Average Error: 0.4 → 0.4
Time: 7.3s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1}{\frac{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}{1 - 5 \cdot \left(v \cdot v\right)}}\]
\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}{\frac{\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)}{1 - 5 \cdot \left(v \cdot v\right)}}
double f(double v, double t) {
        double r331043 = 1.0;
        double r331044 = 5.0;
        double r331045 = v;
        double r331046 = r331045 * r331045;
        double r331047 = r331044 * r331046;
        double r331048 = r331043 - r331047;
        double r331049 = atan2(1.0, 0.0);
        double r331050 = t;
        double r331051 = r331049 * r331050;
        double r331052 = 2.0;
        double r331053 = 3.0;
        double r331054 = r331053 * r331046;
        double r331055 = r331043 - r331054;
        double r331056 = r331052 * r331055;
        double r331057 = sqrt(r331056);
        double r331058 = r331051 * r331057;
        double r331059 = r331043 - r331046;
        double r331060 = r331058 * r331059;
        double r331061 = r331048 / r331060;
        return r331061;
}
↓
double f(double v, double t) {
        double r331062 = 1.0;
        double r331063 = atan2(1.0, 0.0);
        double r331064 = t;
        double r331065 = 2.0;
        double r331066 = 1.0;
        double r331067 = 3.0;
        double r331068 = v;
        double r331069 = r331068 * r331068;
        double r331070 = r331067 * r331069;
        double r331071 = r331066 - r331070;
        double r331072 = r331065 * r331071;
        double r331073 = sqrt(r331072);
        double r331074 = r331064 * r331073;
        double r331075 = r331063 * r331074;
        double r331076 = r331066 - r331069;
        double r331077 = r331075 * r331076;
        double r331078 = 5.0;
        double r331079 = r331078 * r331069;
        double r331080 = r331066 - r331079;
        double r331081 = r331077 / r331080;
        double r331082 = r331062 / r331081;
        return r331082;
}

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 clear-num0.4

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

  5. Applied associate-*l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020056 
(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)))))