Average Error: 14.3 → 0.3
Time: 32.4s
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 r1046932 = atan2(1.0, 0.0);
        double r1046933 = 2.0;
        double r1046934 = r1046932 / r1046933;
        double r1046935 = 1.0;
        double r1046936 = b;
        double r1046937 = r1046936 * r1046936;
        double r1046938 = a;
        double r1046939 = r1046938 * r1046938;
        double r1046940 = r1046937 - r1046939;
        double r1046941 = r1046935 / r1046940;
        double r1046942 = r1046934 * r1046941;
        double r1046943 = r1046935 / r1046938;
        double r1046944 = r1046935 / r1046936;
        double r1046945 = r1046943 - r1046944;
        double r1046946 = r1046942 * r1046945;
        return r1046946;
}
↓
double f(double a, double b) {
        double r1046947 = atan2(1.0, 0.0);
        double r1046948 = 1.0;
        double r1046949 = a;
        double r1046950 = r1046948 / r1046949;
        double r1046951 = b;
        double r1046952 = r1046948 / r1046951;
        double r1046953 = r1046950 - r1046952;
        double r1046954 = r1046949 + r1046951;
        double r1046955 = r1046953 / r1046954;
        double r1046956 = r1046947 * r1046955;
        double r1046957 = 2.0;
        double r1046958 = r1046951 - r1046949;
        double r1046959 = r1046957 * r1046958;
        double r1046960 = r1046956 / r1046959;
        return r1046960;
}

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))))