Average Error: 14.3 → 0.3
Time: 18.5s
Precision: 64
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
↓
\[\frac{\pi \cdot \frac{\frac{1}{a} - \frac{1}{b}}{a + b}}{2 \cdot \left(b - a\right)}\]
\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)
↓
\frac{\pi \cdot \frac{\frac{1}{a} - \frac{1}{b}}{a + b}}{2 \cdot \left(b - a\right)}
double f(double a, double b) {
        double r1094526 = atan2(1.0, 0.0);
        double r1094527 = 2.0;
        double r1094528 = r1094526 / r1094527;
        double r1094529 = 1.0;
        double r1094530 = b;
        double r1094531 = r1094530 * r1094530;
        double r1094532 = a;
        double r1094533 = r1094532 * r1094532;
        double r1094534 = r1094531 - r1094533;
        double r1094535 = r1094529 / r1094534;
        double r1094536 = r1094528 * r1094535;
        double r1094537 = r1094529 / r1094532;
        double r1094538 = r1094529 / r1094530;
        double r1094539 = r1094537 - r1094538;
        double r1094540 = r1094536 * r1094539;
        return r1094540;
}
↓
double f(double a, double b) {
        double r1094541 = atan2(1.0, 0.0);
        double r1094542 = 1.0;
        double r1094543 = a;
        double r1094544 = r1094542 / r1094543;
        double r1094545 = b;
        double r1094546 = r1094542 / r1094545;
        double r1094547 = r1094544 - r1094546;
        double r1094548 = r1094543 + r1094545;
        double r1094549 = r1094547 / r1094548;
        double r1094550 = r1094541 * r1094549;
        double r1094551 = 2.0;
        double r1094552 = r1094545 - r1094543;
        double r1094553 = r1094551 * r1094552;
        double r1094554 = r1094550 / r1094553;
        return r1094554;
}

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 14.3

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

  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 div-inv0.3

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

  7. Applied associate-*l*0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019153 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))