Average Error: 0.5 → 0.5
Time: 7.0s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot \left(t \cdot \sqrt{2}\right)\right) \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
\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 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot \left(t \cdot \sqrt{2}\right)\right) \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)}
double f(double v, double t) {
        double r305224 = 1.0;
        double r305225 = 5.0;
        double r305226 = v;
        double r305227 = r305226 * r305226;
        double r305228 = r305225 * r305227;
        double r305229 = r305224 - r305228;
        double r305230 = atan2(1.0, 0.0);
        double r305231 = t;
        double r305232 = r305230 * r305231;
        double r305233 = 2.0;
        double r305234 = 3.0;
        double r305235 = r305234 * r305227;
        double r305236 = r305224 - r305235;
        double r305237 = r305233 * r305236;
        double r305238 = sqrt(r305237);
        double r305239 = r305232 * r305238;
        double r305240 = r305224 - r305227;
        double r305241 = r305239 * r305240;
        double r305242 = r305229 / r305241;
        return r305242;
}
↓
double f(double v, double t) {
        double r305243 = 1.0;
        double r305244 = 5.0;
        double r305245 = v;
        double r305246 = r305245 * r305245;
        double r305247 = r305244 * r305246;
        double r305248 = r305243 - r305247;
        double r305249 = atan2(1.0, 0.0);
        double r305250 = t;
        double r305251 = 2.0;
        double r305252 = sqrt(r305251);
        double r305253 = r305250 * r305252;
        double r305254 = r305249 * r305253;
        double r305255 = 3.0;
        double r305256 = r305255 * r305246;
        double r305257 = r305243 - r305256;
        double r305258 = sqrt(r305257);
        double r305259 = r305254 * r305258;
        double r305260 = r305243 - r305246;
        double r305261 = r305259 * r305260;
        double r305262 = r305248 / r305261;
        return r305262;
}

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 sqrt-prod0.5

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

  4. Applied associate-*r*0.5

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

  6. Applied associate-*l*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2020046 
(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)))))