Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot e^{im} + \frac{0.5 \cdot \cos re}{e^{im}}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot e^{im} + \frac{0.5 \cdot \cos re}{e^{im}}
double code(double re, double im) {
	return ((double) (((double) (0.5 * ((double) cos(re)))) * ((double) (((double) exp(((double) -(im)))) + ((double) exp(im))))));
}
↓
double code(double re, double im) {
	return ((double) (((double) (((double) (0.5 * ((double) cos(re)))) * ((double) exp(im)))) + ((double) (((double) (0.5 * ((double) cos(re)))) / ((double) exp(im))))));
}

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 +-commutative0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))