Average Error: 0.5 → 0.5
Time: 26.4s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{{1}^{3} - {\left(5 \cdot \left(v \cdot v\right)\right)}^{3}}{\left(\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(1 \cdot 1 + \left(5 \cdot {v}^{2}\right) \cdot \left(1 + 5 \cdot \left(v \cdot v\right)\right)\right)}\]
\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{{1}^{3} - {\left(5 \cdot \left(v \cdot v\right)\right)}^{3}}{\left(\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(1 \cdot 1 + \left(5 \cdot {v}^{2}\right) \cdot \left(1 + 5 \cdot \left(v \cdot v\right)\right)\right)}
double f(double v, double t) {
        double r185186 = 1.0;
        double r185187 = 5.0;
        double r185188 = v;
        double r185189 = r185188 * r185188;
        double r185190 = r185187 * r185189;
        double r185191 = r185186 - r185190;
        double r185192 = atan2(1.0, 0.0);
        double r185193 = t;
        double r185194 = r185192 * r185193;
        double r185195 = 2.0;
        double r185196 = 3.0;
        double r185197 = r185196 * r185189;
        double r185198 = r185186 - r185197;
        double r185199 = r185195 * r185198;
        double r185200 = sqrt(r185199);
        double r185201 = r185194 * r185200;
        double r185202 = r185186 - r185189;
        double r185203 = r185201 * r185202;
        double r185204 = r185191 / r185203;
        return r185204;
}
↓
double f(double v, double t) {
        double r185205 = 1.0;
        double r185206 = 3.0;
        double r185207 = pow(r185205, r185206);
        double r185208 = 5.0;
        double r185209 = v;
        double r185210 = r185209 * r185209;
        double r185211 = r185208 * r185210;
        double r185212 = pow(r185211, r185206);
        double r185213 = r185207 - r185212;
        double r185214 = atan2(1.0, 0.0);
        double r185215 = t;
        double r185216 = 2.0;
        double r185217 = 3.0;
        double r185218 = r185217 * r185210;
        double r185219 = r185205 - r185218;
        double r185220 = r185216 * r185219;
        double r185221 = sqrt(r185220);
        double r185222 = r185215 * r185221;
        double r185223 = r185214 * r185222;
        double r185224 = r185205 - r185210;
        double r185225 = r185223 * r185224;
        double r185226 = r185205 * r185205;
        double r185227 = 2.0;
        double r185228 = pow(r185209, r185227);
        double r185229 = r185208 * r185228;
        double r185230 = r185205 + r185211;
        double r185231 = r185229 * r185230;
        double r185232 = r185226 + r185231;
        double r185233 = r185225 * r185232;
        double r185234 = r185213 / r185233;
        return r185234;
}

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 0.5

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

  3. Applied flip3--0.5

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

  4. Applied associate-/l/0.5

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

  5. Simplified0.5

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

  7. Applied associate-*l*0.5

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

  8. Final simplification0.5

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

Reproduce

herbie shell --seed 2019326 
(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)))))