Average Error: 0.4 → 0.3
Time: 7.5s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{1}{\pi}}{\sqrt{2}} \cdot \frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{t}}{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}}{1 - v \cdot v}\]
\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{1}{\pi}}{\sqrt{2}} \cdot \frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{t}}{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}}{1 - v \cdot v}
double code(double v, double t) {
	return ((1.0 - (5.0 * (v * v))) / (((((double) M_PI) * t) * sqrt((2.0 * (1.0 - (3.0 * (v * v)))))) * (1.0 - (v * v))));
}
↓
double code(double v, double t) {
	return ((((1.0 / ((double) M_PI)) / sqrt(2.0)) * (((1.0 - (5.0 * (v * v))) / t) / sqrt((1.0 - (3.0 * (v * v)))))) / (1.0 - (v * v)));
}

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. Using strategy rm

  3. Applied associate-/r*0.4

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

  5. Applied associate-/r*0.4

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

  7. Applied sqrt-prod0.4

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

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

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

  9. Applied times-frac0.4

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

  10. Applied times-frac0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020103 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  :precision binary64
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))