Average Error: 0.4 → 0.3
Time: 1.9m
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{\left(1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot t}}{\frac{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}{1 + v \cdot v}}\]
\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{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{\left(1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot t}}{\frac{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}{1 + v \cdot v}}
double f(double v, double t) {
        double r9169380 = 1.0;
        double r9169381 = 5.0;
        double r9169382 = v;
        double r9169383 = r9169382 * r9169382;
        double r9169384 = r9169381 * r9169383;
        double r9169385 = r9169380 - r9169384;
        double r9169386 = atan2(1.0, 0.0);
        double r9169387 = t;
        double r9169388 = r9169386 * r9169387;
        double r9169389 = 2.0;
        double r9169390 = 3.0;
        double r9169391 = r9169390 * r9169383;
        double r9169392 = r9169380 - r9169391;
        double r9169393 = r9169389 * r9169392;
        double r9169394 = sqrt(r9169393);
        double r9169395 = r9169388 * r9169394;
        double r9169396 = r9169380 - r9169383;
        double r9169397 = r9169395 * r9169396;
        double r9169398 = r9169385 / r9169397;
        return r9169398;
}
↓
double f(double v, double t) {
        double r9169399 = 1.0;
        double r9169400 = v;
        double r9169401 = r9169400 * r9169400;
        double r9169402 = 5.0;
        double r9169403 = r9169401 * r9169402;
        double r9169404 = r9169399 - r9169403;
        double r9169405 = atan2(1.0, 0.0);
        double r9169406 = r9169404 / r9169405;
        double r9169407 = r9169401 * r9169401;
        double r9169408 = r9169399 - r9169407;
        double r9169409 = t;
        double r9169410 = r9169408 * r9169409;
        double r9169411 = r9169406 / r9169410;
        double r9169412 = 2.0;
        double r9169413 = 6.0;
        double r9169414 = r9169413 * r9169401;
        double r9169415 = r9169412 - r9169414;
        double r9169416 = sqrt(r9169415);
        double r9169417 = r9169399 + r9169401;
        double r9169418 = r9169416 / r9169417;
        double r9169419 = r9169411 / r9169418;
        return r9169419;
}

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 0.4

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

  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 flip--0.3

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

  5. Applied associate-*r/0.3

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

  6. Applied associate-/r/0.3

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

  7. Applied associate-/l*0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019132 
(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)))))