math.exp on complex, imaginary part

Percentage Accurate: 100.0% → 100.0%
Time: 2.4s
Alternatives: 1
Speedup: 1.0×

Specification

?
\[\begin{array}{l} \\ e^{re} \cdot \sin im \end{array} \]
(FPCore (re im) :precision binary64 (* (exp re) (sin im)))
double code(double re, double im) {
	return exp(re) * sin(im);
}

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = exp(re) * sin(im)
end function

public static double code(double re, double im) {
	return Math.exp(re) * Math.sin(im);
}

def code(re, im):
	return math.exp(re) * math.sin(im)

function code(re, im)
	return Float64(exp(re) * sin(im))
end

function tmp = code(re, im)
	tmp = exp(re) * sin(im);
end

code[re_, im_] := N[(N[Exp[re], $MachinePrecision] * N[Sin[im], $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
e^{re} \cdot \sin im
\end{array}

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 1 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 100.0% accurate, 1.0× speedup?

\[\begin{array}{l} \\ e^{re} \cdot \sin im \end{array} \]
(FPCore (re im) :precision binary64 (* (exp re) (sin im)))
double code(double re, double im) {
	return exp(re) * sin(im);
}

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = exp(re) * sin(im)
end function

public static double code(double re, double im) {
	return Math.exp(re) * Math.sin(im);
}

def code(re, im):
	return math.exp(re) * math.sin(im)

function code(re, im)
	return Float64(exp(re) * sin(im))
end

function tmp = code(re, im)
	tmp = exp(re) * sin(im);
end

code[re_, im_] := N[(N[Exp[re], $MachinePrecision] * N[Sin[im], $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
e^{re} \cdot \sin im
\end{array}

Alternative 1: 100.0% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \sin im \cdot e^{re} \end{array} \]
(FPCore (re im) :precision binary64 (* (sin im) (exp re)))
double code(double re, double im) {
	return sin(im) * exp(re);
}

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = sin(im) * exp(re)
end function

public static double code(double re, double im) {
	return Math.sin(im) * Math.exp(re);
}

def code(re, im):
	return math.sin(im) * math.exp(re)

function code(re, im)
	return Float64(sin(im) * exp(re))
end

function tmp = code(re, im)
	tmp = sin(im) * exp(re);
end

code[re_, im_] := N[(N[Sin[im], $MachinePrecision] * N[Exp[re], $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\sin im \cdot e^{re}
\end{array}
Derivation

  1. Initial program 100.0%

    \[e^{re} \cdot \sin im \]
  2. Add Preprocessing

  3. Final simplification100.0%

    \[\leadsto \sin im \cdot e^{re} \]
  4. Add Preprocessing

Reproduce

?
herbie shell --seed 2024341 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))