Average Error: 0.2 → 0.2
Time: 50.2s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1\]
\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(3 + a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r111660091 = a;
        double r111660092 = r111660091 * r111660091;
        double r111660093 = b;
        double r111660094 = r111660093 * r111660093;
        double r111660095 = r111660092 + r111660094;
        double r111660096 = 2.0;
        double r111660097 = pow(r111660095, r111660096);
        double r111660098 = 4.0;
        double r111660099 = 1.0;
        double r111660100 = r111660099 - r111660091;
        double r111660101 = r111660092 * r111660100;
        double r111660102 = 3.0;
        double r111660103 = r111660102 + r111660091;
        double r111660104 = r111660094 * r111660103;
        double r111660105 = r111660101 + r111660104;
        double r111660106 = r111660098 * r111660105;
        double r111660107 = r111660097 + r111660106;
        double r111660108 = r111660107 - r111660099;
        return r111660108;
}
↓
double f(double a, double b) {
        double r111660109 = a;
        double r111660110 = r111660109 * r111660109;
        double r111660111 = b;
        double r111660112 = r111660111 * r111660111;
        double r111660113 = r111660110 + r111660112;
        double r111660114 = 2.0;
        double r111660115 = pow(r111660113, r111660114);
        double r111660116 = 3.0;
        double r111660117 = r111660109 + r111660116;
        double r111660118 = r111660117 * r111660112;
        double r111660119 = 1.0;
        double r111660120 = r111660119 - r111660109;
        double r111660121 = r111660110 * r111660120;
        double r111660122 = r111660118 + r111660121;
        double r111660123 = 4.0;
        double r111660124 = r111660122 * r111660123;
        double r111660125 = r111660115 + r111660124;
        double r111660126 = r111660125 - r111660119;
        return r111660126;
}

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

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

Reproduce

herbie shell --seed 2019128 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))