Average Error: 0.5 → 0.4
Time: 4.4s
Precision: binary64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{t \cdot \left(\pi \cdot \left(\sqrt{2 \cdot \left(1 - v \cdot \left(v \cdot 3\right)\right)} \cdot \left(1 - v \cdot v\right)\right)\right)}\]
\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{1 - 5 \cdot \left(v \cdot v\right)}{t \cdot \left(\pi \cdot \left(\sqrt{2 \cdot \left(1 - v \cdot \left(v \cdot 3\right)\right)} \cdot \left(1 - v \cdot v\right)\right)\right)}
double code(double v, double t) {
	return (((double) (1.0 - ((double) (5.0 * ((double) (v * v)))))) / ((double) (((double) (((double) (((double) M_PI) * t)) * ((double) sqrt(((double) (2.0 * ((double) (1.0 - ((double) (3.0 * ((double) (v * v)))))))))))) * ((double) (1.0 - ((double) (v * v)))))));
}
↓
double code(double v, double t) {
	return (((double) (1.0 - ((double) (5.0 * ((double) (v * v)))))) / ((double) (t * ((double) (((double) M_PI) * ((double) (((double) sqrt(((double) (2.0 * ((double) (1.0 - ((double) (v * ((double) (v * 3.0)))))))))) * ((double) (1.0 - ((double) (v * v)))))))))));
}

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. Simplified0.5

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

  4. Applied pow10.5

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

  5. Applied pow10.5

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

  6. Applied pow-prod-down0.5

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

  7. Applied pow10.5

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

  8. Applied pow-prod-down0.5

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

  9. Applied pow10.5

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

  10. Applied pow-prod-down0.5

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

  11. Simplified0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2020196 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  :precision binary64
  (/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))))