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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 r40644443 = atan2(1.0, 0.0);
        double r40644444 = 2.0;
        double r40644445 = r40644443 / r40644444;
        double r40644446 = 1.0;
        double r40644447 = b;
        double r40644448 = r40644447 * r40644447;
        double r40644449 = a;
        double r40644450 = r40644449 * r40644449;
        double r40644451 = r40644448 - r40644450;
        double r40644452 = r40644446 / r40644451;
        double r40644453 = r40644445 * r40644452;
        double r40644454 = r40644446 / r40644449;
        double r40644455 = r40644446 / r40644447;
        double r40644456 = r40644454 - r40644455;
        double r40644457 = r40644453 * r40644456;
        return r40644457;
}

Reproduce

herbie shell --seed 2019128 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))