Average Error: 0.5 → 0.5
Time: 9.1s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot 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 t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
double f(double v, double t) {
        double r190082 = 1.0;
        double r190083 = 5.0;
        double r190084 = v;
        double r190085 = r190084 * r190084;
        double r190086 = r190083 * r190085;
        double r190087 = r190082 - r190086;
        double r190088 = atan2(1.0, 0.0);
        double r190089 = t;
        double r190090 = r190088 * r190089;
        double r190091 = 2.0;
        double r190092 = 3.0;
        double r190093 = r190092 * r190085;
        double r190094 = r190082 - r190093;
        double r190095 = r190091 * r190094;
        double r190096 = sqrt(r190095);
        double r190097 = r190090 * r190096;
        double r190098 = r190082 - r190085;
        double r190099 = r190097 * r190098;
        double r190100 = r190087 / r190099;
        return r190100;
}
↓
double f(double v, double t) {
        double r190101 = 1.0;
        double r190102 = 5.0;
        double r190103 = v;
        double r190104 = r190103 * r190103;
        double r190105 = r190102 * r190104;
        double r190106 = r190101 - r190105;
        double r190107 = atan2(1.0, 0.0);
        double r190108 = t;
        double r190109 = r190107 * r190108;
        double r190110 = 2.0;
        double r190111 = 3.0;
        double r190112 = r190111 * r190104;
        double r190113 = r190101 - r190112;
        double r190114 = r190110 * r190113;
        double r190115 = sqrt(r190114);
        double r190116 = r190109 * r190115;
        double r190117 = r190101 - r190104;
        double r190118 = r190116 * r190117;
        double r190119 = r190106 / r190118;
        return r190119;
}

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. Final simplification0.5

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

Reproduce

herbie shell --seed 2019354 
(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)))))