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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 r61890398 = atan2(1.0, 0.0);
        double r61890399 = 2.0;
        double r61890400 = r61890398 / r61890399;
        double r61890401 = 1.0;
        double r61890402 = b;
        double r61890403 = r61890402 * r61890402;
        double r61890404 = a;
        double r61890405 = r61890404 * r61890404;
        double r61890406 = r61890403 - r61890405;
        double r61890407 = r61890401 / r61890406;
        double r61890408 = r61890400 * r61890407;
        double r61890409 = r61890401 / r61890404;
        double r61890410 = r61890401 / r61890402;
        double r61890411 = r61890409 - r61890410;
        double r61890412 = r61890408 * r61890411;
        return r61890412;
}

Reproduce

herbie shell --seed 2019121 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))