Average Error: 0.2 → 0.2
Time: 5.1s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\frac{\left(a \cdot a\right) \cdot \left(1 \cdot 1 - a \cdot a\right)}{1 + a} + \left(\sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)}\right) \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)}\right)\right) - 1\]
\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(\frac{\left(a \cdot a\right) \cdot \left(1 \cdot 1 - a \cdot a\right)}{1 + a} + \left(\sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)}\right) \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)}\right)\right) - 1
double f(double a, double b) {
        double r330159 = a;
        double r330160 = r330159 * r330159;
        double r330161 = b;
        double r330162 = r330161 * r330161;
        double r330163 = r330160 + r330162;
        double r330164 = 2.0;
        double r330165 = pow(r330163, r330164);
        double r330166 = 4.0;
        double r330167 = 1.0;
        double r330168 = r330167 - r330159;
        double r330169 = r330160 * r330168;
        double r330170 = 3.0;
        double r330171 = r330170 + r330159;
        double r330172 = r330162 * r330171;
        double r330173 = r330169 + r330172;
        double r330174 = r330166 * r330173;
        double r330175 = r330165 + r330174;
        double r330176 = r330175 - r330167;
        return r330176;
}
↓
double f(double a, double b) {
        double r330177 = a;
        double r330178 = r330177 * r330177;
        double r330179 = b;
        double r330180 = r330179 * r330179;
        double r330181 = r330178 + r330180;
        double r330182 = 2.0;
        double r330183 = pow(r330181, r330182);
        double r330184 = 4.0;
        double r330185 = 1.0;
        double r330186 = r330185 * r330185;
        double r330187 = r330186 - r330178;
        double r330188 = r330178 * r330187;
        double r330189 = r330185 + r330177;
        double r330190 = r330188 / r330189;
        double r330191 = 3.0;
        double r330192 = r330191 + r330177;
        double r330193 = r330180 * r330192;
        double r330194 = cbrt(r330193);
        double r330195 = r330194 * r330194;
        double r330196 = r330195 * r330194;
        double r330197 = r330190 + r330196;
        double r330198 = r330184 * r330197;
        double r330199 = r330183 + r330198;
        double r330200 = r330199 - r330185;
        return r330200;
}

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 flip--0.2

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

  4. Applied associate-*r/0.2

    \[\leadsto \left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\color{blue}{\frac{\left(a \cdot a\right) \cdot \left(1 \cdot 1 - a \cdot a\right)}{1 + a}} + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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))