Average Error: 0.2 → 0.2
Time: 5.7s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
\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(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 r297546 = a;
        double r297547 = r297546 * r297546;
        double r297548 = b;
        double r297549 = r297548 * r297548;
        double r297550 = r297547 + r297549;
        double r297551 = 2.0;
        double r297552 = pow(r297550, r297551);
        double r297553 = 4.0;
        double r297554 = 1.0;
        double r297555 = r297554 - r297546;
        double r297556 = r297547 * r297555;
        double r297557 = 3.0;
        double r297558 = r297557 + r297546;
        double r297559 = r297549 * r297558;
        double r297560 = r297556 + r297559;
        double r297561 = r297553 * r297560;
        double r297562 = r297552 + r297561;
        double r297563 = r297562 - r297554;
        return r297563;
}
↓
double f(double a, double b) {
        double r297564 = a;
        double r297565 = r297564 * r297564;
        double r297566 = b;
        double r297567 = r297566 * r297566;
        double r297568 = r297565 + r297567;
        double r297569 = 2.0;
        double r297570 = pow(r297568, r297569);
        double r297571 = 4.0;
        double r297572 = 1.0;
        double r297573 = r297572 - r297564;
        double r297574 = r297565 * r297573;
        double r297575 = 3.0;
        double r297576 = r297575 + r297564;
        double r297577 = r297567 * r297576;
        double r297578 = r297574 + r297577;
        double r297579 = r297571 * r297578;
        double r297580 = r297570 + r297579;
        double r297581 = r297580 - r297572;
        return r297581;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020020 
(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))