Average Error: 0.2 → 0.2
Time: 5.3s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(a \cdot \left(a \cdot \left(1 + a\right)\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\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(a \cdot \left(a \cdot \left(1 + a\right)\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
double f(double a, double b) {
        double r154301 = a;
        double r154302 = r154301 * r154301;
        double r154303 = b;
        double r154304 = r154303 * r154303;
        double r154305 = r154302 + r154304;
        double r154306 = 2.0;
        double r154307 = pow(r154305, r154306);
        double r154308 = 4.0;
        double r154309 = 1.0;
        double r154310 = r154309 + r154301;
        double r154311 = r154302 * r154310;
        double r154312 = 3.0;
        double r154313 = r154312 * r154301;
        double r154314 = r154309 - r154313;
        double r154315 = r154304 * r154314;
        double r154316 = r154311 + r154315;
        double r154317 = r154308 * r154316;
        double r154318 = r154307 + r154317;
        double r154319 = r154318 - r154309;
        return r154319;
}
↓
double f(double a, double b) {
        double r154320 = a;
        double r154321 = r154320 * r154320;
        double r154322 = b;
        double r154323 = r154322 * r154322;
        double r154324 = r154321 + r154323;
        double r154325 = 2.0;
        double r154326 = pow(r154324, r154325);
        double r154327 = 4.0;
        double r154328 = 1.0;
        double r154329 = r154328 + r154320;
        double r154330 = r154320 * r154329;
        double r154331 = r154320 * r154330;
        double r154332 = 3.0;
        double r154333 = r154332 * r154320;
        double r154334 = r154328 - r154333;
        double r154335 = r154323 * r154334;
        double r154336 = r154331 + r154335;
        double r154337 = r154327 * r154336;
        double r154338 = r154326 + r154337;
        double r154339 = r154338 - r154328;
        return r154339;
}

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. Using strategy rm

  3. Applied associate-*l*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(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))