
        double r222136 = 4.0;
        double r222137 = 1.0;
        double r222138 = r222137 - r222129;
        double r222139 = r222130 * r222138;
        double r222140 = 3.0;
        double r222141 = r222140 + r222129;
        double r222142 = r222132 * r222141;
        double r222143 = r222139 + r222142;
        double r222144 = r222136 * r222143;
        double r222145 = r222135 + r222144;
        double r222146 = r222145 - r222137;
        return r222146;
}
↓
double f(double a, double b) {
        double r222147 = a;
        double r222148 = r222147 * r222147;
        double r222149 = b;
        double r222150 = r222149 * r222149;
        double r222151 = r222148 + r222150;
        double r222152 = 2.0;
        double r222153 = pow(r222151, r222152);
        double r222154 = 3.0;
        double r222155 = r222147 + r222154;
        double r222156 = r222155 * r222150;
        double r222157 = 1.0;
        double r222158 = r222157 - r222147;
        double r222159 = r222148 * r222158;
        double r222160 = r222156 + r222159;
        double r222161 = 4.0;
        double r222162 = r222160 * r222161;
        double r222163 = r222153 + r222162;
        double r222164 = r222163 - r222157;
        return r222164;
}

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

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019196 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 1.0))