Average Error: 0.2 → 0.2
Time: 6.4s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 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} + 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
double f(double a, double b) {
        double r300010 = a;
        double r300011 = r300010 * r300010;
        double r300012 = b;
        double r300013 = r300012 * r300012;
        double r300014 = r300011 + r300013;
        double r300015 = 2.0;
        double r300016 = pow(r300014, r300015);
        double r300017 = 4.0;
        double r300018 = 1.0;
        double r300019 = r300018 - r300010;
        double r300020 = r300011 * r300019;
        double r300021 = 3.0;
        double r300022 = r300021 + r300010;
        double r300023 = r300013 * r300022;
        double r300024 = r300020 + r300023;
        double r300025 = r300017 * r300024;
        double r300026 = r300016 + r300025;
        double r300027 = r300026 - r300018;
        return r300027;
}
↓
double f(double a, double b) {
        double r300028 = a;
        double r300029 = r300028 * r300028;
        double r300030 = b;
        double r300031 = r300030 * r300030;
        double r300032 = r300029 + r300031;
        double r300033 = 2.0;
        double r300034 = pow(r300032, r300033);
        double r300035 = 4.0;
        double r300036 = 1.0;
        double r300037 = r300036 - r300028;
        double r300038 = r300029 * r300037;
        double r300039 = 3.0;
        double r300040 = r300039 + r300028;
        double r300041 = r300031 * r300040;
        double r300042 = r300038 + r300041;
        double r300043 = r300035 * r300042;
        double r300044 = r300034 + r300043;
        double r300045 = r300044 - r300036;
        return r300045;
}

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

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))