Average Error: 0.0 → 0.0
Time: 4.3s
Precision: binary64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot e^{\log \left(2 \cdot \cosh im\right)}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot e^{\log \left(2 \cdot \cosh im\right)}
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))
↓
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (exp (log (* 2.0 (cosh 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)) * exp(log(2.0 * cosh(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 add-exp-log_binary64_7980.0

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

  4. Simplified0.0

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

  6. Applied cosh-undef_binary64_9540.0

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot e^{\log \color{blue}{\left(2 \cdot \cosh im\right)}}\]

  7. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot e^{\log \left(2 \cdot \cosh im\right)}\]

Reproduce

herbie shell --seed 2021060 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))