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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 r62172179 = atan2(1.0, 0.0);
        double r62172180 = 2.0;
        double r62172181 = r62172179 / r62172180;
        double r62172182 = 1.0;
        double r62172183 = b;
        double r62172184 = r62172183 * r62172183;
        double r62172185 = a;
        double r62172186 = r62172185 * r62172185;
        double r62172187 = r62172184 - r62172186;
        double r62172188 = r62172182 / r62172187;
        double r62172189 = r62172181 * r62172188;
        double r62172190 = r62172182 / r62172185;
        double r62172191 = r62172182 / r62172183;
        double r62172192 = r62172190 - r62172191;
        double r62172193 = r62172189 * r62172192;
        return r62172193;
}

Reproduce

herbie shell --seed 2019104 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))