Average Error: 0.1 → 0.1
Time: 6.6s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right) \]
↓
\[\frac{\sin re \cdot \left(2 \cdot \cosh im\right)}{2} \]
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
↓
(FPCore (re im) :precision binary64 (/ (* (sin re) (* 2.0 (cosh im))) 2.0))
double code(double re, double im) {
	return (0.5 * sin(re)) * (exp((0.0 - im)) + exp(im));
}
↓
double code(double re, double im) {
	return (sin(re) * (2.0 * cosh(im))) / 2.0;
}

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * sin(re)) * (exp((0.0d0 - im)) + exp(im))
end function
↓
real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (sin(re) * (2.0d0 * cosh(im))) / 2.0d0
end function

public static double code(double re, double im) {
	return (0.5 * Math.sin(re)) * (Math.exp((0.0 - im)) + Math.exp(im));
}
↓
public static double code(double re, double im) {
	return (Math.sin(re) * (2.0 * Math.cosh(im))) / 2.0;
}

def code(re, im):
	return (0.5 * math.sin(re)) * (math.exp((0.0 - im)) + math.exp(im))
↓
def code(re, im):
	return (math.sin(re) * (2.0 * math.cosh(im))) / 2.0

function code(re, im)
	return Float64(Float64(0.5 * sin(re)) * Float64(exp(Float64(0.0 - im)) + exp(im)))
end
↓
function code(re, im)
	return Float64(Float64(sin(re) * Float64(2.0 * cosh(im))) / 2.0)
end

function tmp = code(re, im)
	tmp = (0.5 * sin(re)) * (exp((0.0 - im)) + exp(im));
end
↓
function tmp = code(re, im)
	tmp = (sin(re) * (2.0 * cosh(im))) / 2.0;
end

code[re_, im_] := N[(N[(0.5 * N[Sin[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[N[(0.0 - im), $MachinePrecision]], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[re_, im_] := N[(N[(N[Sin[re], $MachinePrecision] * N[(2.0 * N[Cosh[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]

\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\frac{\sin re \cdot \left(2 \cdot \cosh im\right)}{2}

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 0.1

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right) \]

  2. Applied egg-rr0.2

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

  3. Applied egg-rr20.1

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

  4. Applied egg-rr0.1

    \[\leadsto \color{blue}{\frac{\sin re \cdot \left(2 \cdot \cosh im\right)}{2}} \]

  5. Final simplification0.1

    \[\leadsto \frac{\sin re \cdot \left(2 \cdot \cosh im\right)}{2} \]

Reproduce

herbie shell --seed 2022153 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))