Average Error: 0.5 → 0.5
Time: 7.8s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}\]
\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(\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)}
double f(double v, double t) {
        double r180323 = 1.0;
        double r180324 = 5.0;
        double r180325 = v;
        double r180326 = r180325 * r180325;
        double r180327 = r180324 * r180326;
        double r180328 = r180323 - r180327;
        double r180329 = atan2(1.0, 0.0);
        double r180330 = t;
        double r180331 = r180329 * r180330;
        double r180332 = 2.0;
        double r180333 = 3.0;
        double r180334 = r180333 * r180326;
        double r180335 = r180323 - r180334;
        double r180336 = r180332 * r180335;
        double r180337 = sqrt(r180336);
        double r180338 = r180331 * r180337;
        double r180339 = r180323 - r180326;
        double r180340 = r180338 * r180339;
        double r180341 = r180328 / r180340;
        return r180341;
}
↓
double f(double v, double t) {
        double r180342 = 1.0;
        double r180343 = 5.0;
        double r180344 = v;
        double r180345 = r180344 * r180344;
        double r180346 = r180343 * r180345;
        double r180347 = r180342 - r180346;
        double r180348 = atan2(1.0, 0.0);
        double r180349 = t;
        double r180350 = 2.0;
        double r180351 = 3.0;
        double r180352 = r180351 * r180345;
        double r180353 = r180342 - r180352;
        double r180354 = r180350 * r180353;
        double r180355 = sqrt(r180354);
        double r180356 = r180349 * r180355;
        double r180357 = r180348 * r180356;
        double r180358 = r180342 - r180345;
        double r180359 = r180357 * r180358;
        double r180360 = r180347 / r180359;
        return r180360;
}

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 associate-*l*0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020049 
(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)))))