Average Error: 0.0 → 0.1
Time: 4.3s
Precision: binary64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5}{\frac{e^{im}}{\cos re}} + e^{im} \cdot \left(0.5 \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5}{\frac{e^{im}}{\cos re}} + e^{im} \cdot \left(0.5 \cdot \cos re\right)
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))
↓
(FPCore (re im)
 :precision binary64
 (+ (/ 0.5 (/ (exp im) (cos re))) (* (exp im) (* 0.5 (cos re)))))
double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}
↓
double code(double re, double im) {
	return (0.5 / (exp(im) / cos(re))) + (exp(im) * (0.5 * cos(re)));
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in_binary640.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \cos re\right) \cdot e^{-im} + \left(0.5 \cdot \cos re\right) \cdot e^{im}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.5 \cdot \cos re}{e^{im}}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]

  5. Simplified0.0

    \[\leadsto \frac{0.5 \cdot \cos re}{e^{im}} + \color{blue}{e^{im} \cdot \left(0.5 \cdot \cos re\right)}\]
  6. Using strategy rm

  7. Applied associate-/l*_binary640.1

    \[\leadsto \color{blue}{\frac{0.5}{\frac{e^{im}}{\cos re}}} + e^{im} \cdot \left(0.5 \cdot \cos re\right)\]

  8. Final simplification0.1

    \[\leadsto \frac{0.5}{\frac{e^{im}}{\cos re}} + e^{im} \cdot \left(0.5 \cdot \cos re\right)\]

Reproduce

herbie shell --seed 2020220 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))