Average Error: 0.1 → 0.1
Time: 7.3s
Precision: binary64
\[0 \leq e \land e \leq 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
(FPCore (e v) :precision binary64 (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))
↓
(FPCore (e v) :precision binary64 (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))
double code(double e, double v) {
	return (e * sin(v)) / (1.0 + (e * cos(v)));
}
↓
double code(double e, double v) {
	return (e * sin(v)) / (1.0 + (e * cos(v)));
}

Error

Bits error versus e

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
  2. Using strategy rm

  3. Applied associate-/l*_binary640.3

    \[\leadsto \color{blue}{\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}}\]

  4. Simplified0.3

    \[\leadsto \frac{e}{\color{blue}{\frac{e \cdot \cos v + 1}{\sin v}}}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity_binary640.3

    \[\leadsto \frac{e}{\frac{e \cdot \cos v + 1}{\color{blue}{1 \cdot \sin v}}}\]

  7. Applied *-un-lft-identity_binary640.3

    \[\leadsto \frac{e}{\frac{\color{blue}{1 \cdot \left(e \cdot \cos v + 1\right)}}{1 \cdot \sin v}}\]

  8. Applied times-frac_binary640.3

    \[\leadsto \frac{e}{\color{blue}{\frac{1}{1} \cdot \frac{e \cdot \cos v + 1}{\sin v}}}\]

  9. Applied *-un-lft-identity_binary640.3

    \[\leadsto \frac{\color{blue}{1 \cdot e}}{\frac{1}{1} \cdot \frac{e \cdot \cos v + 1}{\sin v}}\]

  10. Applied times-frac_binary640.3

    \[\leadsto \color{blue}{\frac{1}{\frac{1}{1}} \cdot \frac{e}{\frac{e \cdot \cos v + 1}{\sin v}}}\]

  11. Simplified0.3

    \[\leadsto \color{blue}{1} \cdot \frac{e}{\frac{e \cdot \cos v + 1}{\sin v}}\]

  12. Simplified0.1

    \[\leadsto 1 \cdot \color{blue}{\frac{e \cdot \sin v}{1 + e \cdot \cos v}}\]

  13. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + e \cdot \cos v}\]

Reproduce

herbie shell --seed 2021174 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))