Average Error: 0.2 → 0.2
Time: 25.9s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1\]
\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} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r5398593 = a;
        double r5398594 = r5398593 * r5398593;
        double r5398595 = b;
        double r5398596 = r5398595 * r5398595;
        double r5398597 = r5398594 + r5398596;
        double r5398598 = 2.0;
        double r5398599 = pow(r5398597, r5398598);
        double r5398600 = 4.0;
        double r5398601 = 1.0;
        double r5398602 = r5398601 - r5398593;
        double r5398603 = r5398594 * r5398602;
        double r5398604 = 3.0;
        double r5398605 = r5398604 + r5398593;
        double r5398606 = r5398596 * r5398605;
        double r5398607 = r5398603 + r5398606;
        double r5398608 = r5398600 * r5398607;
        double r5398609 = r5398599 + r5398608;
        double r5398610 = r5398609 - r5398601;
        return r5398610;
}
↓
double f(double a, double b) {
        double r5398611 = a;
        double r5398612 = r5398611 * r5398611;
        double r5398613 = b;
        double r5398614 = r5398613 * r5398613;
        double r5398615 = r5398612 + r5398614;
        double r5398616 = 2.0;
        double r5398617 = pow(r5398615, r5398616);
        double r5398618 = 3.0;
        double r5398619 = r5398611 + r5398618;
        double r5398620 = r5398619 * r5398614;
        double r5398621 = 1.0;
        double r5398622 = r5398621 - r5398611;
        double r5398623 = r5398612 * r5398622;
        double r5398624 = r5398620 + r5398623;
        double r5398625 = 4.0;
        double r5398626 = r5398624 * r5398625;
        double r5398627 = r5398617 + r5398626;
        double r5398628 = r5398627 - r5398621;
        return r5398628;
}

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

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

Reproduce

herbie shell --seed 2019149 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))