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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 r66046197 = atan2(1.0, 0.0);
        double r66046198 = 2.0;
        double r66046199 = r66046197 / r66046198;
        double r66046200 = 1.0;
        double r66046201 = b;
        double r66046202 = r66046201 * r66046201;
        double r66046203 = a;
        double r66046204 = r66046203 * r66046203;
        double r66046205 = r66046202 - r66046204;
        double r66046206 = r66046200 / r66046205;
        double r66046207 = r66046199 * r66046206;
        double r66046208 = r66046200 / r66046203;
        double r66046209 = r66046200 / r66046201;
        double r66046210 = r66046208 - r66046209;
        double r66046211 = r66046207 * r66046210;
        return r66046211;
}

Reproduce

herbie shell --seed 2019119 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))