Average Error: 0.4 → 0.1
Time: 32.5s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{t}\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
↓
\frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{t}
double f(double v, double t) {
        double r4896269 = 1.0;
        double r4896270 = 5.0;
        double r4896271 = v;
        double r4896272 = r4896271 * r4896271;
        double r4896273 = r4896270 * r4896272;
        double r4896274 = r4896269 - r4896273;
        double r4896275 = atan2(1.0, 0.0);
        double r4896276 = t;
        double r4896277 = r4896275 * r4896276;
        double r4896278 = 2.0;
        double r4896279 = 3.0;
        double r4896280 = r4896279 * r4896272;
        double r4896281 = r4896269 - r4896280;
        double r4896282 = r4896278 * r4896281;
        double r4896283 = sqrt(r4896282);
        double r4896284 = r4896277 * r4896283;
        double r4896285 = r4896269 - r4896272;
        double r4896286 = r4896284 * r4896285;
        double r4896287 = r4896274 / r4896286;
        return r4896287;
}
↓
double f(double v, double t) {
        double r4896288 = 1.0;
        double r4896289 = v;
        double r4896290 = r4896289 * r4896289;
        double r4896291 = 5.0;
        double r4896292 = r4896290 * r4896291;
        double r4896293 = r4896288 - r4896292;
        double r4896294 = atan2(1.0, 0.0);
        double r4896295 = r4896293 / r4896294;
        double r4896296 = r4896288 - r4896290;
        double r4896297 = r4896295 / r4896296;
        double r4896298 = 2.0;
        double r4896299 = 6.0;
        double r4896300 = r4896299 * r4896290;
        double r4896301 = r4896298 - r4896300;
        double r4896302 = sqrt(r4896301);
        double r4896303 = r4896297 / r4896302;
        double r4896304 = t;
        double r4896305 = r4896303 / r4896304;
        return r4896305;
}

Error

Bits error versus v

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]

  2. Simplified0.4

    \[\leadsto \color{blue}{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{t \cdot \pi}}{1 - v \cdot v}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}}\]
  3. Using strategy rm

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

    \[\leadsto \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{t \cdot \pi}}{1 - v \cdot v}}{\color{blue}{1 \cdot \sqrt{2 - \left(v \cdot v\right) \cdot 6}}}\]

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

    \[\leadsto \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{t \cdot \pi}}{\color{blue}{1 \cdot \left(1 - v \cdot v\right)}}}{1 \cdot \sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]

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

    \[\leadsto \frac{\frac{\frac{\color{blue}{1 \cdot \left(1 - \left(v \cdot v\right) \cdot 5\right)}}{t \cdot \pi}}{1 \cdot \left(1 - v \cdot v\right)}}{1 \cdot \sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]

  7. Applied times-frac0.4

    \[\leadsto \frac{\frac{\color{blue}{\frac{1}{t} \cdot \frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}}{1 \cdot \left(1 - v \cdot v\right)}}{1 \cdot \sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]

  8. Applied times-frac0.4

    \[\leadsto \frac{\color{blue}{\frac{\frac{1}{t}}{1} \cdot \frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}}{1 \cdot \sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]

  9. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{\frac{\frac{1}{t}}{1}}{1} \cdot \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}}\]

  10. Simplified0.3

    \[\leadsto \color{blue}{\frac{1}{t}} \cdot \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]
  11. Using strategy rm

  12. Applied associate-*l/0.1

    \[\leadsto \color{blue}{\frac{1 \cdot \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}}{t}}\]

  13. Final simplification0.1

    \[\leadsto \frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{t}\]

Reproduce

herbie shell --seed 2019128 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))