Average Error: 0.5 → 0.1
Time: 26.4s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1 - v \cdot \left(v \cdot 5\right)}{\pi}}{\sqrt{\left(1 - \left(\left(v \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right) \cdot 27\right) \cdot 2}}}{t}}{1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)} \cdot \left(\left(1 + v \cdot v\right) \cdot \sqrt{\left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right) + 3 \cdot \left(v \cdot v\right)\right) + 1}\right)\]
\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{\frac{\frac{\frac{1 - v \cdot \left(v \cdot 5\right)}{\pi}}{\sqrt{\left(1 - \left(\left(v \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right) \cdot 27\right) \cdot 2}}}{t}}{1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)} \cdot \left(\left(1 + v \cdot v\right) \cdot \sqrt{\left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right) + 3 \cdot \left(v \cdot v\right)\right) + 1}\right)
double f(double v, double t) {
        double r6442040 = 1.0;
        double r6442041 = 5.0;
        double r6442042 = v;
        double r6442043 = r6442042 * r6442042;
        double r6442044 = r6442041 * r6442043;
        double r6442045 = r6442040 - r6442044;
        double r6442046 = atan2(1.0, 0.0);
        double r6442047 = t;
        double r6442048 = r6442046 * r6442047;
        double r6442049 = 2.0;
        double r6442050 = 3.0;
        double r6442051 = r6442050 * r6442043;
        double r6442052 = r6442040 - r6442051;
        double r6442053 = r6442049 * r6442052;
        double r6442054 = sqrt(r6442053);
        double r6442055 = r6442048 * r6442054;
        double r6442056 = r6442040 - r6442043;
        double r6442057 = r6442055 * r6442056;
        double r6442058 = r6442045 / r6442057;
        return r6442058;
}
↓
double f(double v, double t) {
        double r6442059 = 1.0;
        double r6442060 = v;
        double r6442061 = 5.0;
        double r6442062 = r6442060 * r6442061;
        double r6442063 = r6442060 * r6442062;
        double r6442064 = r6442059 - r6442063;
        double r6442065 = atan2(1.0, 0.0);
        double r6442066 = r6442064 / r6442065;
        double r6442067 = r6442060 * r6442060;
        double r6442068 = r6442067 * r6442067;
        double r6442069 = r6442067 * r6442068;
        double r6442070 = 27.0;
        double r6442071 = r6442069 * r6442070;
        double r6442072 = r6442059 - r6442071;
        double r6442073 = 2.0;
        double r6442074 = r6442072 * r6442073;
        double r6442075 = sqrt(r6442074);
        double r6442076 = r6442066 / r6442075;
        double r6442077 = t;
        double r6442078 = r6442076 / r6442077;
        double r6442079 = r6442059 - r6442068;
        double r6442080 = r6442078 / r6442079;
        double r6442081 = r6442059 + r6442067;
        double r6442082 = 3.0;
        double r6442083 = r6442082 * r6442067;
        double r6442084 = r6442083 * r6442083;
        double r6442085 = r6442084 + r6442083;
        double r6442086 = r6442085 + r6442059;
        double r6442087 = sqrt(r6442086);
        double r6442088 = r6442081 * r6442087;
        double r6442089 = r6442080 * r6442088;
        return r6442089;
}

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 flip--0.5

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

  4. Applied flip3--0.5

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

  5. Applied associate-*r/0.5

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

  6. Applied sqrt-div0.5

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

  7. Applied associate-*r/0.5

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

  8. Applied frac-times0.5

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

  9. Applied associate-/r/0.5

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

  10. Simplified0.4

    \[\leadsto \color{blue}{\frac{\frac{\frac{1 - v \cdot \left(v \cdot 5\right)}{\sqrt{\left(1 - \left(27 \cdot \left(\left(v \cdot v\right) \cdot v\right)\right) \cdot \left(\left(v \cdot v\right) \cdot v\right)\right) \cdot 2}}}{\pi \cdot t}}{1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)}} \cdot \left(\sqrt{1 \cdot 1 + \left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right) + 1 \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)} \cdot \left(1 + v \cdot v\right)\right)\]
  11. Using strategy rm

  12. Applied associate-/r*0.1

    \[\leadsto \frac{\color{blue}{\frac{\frac{\frac{1 - v \cdot \left(v \cdot 5\right)}{\sqrt{\left(1 - \left(27 \cdot \left(\left(v \cdot v\right) \cdot v\right)\right) \cdot \left(\left(v \cdot v\right) \cdot v\right)\right) \cdot 2}}}{\pi}}{t}}}{1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)} \cdot \left(\sqrt{1 \cdot 1 + \left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right) + 1 \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)} \cdot \left(1 + v \cdot v\right)\right)\]

  13. Simplified0.1

    \[\leadsto \frac{\frac{\color{blue}{\frac{\frac{1 - \left(5 \cdot v\right) \cdot v}{\pi}}{\sqrt{2 \cdot \left(1 - \left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)\right) \cdot 27\right)}}}}{t}}{1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)} \cdot \left(\sqrt{1 \cdot 1 + \left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right) + 1 \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)} \cdot \left(1 + v \cdot v\right)\right)\]

  14. Final simplification0.1

    \[\leadsto \frac{\frac{\frac{\frac{1 - v \cdot \left(v \cdot 5\right)}{\pi}}{\sqrt{\left(1 - \left(\left(v \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right) \cdot 27\right) \cdot 2}}}{t}}{1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)} \cdot \left(\left(1 + v \cdot v\right) \cdot \sqrt{\left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right) + 3 \cdot \left(v \cdot v\right)\right) + 1}\right)\]

Reproduce

herbie shell --seed 2019163 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))