Average Error: 0.2 → 0.2
Time: 19.9s
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 r218556 = a;
        double r218557 = r218556 * r218556;
        double r218558 = b;
        double r218559 = r218558 * r218558;
        double r218560 = r218557 + r218559;
        double r218561 = 2.0;
        double r218562 = pow(r218560, r218561);
        double r218563 = 4.0;
        double r218564 = 1.0;
        double r218565 = r218564 - r218556;
        double r218566 = r218557 * r218565;
        double r218567 = 3.0;
        double r218568 = r218567 + r218556;
        double r218569 = r218559 * r218568;
        double r218570 = r218566 + r218569;
        double r218571 = r218563 * r218570;
        double r218572 = r218562 + r218571;
        double r218573 = r218572 - r218564;
        return r218573;
}
↓
double f(double a, double b) {
        double r218574 = a;
        double r218575 = r218574 * r218574;
        double r218576 = b;
        double r218577 = r218576 * r218576;
        double r218578 = r218575 + r218577;
        double r218579 = 2.0;
        double r218580 = pow(r218578, r218579);
        double r218581 = 3.0;
        double r218582 = r218574 + r218581;
        double r218583 = r218582 * r218577;
        double r218584 = 1.0;
        double r218585 = r218584 - r218574;
        double r218586 = r218575 * r218585;
        double r218587 = r218583 + r218586;
        double r218588 = 4.0;
        double r218589 = r218587 * r218588;
        double r218590 = r218580 + r218589;
        double r218591 = r218590 - r218584;
        return r218591;
}

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 2019194 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 1.0))