math.sin on complex, real part

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 2

Speedup: 1.0×

• 51.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * sin(re)) * (exp((0.0 - im)) + exp(im));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * sin(re)) * (exp((0.0 - im)) + exp(im));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(\sin re \cdot \left(e^{-im} + e^{im}\right)\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* 0.5 (* (sin re) (+ (exp (- im)) (exp im)))))

C

double code(double re, double im) {
	return 0.5 * (sin(re) * (exp(-im) + exp(im)));
}

Fortran

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

Java

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

Python

def code(re, im):
	return 0.5 * (math.sin(re) * (math.exp(-im) + math.exp(im)))

Julia

function code(re, im)
	return Float64(0.5 * Float64(sin(re) * Float64(exp(Float64(-im)) + exp(im))))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right) \]
2. Step-by-step derivation

   1. remove-double-neg 100.0%

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

   2. sin-neg 100.0%

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

   3. distribute-rgt-neg-in 100.0%

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

   4. /-rgt-identity 100.0%

      \[\leadsto \left(-\color{blue}{\frac{0.5 \cdot \sin \left(-re\right)}{1}}\right) \cdot \left(e^{0 - im} + e^{im}\right) \]

   5. exp-0 100.0%

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

   6. distribute-neg-frac2 100.0%

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

   7. exp-0 100.0%

      \[\leadsto \frac{0.5 \cdot \sin \left(-re\right)}{-\color{blue}{1}} \cdot \left(e^{0 - im} + e^{im}\right) \]

   8. metadata-eval 100.0%

      \[\leadsto \frac{0.5 \cdot \sin \left(-re\right)}{\color{blue}{-1}} \cdot \left(e^{0 - im} + e^{im}\right) \]

   9. associate-*l/ 100.0%

      \[\leadsto \color{blue}{\frac{\left(0.5 \cdot \sin \left(-re\right)\right) \cdot \left(e^{0 - im} + e^{im}\right)}{-1}} \]

   10. associate-*l* 100.0%

       \[\leadsto \frac{\color{blue}{0.5 \cdot \left(\sin \left(-re\right) \cdot \left(e^{0 - im} + e^{im}\right)\right)}}{-1} \]

   11. associate-*r/ 100.0%

       \[\leadsto \color{blue}{0.5 \cdot \frac{\sin \left(-re\right) \cdot \left(e^{0 - im} + e^{im}\right)}{-1}} \]

   12. associate-*l/ 100.0%

       \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{\sin \left(-re\right)}{-1} \cdot \left(e^{0 - im} + e^{im}\right)\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{0.5 \cdot \left(\sin re \cdot \left(e^{-im} + e^{im}\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 63.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(re \cdot \left(e^{-im} + e^{im}\right)\right) \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (* 0.5 (* re (+ (exp (- im)) (exp im)))))

C

double code(double re, double im) {
	return 0.5 * (re * (exp(-im) + exp(im)));
}

Fortran

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

Java

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

Python

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

Julia

function code(re, im)
	return Float64(0.5 * Float64(re * Float64(exp(Float64(-im)) + exp(im))))
end

MATLAB

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

Wolfram

code[re_, im_] := N[(0.5 * N[(re * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right) \]
2. Step-by-step derivation

   1. remove-double-neg 100.0%

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

   2. sin-neg 100.0%

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

   3. distribute-rgt-neg-in 100.0%

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

   4. /-rgt-identity 100.0%

      \[\leadsto \left(-\color{blue}{\frac{0.5 \cdot \sin \left(-re\right)}{1}}\right) \cdot \left(e^{0 - im} + e^{im}\right) \]

   5. exp-0 100.0%

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

   6. distribute-neg-frac2 100.0%

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

   7. exp-0 100.0%

      \[\leadsto \frac{0.5 \cdot \sin \left(-re\right)}{-\color{blue}{1}} \cdot \left(e^{0 - im} + e^{im}\right) \]

   8. metadata-eval 100.0%

      \[\leadsto \frac{0.5 \cdot \sin \left(-re\right)}{\color{blue}{-1}} \cdot \left(e^{0 - im} + e^{im}\right) \]

   9. associate-*l/ 100.0%

      \[\leadsto \color{blue}{\frac{\left(0.5 \cdot \sin \left(-re\right)\right) \cdot \left(e^{0 - im} + e^{im}\right)}{-1}} \]

   10. associate-*l* 100.0%

       \[\leadsto \frac{\color{blue}{0.5 \cdot \left(\sin \left(-re\right) \cdot \left(e^{0 - im} + e^{im}\right)\right)}}{-1} \]

   11. associate-*r/ 100.0%

       \[\leadsto \color{blue}{0.5 \cdot \frac{\sin \left(-re\right) \cdot \left(e^{0 - im} + e^{im}\right)}{-1}} \]

   12. associate-*l/ 100.0%

       \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{\sin \left(-re\right)}{-1} \cdot \left(e^{0 - im} + e^{im}\right)\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{0.5 \cdot \left(\sin re \cdot \left(e^{-im} + e^{im}\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in re around 0 63.4%

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

Reproduce

herbie shell --seed 2024096 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))