Average Error: 14.1 → 0.3
Time: 15.6s
Precision: 64
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
↓
\[\frac{\frac{1}{a} - \frac{1}{b}}{b - a} \cdot \frac{\frac{\pi}{a + b}}{2}\]
\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)
↓
\frac{\frac{1}{a} - \frac{1}{b}}{b - a} \cdot \frac{\frac{\pi}{a + b}}{2}
double f(double a, double b) {
        double r730508 = atan2(1.0, 0.0);
        double r730509 = 2.0;
        double r730510 = r730508 / r730509;
        double r730511 = 1.0;
        double r730512 = b;
        double r730513 = r730512 * r730512;
        double r730514 = a;
        double r730515 = r730514 * r730514;
        double r730516 = r730513 - r730515;
        double r730517 = r730511 / r730516;
        double r730518 = r730510 * r730517;
        double r730519 = r730511 / r730514;
        double r730520 = r730511 / r730512;
        double r730521 = r730519 - r730520;
        double r730522 = r730518 * r730521;
        return r730522;
}
↓
double f(double a, double b) {
        double r730523 = 1.0;
        double r730524 = a;
        double r730525 = r730523 / r730524;
        double r730526 = b;
        double r730527 = r730523 / r730526;
        double r730528 = r730525 - r730527;
        double r730529 = r730526 - r730524;
        double r730530 = r730528 / r730529;
        double r730531 = atan2(1.0, 0.0);
        double r730532 = r730524 + r730526;
        double r730533 = r730531 / r730532;
        double r730534 = 2.0;
        double r730535 = r730533 / r730534;
        double r730536 = r730530 * r730535;
        return r730536;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.1

    \[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]

  2. Simplified9.1

    \[\leadsto \color{blue}{\frac{\frac{\pi}{a + b}}{2 \cdot \left(b - a\right)} \cdot \left(\frac{1}{a} - \frac{1}{b}\right)}\]
  3. Using strategy rm

  4. Applied associate-*l/0.3

    \[\leadsto \color{blue}{\frac{\frac{\pi}{a + b} \cdot \left(\frac{1}{a} - \frac{1}{b}\right)}{2 \cdot \left(b - a\right)}}\]
  5. Using strategy rm

  6. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{\frac{\pi}{a + b}}{2} \cdot \frac{\frac{1}{a} - \frac{1}{b}}{b - a}}\]

  7. Final simplification0.3

    \[\leadsto \frac{\frac{1}{a} - \frac{1}{b}}{b - a} \cdot \frac{\frac{\pi}{a + b}}{2}\]

Reproduce

herbie shell --seed 2019154 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))