Average Error: 0.5 → 0.5
Time: 33.2s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\sqrt[3]{1 - 5 \cdot \left(v \cdot v\right)} \cdot \sqrt[3]{1 - 5 \cdot \left(v \cdot v\right)}}{\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}} \cdot \frac{\sqrt[3]{1 - 5 \cdot \left(v \cdot v\right)}}{1 - v \cdot v}\]
\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{\sqrt[3]{1 - 5 \cdot \left(v \cdot v\right)} \cdot \sqrt[3]{1 - 5 \cdot \left(v \cdot v\right)}}{\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}} \cdot \frac{\sqrt[3]{1 - 5 \cdot \left(v \cdot v\right)}}{1 - v \cdot v}
double f(double v, double t) {
        double r188045 = 1.0;
        double r188046 = 5.0;
        double r188047 = v;
        double r188048 = r188047 * r188047;
        double r188049 = r188046 * r188048;
        double r188050 = r188045 - r188049;
        double r188051 = atan2(1.0, 0.0);
        double r188052 = t;
        double r188053 = r188051 * r188052;
        double r188054 = 2.0;
        double r188055 = 3.0;
        double r188056 = r188055 * r188048;
        double r188057 = r188045 - r188056;
        double r188058 = r188054 * r188057;
        double r188059 = sqrt(r188058);
        double r188060 = r188053 * r188059;
        double r188061 = r188045 - r188048;
        double r188062 = r188060 * r188061;
        double r188063 = r188050 / r188062;
        return r188063;
}
↓
double f(double v, double t) {
        double r188064 = 1.0;
        double r188065 = 5.0;
        double r188066 = v;
        double r188067 = r188066 * r188066;
        double r188068 = r188065 * r188067;
        double r188069 = r188064 - r188068;
        double r188070 = cbrt(r188069);
        double r188071 = r188070 * r188070;
        double r188072 = atan2(1.0, 0.0);
        double r188073 = t;
        double r188074 = r188072 * r188073;
        double r188075 = 2.0;
        double r188076 = 3.0;
        double r188077 = r188076 * r188067;
        double r188078 = r188064 - r188077;
        double r188079 = r188075 * r188078;
        double r188080 = sqrt(r188079);
        double r188081 = r188074 * r188080;
        double r188082 = r188071 / r188081;
        double r188083 = r188064 - r188067;
        double r188084 = r188070 / r188083;
        double r188085 = r188082 * r188084;
        return r188085;
}

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 add-cube-cbrt0.5

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

  4. Applied times-frac0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019199 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))))