Average Error: 0.2 → 0.2
Time: 6.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\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(\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
double f(double a, double b) {
        double r276635 = a;
        double r276636 = r276635 * r276635;
        double r276637 = b;
        double r276638 = r276637 * r276637;
        double r276639 = r276636 + r276638;
        double r276640 = 2.0;
        double r276641 = pow(r276639, r276640);
        double r276642 = 4.0;
        double r276643 = 1.0;
        double r276644 = r276643 + r276635;
        double r276645 = r276636 * r276644;
        double r276646 = 3.0;
        double r276647 = r276646 * r276635;
        double r276648 = r276643 - r276647;
        double r276649 = r276638 * r276648;
        double r276650 = r276645 + r276649;
        double r276651 = r276642 * r276650;
        double r276652 = r276641 + r276651;
        double r276653 = r276652 - r276643;
        return r276653;
}
↓
double f(double a, double b) {
        double r276654 = a;
        double r276655 = r276654 * r276654;
        double r276656 = b;
        double r276657 = r276656 * r276656;
        double r276658 = r276655 + r276657;
        double r276659 = 2.0;
        double r276660 = pow(r276658, r276659);
        double r276661 = 4.0;
        double r276662 = 1.0;
        double r276663 = r276662 + r276654;
        double r276664 = r276655 * r276663;
        double r276665 = 3.0;
        double r276666 = r276665 * r276654;
        double r276667 = r276662 - r276666;
        double r276668 = r276657 * r276667;
        double r276669 = r276664 + r276668;
        double r276670 = r276661 * r276669;
        double r276671 = r276660 + r276670;
        double r276672 = r276671 - r276662;
        return r276672;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(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))