Average Error: 0.0 → 0.3
Time: 2.7s
Precision: binary64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \log \left(e^{e^{-im}} \cdot e^{e^{im}}\right) \]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \log \left(e^{e^{-im}} \cdot e^{e^{im}}\right)

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))
↓
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (log (* (exp (exp (- im))) (exp (exp im))))))
double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}
↓
double code(double re, double im) {
	return (0.5 * cos(re)) * log(exp(exp(-im)) * exp(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. Applied add-log-exp_binary640.1

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

  3. Applied add-log-exp_binary640.3

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

  4. Applied sum-log_binary640.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2022067 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))