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\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)
double f(double a, double b) {
        double r1575685 = atan2(1.0, 0.0);
        double r1575686 = 2.0;
        double r1575687 = r1575685 / r1575686;
        double r1575688 = 1.0;
        double r1575689 = b;
        double r1575690 = r1575689 * r1575689;
        double r1575691 = a;
        double r1575692 = r1575691 * r1575691;
        double r1575693 = r1575690 - r1575692;
        double r1575694 = r1575688 / r1575693;
        double r1575695 = r1575687 * r1575694;
        double r1575696 = r1575688 / r1575691;
        double r1575697 = r1575688 / r1575689;
        double r1575698 = r1575696 - r1575697;
        double r1575699 = r1575695 * r1575698;
        return r1575699;
}

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b))))