Average Error: 0.2 → 0.2
Time: 22.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left(4 \cdot \left(\left(b \cdot b\right) \cdot \left(1 - a \cdot 3\right) + \frac{\left(1 \cdot 1 - a \cdot a\right) \cdot \left(a \cdot a\right)}{1 - a}\right) + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\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(4 \cdot \left(\left(b \cdot b\right) \cdot \left(1 - a \cdot 3\right) + \frac{\left(1 \cdot 1 - a \cdot a\right) \cdot \left(a \cdot a\right)}{1 - a}\right) + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r9314515 = a;
        double r9314516 = r9314515 * r9314515;
        double r9314517 = b;
        double r9314518 = r9314517 * r9314517;
        double r9314519 = r9314516 + r9314518;
        double r9314520 = 2.0;
        double r9314521 = pow(r9314519, r9314520);
        double r9314522 = 4.0;
        double r9314523 = 1.0;
        double r9314524 = r9314523 + r9314515;
        double r9314525 = r9314516 * r9314524;
        double r9314526 = 3.0;
        double r9314527 = r9314526 * r9314515;
        double r9314528 = r9314523 - r9314527;
        double r9314529 = r9314518 * r9314528;
        double r9314530 = r9314525 + r9314529;
        double r9314531 = r9314522 * r9314530;
        double r9314532 = r9314521 + r9314531;
        double r9314533 = r9314532 - r9314523;
        return r9314533;
}
↓
double f(double a, double b) {
        double r9314534 = 4.0;
        double r9314535 = b;
        double r9314536 = r9314535 * r9314535;
        double r9314537 = 1.0;
        double r9314538 = a;
        double r9314539 = 3.0;
        double r9314540 = r9314538 * r9314539;
        double r9314541 = r9314537 - r9314540;
        double r9314542 = r9314536 * r9314541;
        double r9314543 = r9314537 * r9314537;
        double r9314544 = r9314538 * r9314538;
        double r9314545 = r9314543 - r9314544;
        double r9314546 = r9314545 * r9314544;
        double r9314547 = r9314537 - r9314538;
        double r9314548 = r9314546 / r9314547;
        double r9314549 = r9314542 + r9314548;
        double r9314550 = r9314534 * r9314549;
        double r9314551 = r9314544 + r9314536;
        double r9314552 = 2.0;
        double r9314553 = pow(r9314551, r9314552);
        double r9314554 = r9314550 + r9314553;
        double r9314555 = r9314554 - r9314537;
        return r9314555;
}

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 flip-+0.2

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

  4. Applied associate-*r/0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0))