Average Error: 0.1 → 0.1
Time: 4.9s
Precision: binary64
\[0 \leq e \land e \leq 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[e \cdot \frac{\sin v}{1 + \log \left({\left(e^{e}\right)}^{\left(\cos v\right)}\right)}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
e \cdot \frac{\sin v}{1 + \log \left({\left(e^{e}\right)}^{\left(\cos v\right)}\right)}
double code(double e, double v) {
	return (((double) (e * ((double) sin(v)))) / ((double) (1.0 + ((double) (e * ((double) cos(v)))))));
}
↓
double code(double e, double v) {
	return ((double) (e * (((double) sin(v)) / ((double) (1.0 + ((double) log(((double) pow(((double) exp(e)), ((double) 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. Simplified0.1

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

  4. Applied add-log-exp0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020196 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))