Average Error: 0.1 → 0.1
Time: 4.6s
Precision: binary64
\[0 \leq e \land e \leq 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[e \cdot \frac{\sin v}{\log \left(e^{e \cdot \cos v}\right) + 1}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
e \cdot \frac{\sin v}{\log \left(e^{e \cdot \cos v}\right) + 1}
(FPCore (e v) :precision binary64 (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))
↓
(FPCore (e v)
 :precision binary64
 (* e (/ (sin v) (+ (log (exp (* e (cos v)))) 1.0))))
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) / (log(exp(e * cos(v))) + 1.0));
}

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 *-un-lft-identity_binary640.1

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

  4. Applied times-frac_binary640.1

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  8. Applied add-log-exp_binary640.1

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

  9. Final simplification0.1

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

Alternatives

Reproduce

herbie shell --seed 2021110 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))