Average Error: 0.5 → 0.1
Time: 43.0s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1 - \left(5 \cdot v\right) \cdot v}{1 - v \cdot v}}{\pi}}{\sqrt{8 + -216 \cdot \left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)\right)}}}{t} \cdot \sqrt{\left(4 - 2 \cdot \left(\left(v \cdot v\right) \cdot -6\right)\right) + \left(\left(v \cdot v\right) \cdot -6\right) \cdot \left(\left(v \cdot v\right) \cdot -6\right)}\]
\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 - \left(5 \cdot v\right) \cdot v}{1 - v \cdot v}}{\pi}}{\sqrt{8 + -216 \cdot \left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)\right)}}}{t} \cdot \sqrt{\left(4 - 2 \cdot \left(\left(v \cdot v\right) \cdot -6\right)\right) + \left(\left(v \cdot v\right) \cdot -6\right) \cdot \left(\left(v \cdot v\right) \cdot -6\right)}
double f(double v, double t) {
        double r4344483 = 1.0;
        double r4344484 = 5.0;
        double r4344485 = v;
        double r4344486 = r4344485 * r4344485;
        double r4344487 = r4344484 * r4344486;
        double r4344488 = r4344483 - r4344487;
        double r4344489 = atan2(1.0, 0.0);
        double r4344490 = t;
        double r4344491 = r4344489 * r4344490;
        double r4344492 = 2.0;
        double r4344493 = 3.0;
        double r4344494 = r4344493 * r4344486;
        double r4344495 = r4344483 - r4344494;
        double r4344496 = r4344492 * r4344495;
        double r4344497 = sqrt(r4344496);
        double r4344498 = r4344491 * r4344497;
        double r4344499 = r4344483 - r4344486;
        double r4344500 = r4344498 * r4344499;
        double r4344501 = r4344488 / r4344500;
        return r4344501;
}
↓
double f(double v, double t) {
        double r4344502 = 1.0;
        double r4344503 = 5.0;
        double r4344504 = v;
        double r4344505 = r4344503 * r4344504;
        double r4344506 = r4344505 * r4344504;
        double r4344507 = r4344502 - r4344506;
        double r4344508 = r4344504 * r4344504;
        double r4344509 = r4344502 - r4344508;
        double r4344510 = r4344507 / r4344509;
        double r4344511 = atan2(1.0, 0.0);
        double r4344512 = r4344510 / r4344511;
        double r4344513 = 8.0;
        double r4344514 = -216.0;
        double r4344515 = r4344508 * r4344508;
        double r4344516 = r4344515 * r4344508;
        double r4344517 = r4344514 * r4344516;
        double r4344518 = r4344513 + r4344517;
        double r4344519 = sqrt(r4344518);
        double r4344520 = r4344512 / r4344519;
        double r4344521 = t;
        double r4344522 = r4344520 / r4344521;
        double r4344523 = 4.0;
        double r4344524 = 2.0;
        double r4344525 = -6.0;
        double r4344526 = r4344508 * r4344525;
        double r4344527 = r4344524 * r4344526;
        double r4344528 = r4344523 - r4344527;
        double r4344529 = r4344526 * r4344526;
        double r4344530 = r4344528 + r4344529;
        double r4344531 = sqrt(r4344530);
        double r4344532 = r4344522 * r4344531;
        return r4344532;
}

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

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

  4. Applied flip3-+0.3

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

  5. Applied sqrt-div0.3

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

  6. Applied associate-*r/0.3

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

  7. Applied associate-/r/0.3

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

  8. Simplified0.1

    \[\leadsto \color{blue}{\frac{\frac{\frac{\frac{1 - v \cdot \left(5 \cdot v\right)}{1 - v \cdot v}}{\pi}}{\sqrt{8 + -216 \cdot \left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)\right)}}}{t}} \cdot \sqrt{\left(-6 \cdot \left(v \cdot v\right)\right) \cdot \left(-6 \cdot \left(v \cdot v\right)\right) + \left(2 \cdot 2 - \left(-6 \cdot \left(v \cdot v\right)\right) \cdot 2\right)}\]

  9. Final simplification0.1

    \[\leadsto \frac{\frac{\frac{\frac{1 - \left(5 \cdot v\right) \cdot v}{1 - v \cdot v}}{\pi}}{\sqrt{8 + -216 \cdot \left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)\right)}}}{t} \cdot \sqrt{\left(4 - 2 \cdot \left(\left(v \cdot v\right) \cdot -6\right)\right) + \left(\left(v \cdot v\right) \cdot -6\right) \cdot \left(\left(v \cdot v\right) \cdot -6\right)}\]

Reproduce

herbie shell --seed 2019152 
(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)))))