Average Error: 0.2 → 0.5
Time: 4.9s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left(\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}}\right) \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 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(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}}\right) \cdot \sqrt[3]{{\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
double f(double a, double b) {
        double r306733 = a;
        double r306734 = r306733 * r306733;
        double r306735 = b;
        double r306736 = r306735 * r306735;
        double r306737 = r306734 + r306736;
        double r306738 = 2.0;
        double r306739 = pow(r306737, r306738);
        double r306740 = 4.0;
        double r306741 = 1.0;
        double r306742 = r306741 - r306733;
        double r306743 = r306734 * r306742;
        double r306744 = 3.0;
        double r306745 = r306744 + r306733;
        double r306746 = r306736 * r306745;
        double r306747 = r306743 + r306746;
        double r306748 = r306740 * r306747;
        double r306749 = r306739 + r306748;
        double r306750 = r306749 - r306741;
        return r306750;
}
↓
double f(double a, double b) {
        double r306751 = a;
        double r306752 = r306751 * r306751;
        double r306753 = b;
        double r306754 = r306753 * r306753;
        double r306755 = r306752 + r306754;
        double r306756 = 2.0;
        double r306757 = pow(r306755, r306756);
        double r306758 = cbrt(r306757);
        double r306759 = r306758 * r306758;
        double r306760 = r306759 * r306758;
        double r306761 = 4.0;
        double r306762 = 1.0;
        double r306763 = r306762 - r306751;
        double r306764 = r306752 * r306763;
        double r306765 = 3.0;
        double r306766 = r306765 + r306751;
        double r306767 = r306754 * r306766;
        double r306768 = r306764 + r306767;
        double r306769 = r306761 * r306768;
        double r306770 = r306760 + r306769;
        double r306771 = r306770 - r306762;
        return r306771;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020062 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))