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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 r30656135 = atan2(1.0, 0.0);
        double r30656136 = 2.0;
        double r30656137 = r30656135 / r30656136;
        double r30656138 = 1.0;
        double r30656139 = b;
        double r30656140 = r30656139 * r30656139;
        double r30656141 = a;
        double r30656142 = r30656141 * r30656141;
        double r30656143 = r30656140 - r30656142;
        double r30656144 = r30656138 / r30656143;
        double r30656145 = r30656137 * r30656144;
        double r30656146 = r30656138 / r30656141;
        double r30656147 = r30656138 / r30656139;
        double r30656148 = r30656146 - r30656147;
        double r30656149 = r30656145 * r30656148;
        return r30656149;
}

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))