Average Error: 0.2 → 0.2
Time: 25.5s
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 r10892090 = a;
        double r10892091 = r10892090 * r10892090;
        double r10892092 = b;
        double r10892093 = r10892092 * r10892092;
        double r10892094 = r10892091 + r10892093;
        double r10892095 = 2.0;
        double r10892096 = pow(r10892094, r10892095);
        double r10892097 = 4.0;
        double r10892098 = 1.0;
        double r10892099 = r10892098 + r10892090;
        double r10892100 = r10892091 * r10892099;
        double r10892101 = 3.0;
        double r10892102 = r10892101 * r10892090;
        double r10892103 = r10892098 - r10892102;
        double r10892104 = r10892093 * r10892103;
        double r10892105 = r10892100 + r10892104;
        double r10892106 = r10892097 * r10892105;
        double r10892107 = r10892096 + r10892106;
        double r10892108 = r10892107 - r10892098;
        return r10892108;
}
↓
double f(double a, double b) {
        double r10892109 = a;
        double r10892110 = r10892109 * r10892109;
        double r10892111 = b;
        double r10892112 = r10892111 * r10892111;
        double r10892113 = r10892110 + r10892112;
        double r10892114 = 2.0;
        double r10892115 = pow(r10892113, r10892114);
        double r10892116 = 1.0;
        double r10892117 = r10892109 + r10892116;
        double r10892118 = r10892110 * r10892117;
        double r10892119 = 3.0;
        double r10892120 = r10892119 * r10892109;
        double r10892121 = r10892116 - r10892120;
        double r10892122 = r10892112 * r10892121;
        double r10892123 = r10892118 + r10892122;
        double r10892124 = 4.0;
        double r10892125 = r10892123 * r10892124;
        double r10892126 = r10892115 + r10892125;
        double r10892127 = r10892126 - r10892116;
        return r10892127;
}

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 2019171 
(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))