Average Error: 0.2 → 0.2
Time: 7.0s
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 r373170 = a;
        double r373171 = r373170 * r373170;
        double r373172 = b;
        double r373173 = r373172 * r373172;
        double r373174 = r373171 + r373173;
        double r373175 = 2.0;
        double r373176 = pow(r373174, r373175);
        double r373177 = 4.0;
        double r373178 = 1.0;
        double r373179 = r373178 + r373170;
        double r373180 = r373171 * r373179;
        double r373181 = 3.0;
        double r373182 = r373181 * r373170;
        double r373183 = r373178 - r373182;
        double r373184 = r373173 * r373183;
        double r373185 = r373180 + r373184;
        double r373186 = r373177 * r373185;
        double r373187 = r373176 + r373186;
        double r373188 = r373187 - r373178;
        return r373188;
}
↓
double f(double a, double b) {
        double r373189 = a;
        double r373190 = r373189 * r373189;
        double r373191 = b;
        double r373192 = r373191 * r373191;
        double r373193 = r373190 + r373192;
        double r373194 = 2.0;
        double r373195 = pow(r373193, r373194);
        double r373196 = 4.0;
        double r373197 = 1.0;
        double r373198 = r373197 + r373189;
        double r373199 = r373190 * r373198;
        double r373200 = 3.0;
        double r373201 = r373200 * r373189;
        double r373202 = r373197 - r373201;
        double r373203 = r373192 * r373202;
        double r373204 = r373199 + r373203;
        double r373205 = r373196 * r373204;
        double r373206 = r373195 + r373205;
        double r373207 = r373206 - r373197;
        return r373207;
}

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 2019354 +o rules:numerics
(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))