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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 r42765318 = atan2(1.0, 0.0);
        double r42765319 = 2.0;
        double r42765320 = r42765318 / r42765319;
        double r42765321 = 1.0;
        double r42765322 = b;
        double r42765323 = r42765322 * r42765322;
        double r42765324 = a;
        double r42765325 = r42765324 * r42765324;
        double r42765326 = r42765323 - r42765325;
        double r42765327 = r42765321 / r42765326;
        double r42765328 = r42765320 * r42765327;
        double r42765329 = r42765321 / r42765324;
        double r42765330 = r42765321 / r42765322;
        double r42765331 = r42765329 - r42765330;
        double r42765332 = r42765328 * r42765331;
        return r42765332;
}

Reproduce

herbie shell --seed 2019125 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))