Average Error: 14.0 → 0.3
Time: 28.3s
Precision: 64
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
↓
\[\frac{\frac{\frac{\pi}{a} - \frac{\pi}{b}}{a + b}}{2 \cdot \left(b - a\right)}\]
\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{\frac{\pi}{a} - \frac{\pi}{b}}{a + b}}{2 \cdot \left(b - a\right)}
double f(double a, double b) {
        double r1404323 = atan2(1.0, 0.0);
        double r1404324 = 2.0;
        double r1404325 = r1404323 / r1404324;
        double r1404326 = 1.0;
        double r1404327 = b;
        double r1404328 = r1404327 * r1404327;
        double r1404329 = a;
        double r1404330 = r1404329 * r1404329;
        double r1404331 = r1404328 - r1404330;
        double r1404332 = r1404326 / r1404331;
        double r1404333 = r1404325 * r1404332;
        double r1404334 = r1404326 / r1404329;
        double r1404335 = r1404326 / r1404327;
        double r1404336 = r1404334 - r1404335;
        double r1404337 = r1404333 * r1404336;
        return r1404337;
}
↓
double f(double a, double b) {
        double r1404338 = atan2(1.0, 0.0);
        double r1404339 = a;
        double r1404340 = r1404338 / r1404339;
        double r1404341 = b;
        double r1404342 = r1404338 / r1404341;
        double r1404343 = r1404340 - r1404342;
        double r1404344 = r1404339 + r1404341;
        double r1404345 = r1404343 / r1404344;
        double r1404346 = 2.0;
        double r1404347 = r1404341 - r1404339;
        double r1404348 = r1404346 * r1404347;
        double r1404349 = r1404345 / r1404348;
        return r1404349;
}

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 14.0

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

  2. Simplified0.3

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

  4. Applied *-un-lft-identity0.3

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

  5. Applied associate-/r*0.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019138 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))