Average Error: 14.2 → 0.3
Time: 20.6s
Precision: 64
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
↓
\[\frac{\frac{\pi}{a + b} \cdot \left(\frac{1}{a} - \frac{1}{b}\right)}{2 \cdot \left(b - a\right)}\]
\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{\pi}{a + b} \cdot \left(\frac{1}{a} - \frac{1}{b}\right)}{2 \cdot \left(b - a\right)}
double f(double a, double b) {
        double r829430 = atan2(1.0, 0.0);
        double r829431 = 2.0;
        double r829432 = r829430 / r829431;
        double r829433 = 1.0;
        double r829434 = b;
        double r829435 = r829434 * r829434;
        double r829436 = a;
        double r829437 = r829436 * r829436;
        double r829438 = r829435 - r829437;
        double r829439 = r829433 / r829438;
        double r829440 = r829432 * r829439;
        double r829441 = r829433 / r829436;
        double r829442 = r829433 / r829434;
        double r829443 = r829441 - r829442;
        double r829444 = r829440 * r829443;
        return r829444;
}
↓
double f(double a, double b) {
        double r829445 = atan2(1.0, 0.0);
        double r829446 = a;
        double r829447 = b;
        double r829448 = r829446 + r829447;
        double r829449 = r829445 / r829448;
        double r829450 = 1.0;
        double r829451 = r829450 / r829446;
        double r829452 = r829450 / r829447;
        double r829453 = r829451 - r829452;
        double r829454 = r829449 * r829453;
        double r829455 = 2.0;
        double r829456 = r829447 - r829446;
        double r829457 = r829455 * r829456;
        double r829458 = r829454 / r829457;
        return r829458;
}

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 14.2

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

  2. Simplified9.0

    \[\leadsto \color{blue}{\frac{\frac{\pi}{a + b}}{2 \cdot \left(b - a\right)} \cdot \left(\frac{1}{a} - \frac{1}{b}\right)}\]
  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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019152 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))