Average Error: 0.2 → 0.2
Time: 6.7s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 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} + 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
double f(double a, double b) {
        double r221049 = a;
        double r221050 = r221049 * r221049;
        double r221051 = b;
        double r221052 = r221051 * r221051;
        double r221053 = r221050 + r221052;
        double r221054 = 2.0;
        double r221055 = pow(r221053, r221054);
        double r221056 = 4.0;
        double r221057 = 1.0;
        double r221058 = r221057 + r221049;
        double r221059 = r221050 * r221058;
        double r221060 = 3.0;
        double r221061 = r221060 * r221049;
        double r221062 = r221057 - r221061;
        double r221063 = r221052 * r221062;
        double r221064 = r221059 + r221063;
        double r221065 = r221056 * r221064;
        double r221066 = r221055 + r221065;
        double r221067 = r221066 - r221057;
        return r221067;
}
↓
double f(double a, double b) {
        double r221068 = a;
        double r221069 = r221068 * r221068;
        double r221070 = b;
        double r221071 = r221070 * r221070;
        double r221072 = r221069 + r221071;
        double r221073 = 2.0;
        double r221074 = pow(r221072, r221073);
        double r221075 = 4.0;
        double r221076 = 1.0;
        double r221077 = r221076 + r221068;
        double r221078 = r221069 * r221077;
        double r221079 = 3.0;
        double r221080 = r221079 * r221068;
        double r221081 = r221076 - r221080;
        double r221082 = r221071 * r221081;
        double r221083 = r221078 + r221082;
        double r221084 = r221075 * r221083;
        double r221085 = r221074 + r221084;
        double r221086 = r221085 - r221076;
        return r221086;
}

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

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

Reproduce

herbie shell --seed 2019353 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))