Average Error: 0.0 → 0.0
Time: 4.8s
Precision: binary64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[0.5 \cdot \frac{\cos re}{e^{im}} + 0.5 \cdot \left(\cos re \cdot e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
0.5 \cdot \frac{\cos re}{e^{im}} + 0.5 \cdot \left(\cos re \cdot e^{im}\right)
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) (0.5 * (((double) cos(re)) / ((double) exp(im))))) + ((double) (0.5 * ((double) (((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 distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020196 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))