Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\sqrt[3]{{\left(\cos v \cdot e + 1\right)}^{3}}}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{\sqrt[3]{{\left(\cos v \cdot e + 1\right)}^{3}}}
double code(double e, double v) {
	return ((double) (((double) (e * ((double) sin(v)))) / ((double) (1.0 + ((double) (e * ((double) cos(v))))))));
}
↓
double code(double e, double v) {
	return ((double) (((double) (e * ((double) sin(v)))) / ((double) cbrt(((double) pow(((double) (((double) (((double) cos(v)) * e)) + 1.0)), 3.0))))));
}

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 add-cbrt-cube0.1

    \[\leadsto \frac{e \cdot \sin v}{\color{blue}{\sqrt[3]{\left(\left(1 + e \cdot \cos v\right) \cdot \left(1 + e \cdot \cos v\right)\right) \cdot \left(1 + e \cdot \cos v\right)}}}\]

  4. Simplified0.1

    \[\leadsto \frac{e \cdot \sin v}{\sqrt[3]{\color{blue}{{\left(\cos v \cdot e + 1\right)}^{3}}}}\]

  5. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{\sqrt[3]{{\left(\cos v \cdot e + 1\right)}^{3}}}\]

Reproduce

herbie shell --seed 2020131 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))