Average Error: 0.5 → 0.1
Time: 50.5s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{t}\]
\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 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{t}
double f(double v, double t) {
        double r7179518 = 1.0;
        double r7179519 = 5.0;
        double r7179520 = v;
        double r7179521 = r7179520 * r7179520;
        double r7179522 = r7179519 * r7179521;
        double r7179523 = r7179518 - r7179522;
        double r7179524 = atan2(1.0, 0.0);
        double r7179525 = t;
        double r7179526 = r7179524 * r7179525;
        double r7179527 = 2.0;
        double r7179528 = 3.0;
        double r7179529 = r7179528 * r7179521;
        double r7179530 = r7179518 - r7179529;
        double r7179531 = r7179527 * r7179530;
        double r7179532 = sqrt(r7179531);
        double r7179533 = r7179526 * r7179532;
        double r7179534 = r7179518 - r7179521;
        double r7179535 = r7179533 * r7179534;
        double r7179536 = r7179523 / r7179535;
        return r7179536;
}
↓
double f(double v, double t) {
        double r7179537 = 1.0;
        double r7179538 = v;
        double r7179539 = r7179538 * r7179538;
        double r7179540 = 5.0;
        double r7179541 = r7179539 * r7179540;
        double r7179542 = r7179537 - r7179541;
        double r7179543 = atan2(1.0, 0.0);
        double r7179544 = r7179542 / r7179543;
        double r7179545 = r7179537 - r7179539;
        double r7179546 = r7179544 / r7179545;
        double r7179547 = 2.0;
        double r7179548 = 6.0;
        double r7179549 = r7179548 * r7179539;
        double r7179550 = r7179547 - r7179549;
        double r7179551 = sqrt(r7179550);
        double r7179552 = r7179546 / r7179551;
        double r7179553 = t;
        double r7179554 = r7179552 / r7179553;
        return r7179554;
}

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. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{t \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.3

    \[\leadsto \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{t \cdot \left(1 - v \cdot v\right)}}{\sqrt{\color{blue}{1 \cdot \left(2 - 6 \cdot \left(v \cdot v\right)\right)}}}\]

  5. Applied sqrt-prod0.3

    \[\leadsto \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{t \cdot \left(1 - v \cdot v\right)}}{\color{blue}{\sqrt{1} \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}\]

  6. Applied *-un-lft-identity0.3

    \[\leadsto \frac{\frac{\color{blue}{1 \cdot \frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}}{t \cdot \left(1 - v \cdot v\right)}}{\sqrt{1} \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  7. Applied times-frac0.4

    \[\leadsto \frac{\color{blue}{\frac{1}{t} \cdot \frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}}{\sqrt{1} \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  8. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{t}}{\sqrt{1}} \cdot \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}\]

  9. Simplified0.3

    \[\leadsto \color{blue}{\frac{1}{t}} \cdot \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
  10. Using strategy rm

  11. Applied associate-*l/0.1

    \[\leadsto \color{blue}{\frac{1 \cdot \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{t}}\]

  12. Final simplification0.1

    \[\leadsto \frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{t}\]

Reproduce

herbie shell --seed 2019133 
(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)))))