Average Error: 0.2 → 0.2
Time: 4.7s
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 r160080 = a;
        double r160081 = r160080 * r160080;
        double r160082 = b;
        double r160083 = r160082 * r160082;
        double r160084 = r160081 + r160083;
        double r160085 = 2.0;
        double r160086 = pow(r160084, r160085);
        double r160087 = 4.0;
        double r160088 = 1.0;
        double r160089 = r160088 + r160080;
        double r160090 = r160081 * r160089;
        double r160091 = 3.0;
        double r160092 = r160091 * r160080;
        double r160093 = r160088 - r160092;
        double r160094 = r160083 * r160093;
        double r160095 = r160090 + r160094;
        double r160096 = r160087 * r160095;
        double r160097 = r160086 + r160096;
        double r160098 = r160097 - r160088;
        return r160098;
}
↓
double f(double a, double b) {
        double r160099 = a;
        double r160100 = r160099 * r160099;
        double r160101 = b;
        double r160102 = r160101 * r160101;
        double r160103 = r160100 + r160102;
        double r160104 = 2.0;
        double r160105 = pow(r160103, r160104);
        double r160106 = 4.0;
        double r160107 = 1.0;
        double r160108 = r160107 + r160099;
        double r160109 = r160100 * r160108;
        double r160110 = 3.0;
        double r160111 = r160110 * r160099;
        double r160112 = r160107 - r160111;
        double r160113 = r160102 * r160112;
        double r160114 = r160109 + r160113;
        double r160115 = r160106 * r160114;
        double r160116 = r160105 + r160115;
        double r160117 = r160116 - r160107;
        return r160117;
}

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 2020065 
(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))