Average Error: 0.0 → 0.0
Time: 4.4s
Precision: binary64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cosh im \cdot \cos re\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cosh im \cdot \cos re
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))
↓
(FPCore (re im) :precision binary64 (* (cosh im) (cos re)))
double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}
↓
double code(double re, double im) {
	return cosh(im) * 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 add-cbrt-cube_binary640.2

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \color{blue}{\sqrt[3]{\left(\left(e^{-im} + e^{im}\right) \cdot \left(e^{-im} + e^{im}\right)\right) \cdot \left(e^{-im} + e^{im}\right)}}\]

  4. Simplified0.2

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \sqrt[3]{\color{blue}{{\left(e^{im} + e^{-im}\right)}^{3}}}\]
  5. Using strategy rm

  6. Applied cosh-undef_binary640.2

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \sqrt[3]{{\color{blue}{\left(2 \cdot \cosh im\right)}}^{3}}\]

  7. Applied unpow-prod-down_binary640.2

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \sqrt[3]{\color{blue}{{2}^{3} \cdot {\cosh im}^{3}}}\]

  8. Simplified0.2

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \sqrt[3]{\color{blue}{8} \cdot {\cosh im}^{3}}\]

  9. Taylor expanded around inf 0.0

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

  10. Simplified0.0

    \[\leadsto \color{blue}{\cosh im \cdot \cos re}\]

  11. Final simplification0.0

    \[\leadsto \cosh im \cdot \cos re\]

Reproduce

herbie shell --seed 2021173 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))