Average Error: 0.5 → 0.1
Time: 32.4s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1 - v \cdot \left(v \cdot 5\right)}{\pi}}{\sqrt{2 \cdot \left(\left(1 \cdot 1\right) \cdot 1 - \left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}}}{t}}{\left(1 - v \cdot v\right) \cdot \left(v \cdot v + 1\right)} \cdot \left(\sqrt{\left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot 1 + \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right) + 1 \cdot 1} \cdot \left(v \cdot v + 1\right)\right)\]
\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{2 \cdot \left(\left(1 \cdot 1\right) \cdot 1 - \left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}}}{t}}{\left(1 - v \cdot v\right) \cdot \left(v \cdot v + 1\right)} \cdot \left(\sqrt{\left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot 1 + \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right) + 1 \cdot 1} \cdot \left(v \cdot v + 1\right)\right)
double f(double v, double t) {
        double r9730077 = 1.0;
        double r9730078 = 5.0;
        double r9730079 = v;
        double r9730080 = r9730079 * r9730079;
        double r9730081 = r9730078 * r9730080;
        double r9730082 = r9730077 - r9730081;
        double r9730083 = atan2(1.0, 0.0);
        double r9730084 = t;
        double r9730085 = r9730083 * r9730084;
        double r9730086 = 2.0;
        double r9730087 = 3.0;
        double r9730088 = r9730087 * r9730080;
        double r9730089 = r9730077 - r9730088;
        double r9730090 = r9730086 * r9730089;
        double r9730091 = sqrt(r9730090);
        double r9730092 = r9730085 * r9730091;
        double r9730093 = r9730077 - r9730080;
        double r9730094 = r9730092 * r9730093;
        double r9730095 = r9730082 / r9730094;
        return r9730095;
}
↓
double f(double v, double t) {
        double r9730096 = 1.0;
        double r9730097 = v;
        double r9730098 = 5.0;
        double r9730099 = r9730097 * r9730098;
        double r9730100 = r9730097 * r9730099;
        double r9730101 = r9730096 - r9730100;
        double r9730102 = atan2(1.0, 0.0);
        double r9730103 = r9730101 / r9730102;
        double r9730104 = 2.0;
        double r9730105 = r9730096 * r9730096;
        double r9730106 = r9730105 * r9730096;
        double r9730107 = 3.0;
        double r9730108 = r9730097 * r9730097;
        double r9730109 = r9730107 * r9730108;
        double r9730110 = r9730109 * r9730109;
        double r9730111 = r9730110 * r9730109;
        double r9730112 = r9730106 - r9730111;
        double r9730113 = r9730104 * r9730112;
        double r9730114 = sqrt(r9730113);
        double r9730115 = r9730103 / r9730114;
        double r9730116 = t;
        double r9730117 = r9730115 / r9730116;
        double r9730118 = r9730096 - r9730108;
        double r9730119 = r9730108 + r9730096;
        double r9730120 = r9730118 * r9730119;
        double r9730121 = r9730117 / r9730120;
        double r9730122 = r9730109 * r9730096;
        double r9730123 = r9730122 + r9730110;
        double r9730124 = r9730123 + r9730105;
        double r9730125 = sqrt(r9730124);
        double r9730126 = r9730125 * r9730119;
        double r9730127 = r9730121 * r9730126;
        return r9730127;
}

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. Simplified0.3

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

  12. Applied associate-/r*0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 
(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)))))