Average Error: 0.2 → 0.2
Time: 17.7s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + b \cdot \left(b \cdot \left(3 + a\right)\right)\right)\right) - 1\]
\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(a \cdot a\right) \cdot \left(1 - a\right) + b \cdot \left(b \cdot \left(3 + a\right)\right)\right)\right) - 1
double f(double a, double b) {
        double r167160 = a;
        double r167161 = r167160 * r167160;
        double r167162 = b;
        double r167163 = r167162 * r167162;
        double r167164 = r167161 + r167163;
        double r167165 = 2.0;
        double r167166 = pow(r167164, r167165);
        double r167167 = 4.0;
        double r167168 = 1.0;
        double r167169 = r167168 - r167160;
        double r167170 = r167161 * r167169;
        double r167171 = 3.0;
        double r167172 = r167171 + r167160;
        double r167173 = r167163 * r167172;
        double r167174 = r167170 + r167173;
        double r167175 = r167167 * r167174;
        double r167176 = r167166 + r167175;
        double r167177 = r167176 - r167168;
        return r167177;
}
↓
double f(double a, double b) {
        double r167178 = a;
        double r167179 = r167178 * r167178;
        double r167180 = b;
        double r167181 = r167180 * r167180;
        double r167182 = r167179 + r167181;
        double r167183 = 2.0;
        double r167184 = pow(r167182, r167183);
        double r167185 = 4.0;
        double r167186 = 1.0;
        double r167187 = r167186 - r167178;
        double r167188 = r167179 * r167187;
        double r167189 = 3.0;
        double r167190 = r167189 + r167178;
        double r167191 = r167180 * r167190;
        double r167192 = r167180 * r167191;
        double r167193 = r167188 + r167192;
        double r167194 = r167185 * r167193;
        double r167195 = r167184 + r167194;
        double r167196 = r167195 - r167186;
        return r167196;
}

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 associate-*l*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019291 
(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))