Average Error: 0.2 → 0.2
Time: 49.6s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\sqrt{{\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} \cdot \sqrt{{\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} - 1\]
\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
↓
\sqrt{{\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} \cdot \sqrt{{\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} - 1
double f(double a, double b) {
        double r6302146 = a;
        double r6302147 = r6302146 * r6302146;
        double r6302148 = b;
        double r6302149 = r6302148 * r6302148;
        double r6302150 = r6302147 + r6302149;
        double r6302151 = 2.0;
        double r6302152 = pow(r6302150, r6302151);
        double r6302153 = 4.0;
        double r6302154 = 1.0;
        double r6302155 = r6302154 + r6302146;
        double r6302156 = r6302147 * r6302155;
        double r6302157 = 3.0;
        double r6302158 = r6302157 * r6302146;
        double r6302159 = r6302154 - r6302158;
        double r6302160 = r6302149 * r6302159;
        double r6302161 = r6302156 + r6302160;
        double r6302162 = r6302153 * r6302161;
        double r6302163 = r6302152 + r6302162;
        double r6302164 = r6302163 - r6302154;
        return r6302164;
}
↓
double f(double a, double b) {
        double r6302165 = a;
        double r6302166 = r6302165 * r6302165;
        double r6302167 = b;
        double r6302168 = r6302167 * r6302167;
        double r6302169 = r6302166 + r6302168;
        double r6302170 = 2.0;
        double r6302171 = pow(r6302169, r6302170);
        double r6302172 = 1.0;
        double r6302173 = r6302165 + r6302172;
        double r6302174 = r6302166 * r6302173;
        double r6302175 = 3.0;
        double r6302176 = r6302175 * r6302165;
        double r6302177 = r6302172 - r6302176;
        double r6302178 = r6302168 * r6302177;
        double r6302179 = r6302174 + r6302178;
        double r6302180 = 4.0;
        double r6302181 = r6302179 * r6302180;
        double r6302182 = r6302171 + r6302181;
        double r6302183 = sqrt(r6302182);
        double r6302184 = r6302183 * r6302183;
        double r6302185 = r6302184 - r6302172;
        return r6302185;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019168 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0))