Average Error: 14.2 → 0.3
Time: 18.0s
Precision: 64
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
↓
\[\frac{\pi \cdot \frac{\frac{\frac{1}{2}}{a} - \frac{\frac{1}{2}}{b}}{b - a}}{a + b}\]
\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{\frac{1}{2}}{a} - \frac{\frac{1}{2}}{b}}{b - a}}{a + b}
double f(double a, double b) {
        double r1397205 = atan2(1.0, 0.0);
        double r1397206 = 2.0;
        double r1397207 = r1397205 / r1397206;
        double r1397208 = 1.0;
        double r1397209 = b;
        double r1397210 = r1397209 * r1397209;
        double r1397211 = a;
        double r1397212 = r1397211 * r1397211;
        double r1397213 = r1397210 - r1397212;
        double r1397214 = r1397208 / r1397213;
        double r1397215 = r1397207 * r1397214;
        double r1397216 = r1397208 / r1397211;
        double r1397217 = r1397208 / r1397209;
        double r1397218 = r1397216 - r1397217;
        double r1397219 = r1397215 * r1397218;
        return r1397219;
}
↓
double f(double a, double b) {
        double r1397220 = atan2(1.0, 0.0);
        double r1397221 = 0.5;
        double r1397222 = a;
        double r1397223 = r1397221 / r1397222;
        double r1397224 = b;
        double r1397225 = r1397221 / r1397224;
        double r1397226 = r1397223 - r1397225;
        double r1397227 = r1397224 - r1397222;
        double r1397228 = r1397226 / r1397227;
        double r1397229 = r1397220 * r1397228;
        double r1397230 = r1397222 + r1397224;
        double r1397231 = r1397229 / r1397230;
        return r1397231;
}

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. Simplified9.5

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

  4. Applied *-un-lft-identity9.5

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

  5. Applied div-inv9.5

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

  6. Applied times-frac9.5

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

  7. Applied *-un-lft-identity9.5

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

  8. Applied div-inv9.5

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

  9. Applied times-frac9.5

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

  10. Applied distribute-lft-out--9.5

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

  11. Applied times-frac0.3

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

  12. Simplified0.3

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

  13. Simplified0.3

    \[\leadsto \frac{\pi}{a + b} \cdot \color{blue}{\frac{\frac{\frac{1}{2}}{a} - \frac{\frac{1}{2}}{b}}{b - a}}\]
  14. Using strategy rm

  15. Applied associate-*l/0.3

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

  16. Final simplification0.3

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

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))))