Average Error: 0.2 → 0.2
Time: 24.6s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1\]
\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 r4316089 = a;
        double r4316090 = r4316089 * r4316089;
        double r4316091 = b;
        double r4316092 = r4316091 * r4316091;
        double r4316093 = r4316090 + r4316092;
        double r4316094 = 2.0;
        double r4316095 = pow(r4316093, r4316094);
        double r4316096 = 4.0;
        double r4316097 = 1.0;
        double r4316098 = r4316097 + r4316089;
        double r4316099 = r4316090 * r4316098;
        double r4316100 = 3.0;
        double r4316101 = r4316100 * r4316089;
        double r4316102 = r4316097 - r4316101;
        double r4316103 = r4316092 * r4316102;
        double r4316104 = r4316099 + r4316103;
        double r4316105 = r4316096 * r4316104;
        double r4316106 = r4316095 + r4316105;
        double r4316107 = r4316106 - r4316097;
        return r4316107;
}
↓
double f(double a, double b) {
        double r4316108 = a;
        double r4316109 = r4316108 * r4316108;
        double r4316110 = b;
        double r4316111 = r4316110 * r4316110;
        double r4316112 = r4316109 + r4316111;
        double r4316113 = 2.0;
        double r4316114 = pow(r4316112, r4316113);
        double r4316115 = 1.0;
        double r4316116 = r4316108 + r4316115;
        double r4316117 = r4316109 * r4316116;
        double r4316118 = 3.0;
        double r4316119 = r4316118 * r4316108;
        double r4316120 = r4316115 - r4316119;
        double r4316121 = r4316111 * r4316120;
        double r4316122 = r4316117 + r4316121;
        double r4316123 = 4.0;
        double r4316124 = r4316122 * r4316123;
        double r4316125 = r4316114 + r4316124;
        double r4316126 = r4316125 - r4316115;
        return r4316126;
}

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 2019152 
(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))