Average Error: 0.2 → 0.2
Time: 5.2s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(a \cdot \left(a \cdot \left(1 + a\right)\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\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(a \cdot \left(a \cdot \left(1 + a\right)\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
double f(double a, double b) {
        double r314574 = a;
        double r314575 = r314574 * r314574;
        double r314576 = b;
        double r314577 = r314576 * r314576;
        double r314578 = r314575 + r314577;
        double r314579 = 2.0;
        double r314580 = pow(r314578, r314579);
        double r314581 = 4.0;
        double r314582 = 1.0;
        double r314583 = r314582 + r314574;
        double r314584 = r314575 * r314583;
        double r314585 = 3.0;
        double r314586 = r314585 * r314574;
        double r314587 = r314582 - r314586;
        double r314588 = r314577 * r314587;
        double r314589 = r314584 + r314588;
        double r314590 = r314581 * r314589;
        double r314591 = r314580 + r314590;
        double r314592 = r314591 - r314582;
        return r314592;
}
↓
double f(double a, double b) {
        double r314593 = a;
        double r314594 = r314593 * r314593;
        double r314595 = b;
        double r314596 = r314595 * r314595;
        double r314597 = r314594 + r314596;
        double r314598 = 2.0;
        double r314599 = pow(r314597, r314598);
        double r314600 = 4.0;
        double r314601 = 1.0;
        double r314602 = r314601 + r314593;
        double r314603 = r314593 * r314602;
        double r314604 = r314593 * r314603;
        double r314605 = 3.0;
        double r314606 = r314605 * r314593;
        double r314607 = r314601 - r314606;
        double r314608 = r314596 * r314607;
        double r314609 = r314604 + r314608;
        double r314610 = r314600 * r314609;
        double r314611 = r314599 + r314610;
        double r314612 = r314611 - r314601;
        return r314612;
}

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 associate-*l*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(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))