Average Error: 0.0 → 0.0
Time: 6.0s
Precision: binary64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
↓
\[\begin{array}{l} t_0 := 0.5 \cdot \cos re\\ t_0 \cdot e^{-im} + t_0 \cdot e^{im} \end{array} \]
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))
↓
(FPCore (re im)
 :precision binary64
 (let* ((t_0 (* 0.5 (cos re)))) (+ (* t_0 (exp (- im))) (* t_0 (exp im)))))
double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}
↓
double code(double re, double im) {
	double t_0 = 0.5 * cos(re);
	return (t_0 * exp(-im)) + (t_0 * exp(im));
}

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * cos(re)) * (exp(-im) + exp(im))
end function
↓
real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: t_0
    t_0 = 0.5d0 * cos(re)
    code = (t_0 * exp(-im)) + (t_0 * exp(im))
end function

public static double code(double re, double im) {
	return (0.5 * Math.cos(re)) * (Math.exp(-im) + Math.exp(im));
}
↓
public static double code(double re, double im) {
	double t_0 = 0.5 * Math.cos(re);
	return (t_0 * Math.exp(-im)) + (t_0 * Math.exp(im));
}

def code(re, im):
	return (0.5 * math.cos(re)) * (math.exp(-im) + math.exp(im))
↓
def code(re, im):
	t_0 = 0.5 * math.cos(re)
	return (t_0 * math.exp(-im)) + (t_0 * math.exp(im))

function code(re, im)
	return Float64(Float64(0.5 * cos(re)) * Float64(exp(Float64(-im)) + exp(im)))
end
↓
function code(re, im)
	t_0 = Float64(0.5 * cos(re))
	return Float64(Float64(t_0 * exp(Float64(-im))) + Float64(t_0 * exp(im)))
end

function tmp = code(re, im)
	tmp = (0.5 * cos(re)) * (exp(-im) + exp(im));
end
↓
function tmp = code(re, im)
	t_0 = 0.5 * cos(re);
	tmp = (t_0 * exp(-im)) + (t_0 * exp(im));
end

code[re_, im_] := N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[re_, im_] := Block[{t$95$0 = N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision]}, N[(N[(t$95$0 * N[Exp[(-im)], $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\begin{array}{l}
t_0 := 0.5 \cdot \cos re\\
t_0 \cdot e^{-im} + t_0 \cdot e^{im}
\end{array}

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 egg-rr0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022153 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))