Average Error: 0.2 → 0.1
Time: 37.5s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left(\left(b \cdot b\right) \cdot \left(3 + a\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4 - \left(1 - \left(\sqrt{a \cdot a + b \cdot b} \cdot \left(a \cdot a + b \cdot b\right)\right) \cdot \sqrt{a \cdot a + b \cdot b}\right)\]
\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(b \cdot b\right) \cdot \left(3 + a\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4 - \left(1 - \left(\sqrt{a \cdot a + b \cdot b} \cdot \left(a \cdot a + b \cdot b\right)\right) \cdot \sqrt{a \cdot a + b \cdot b}\right)
double f(double a, double b) {
        double r57535706 = a;
        double r57535707 = r57535706 * r57535706;
        double r57535708 = b;
        double r57535709 = r57535708 * r57535708;
        double r57535710 = r57535707 + r57535709;
        double r57535711 = 2.0;
        double r57535712 = pow(r57535710, r57535711);
        double r57535713 = 4.0;
        double r57535714 = 1.0;
        double r57535715 = r57535714 - r57535706;
        double r57535716 = r57535707 * r57535715;
        double r57535717 = 3.0;
        double r57535718 = r57535717 + r57535706;
        double r57535719 = r57535709 * r57535718;
        double r57535720 = r57535716 + r57535719;
        double r57535721 = r57535713 * r57535720;
        double r57535722 = r57535712 + r57535721;
        double r57535723 = r57535722 - r57535714;
        return r57535723;
}
↓
double f(double a, double b) {
        double r57535724 = b;
        double r57535725 = r57535724 * r57535724;
        double r57535726 = 3.0;
        double r57535727 = a;
        double r57535728 = r57535726 + r57535727;
        double r57535729 = r57535725 * r57535728;
        double r57535730 = r57535727 * r57535727;
        double r57535731 = 1.0;
        double r57535732 = r57535731 - r57535727;
        double r57535733 = r57535730 * r57535732;
        double r57535734 = r57535729 + r57535733;
        double r57535735 = 4.0;
        double r57535736 = r57535734 * r57535735;
        double r57535737 = r57535730 + r57535725;
        double r57535738 = sqrt(r57535737);
        double r57535739 = r57535738 * r57535737;
        double r57535740 = r57535739 * r57535738;
        double r57535741 = r57535731 - r57535740;
        double r57535742 = r57535736 - r57535741;
        return r57535742;
}

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. Simplified0.2

    \[\leadsto \color{blue}{\left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4 - \left(1 - \left(a \cdot a + b \cdot b\right) \cdot \left(a \cdot a + b \cdot b\right)\right)}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.2

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

  5. Applied associate-*l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019119 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))