Average Error: 0.2 → 0.2
Time: 6.2s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(\left(a \cdot a\right) \cdot \left(\sqrt[3]{1 + a} \cdot \sqrt[3]{1 + a}\right)\right) \cdot \sqrt[3]{1 + a} + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\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(\left(a \cdot a\right) \cdot \left(\sqrt[3]{1 + a} \cdot \sqrt[3]{1 + a}\right)\right) \cdot \sqrt[3]{1 + a} + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
double f(double a, double b) {
        double r275688 = a;
        double r275689 = r275688 * r275688;
        double r275690 = b;
        double r275691 = r275690 * r275690;
        double r275692 = r275689 + r275691;
        double r275693 = 2.0;
        double r275694 = pow(r275692, r275693);
        double r275695 = 4.0;
        double r275696 = 1.0;
        double r275697 = r275696 + r275688;
        double r275698 = r275689 * r275697;
        double r275699 = 3.0;
        double r275700 = r275699 * r275688;
        double r275701 = r275696 - r275700;
        double r275702 = r275691 * r275701;
        double r275703 = r275698 + r275702;
        double r275704 = r275695 * r275703;
        double r275705 = r275694 + r275704;
        double r275706 = r275705 - r275696;
        return r275706;
}
↓
double f(double a, double b) {
        double r275707 = a;
        double r275708 = r275707 * r275707;
        double r275709 = b;
        double r275710 = r275709 * r275709;
        double r275711 = r275708 + r275710;
        double r275712 = 2.0;
        double r275713 = pow(r275711, r275712);
        double r275714 = 4.0;
        double r275715 = 1.0;
        double r275716 = r275715 + r275707;
        double r275717 = cbrt(r275716);
        double r275718 = r275717 * r275717;
        double r275719 = r275708 * r275718;
        double r275720 = r275719 * r275717;
        double r275721 = 3.0;
        double r275722 = r275721 * r275707;
        double r275723 = r275715 - r275722;
        double r275724 = r275710 * r275723;
        double r275725 = r275720 + r275724;
        double r275726 = r275714 * r275725;
        double r275727 = r275713 + r275726;
        double r275728 = r275727 - r275715;
        return r275728;
}

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 add-cube-cbrt0.2

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019356 
(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))