Average Error: 0.1 → 0.1
Time: 5.4s
Precision: binary64
Cost: 13376
\[0 \leq e \land e \leq 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
\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

Alternatives

Alternative 1
Error0.1
Cost13376
\[\sin v \cdot \frac{e}{1 + e \cdot \cos v}\]
Alternative 2
Error0.3
Cost13376
\[\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}\]
Alternative 3
Error0.7
Cost6848
\[\frac{e \cdot \sin v}{e + 1}\]
Alternative 4
Error0.8
Cost6848
\[\frac{e}{\frac{e + 1}{\sin v}}\]
Alternative 5
Error1.4
Cost6592
\[e \cdot \sin v\]
Alternative 6
Error30.2
Cost1088
\[\frac{e}{\frac{1}{v} + \left(v \cdot \left(0.16666666666666666 + e \cdot -0.3333333333333333\right) + \frac{e}{v}\right)}\]
Alternative 7
Error30.9
Cost448
\[\frac{e \cdot v}{e + 1}\]
Alternative 8
Error45.8
Cost64
\[0\]
Alternative 9
Error61.7
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))