Average Error: 0.4 → 0.4
Time: 7.6s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1}{\frac{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}{1 - 5 \cdot \left(v \cdot v\right)}}\]
\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(\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)}}
double f(double v, double t) {
        double r187072 = 1.0;
        double r187073 = 5.0;
        double r187074 = v;
        double r187075 = r187074 * r187074;
        double r187076 = r187073 * r187075;
        double r187077 = r187072 - r187076;
        double r187078 = atan2(1.0, 0.0);
        double r187079 = t;
        double r187080 = r187078 * r187079;
        double r187081 = 2.0;
        double r187082 = 3.0;
        double r187083 = r187082 * r187075;
        double r187084 = r187072 - r187083;
        double r187085 = r187081 * r187084;
        double r187086 = sqrt(r187085);
        double r187087 = r187080 * r187086;
        double r187088 = r187072 - r187075;
        double r187089 = r187087 * r187088;
        double r187090 = r187077 / r187089;
        return r187090;
}
↓
double f(double v, double t) {
        double r187091 = 1.0;
        double r187092 = atan2(1.0, 0.0);
        double r187093 = t;
        double r187094 = r187092 * r187093;
        double r187095 = 2.0;
        double r187096 = 1.0;
        double r187097 = 3.0;
        double r187098 = v;
        double r187099 = r187098 * r187098;
        double r187100 = r187097 * r187099;
        double r187101 = r187096 - r187100;
        double r187102 = r187095 * r187101;
        double r187103 = sqrt(r187102);
        double r187104 = r187094 * r187103;
        double r187105 = r187096 - r187099;
        double r187106 = r187104 * r187105;
        double r187107 = 5.0;
        double r187108 = r187107 * r187099;
        double r187109 = r187096 - r187108;
        double r187110 = r187106 / r187109;
        double r187111 = r187091 / r187110;
        return r187111;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(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)))))