Average Error: 0.2 → 0.2
Time: 21.1s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(\sqrt[3]{\left(a \cdot a\right) \cdot \left(1 - a\right)} \cdot \sqrt[3]{\left(a \cdot a\right) \cdot \left(1 - a\right)}\right) \cdot \sqrt[3]{\left(a \cdot a\right) \cdot \left(1 - a\right)} + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
\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(\sqrt[3]{\left(a \cdot a\right) \cdot \left(1 - a\right)} \cdot \sqrt[3]{\left(a \cdot a\right) \cdot \left(1 - a\right)}\right) \cdot \sqrt[3]{\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 r159065 = a;
        double r159066 = r159065 * r159065;
        double r159067 = b;
        double r159068 = r159067 * r159067;
        double r159069 = r159066 + r159068;
        double r159070 = 2.0;
        double r159071 = pow(r159069, r159070);
        double r159072 = 4.0;
        double r159073 = 1.0;
        double r159074 = r159073 - r159065;
        double r159075 = r159066 * r159074;
        double r159076 = 3.0;
        double r159077 = r159076 + r159065;
        double r159078 = r159068 * r159077;
        double r159079 = r159075 + r159078;
        double r159080 = r159072 * r159079;
        double r159081 = r159071 + r159080;
        double r159082 = r159081 - r159073;
        return r159082;
}
↓
double f(double a, double b) {
        double r159083 = a;
        double r159084 = r159083 * r159083;
        double r159085 = b;
        double r159086 = r159085 * r159085;
        double r159087 = r159084 + r159086;
        double r159088 = 2.0;
        double r159089 = pow(r159087, r159088);
        double r159090 = 4.0;
        double r159091 = 1.0;
        double r159092 = r159091 - r159083;
        double r159093 = r159084 * r159092;
        double r159094 = cbrt(r159093);
        double r159095 = r159094 * r159094;
        double r159096 = r159095 * r159094;
        double r159097 = 3.0;
        double r159098 = r159097 + r159083;
        double r159099 = r159086 * r159098;
        double r159100 = r159096 + r159099;
        double r159101 = r159090 * r159100;
        double r159102 = r159089 + r159101;
        double r159103 = r159102 - r159091;
        return r159103;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019304 
(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))