Average Error: 0.1 → 0.1
Time: 8.8s
Precision: binary64
\[0 \leq e \land e \leq 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + \sqrt[3]{{\left(e \cdot \cos v\right)}^{3}}}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + \sqrt[3]{{\left(e \cdot \cos v\right)}^{3}}}
(FPCore (e v) :precision binary64 (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))
↓
(FPCore (e v)
 :precision binary64
 (/ (* e (sin v)) (+ 1.0 (cbrt (pow (* e (cos v)) 3.0)))))
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)) / (1.0 + cbrt(pow((e * cos(v)), 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-cube_binary64_11370.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2021050 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))