Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A

Percentage Accurate: 77.5% → 99.8%

Time: 8.9s

Alternatives: 6

Speedup: 3.1×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \frac{\left(\frac{8}{3} \cdot t\_0\right) \cdot t\_0}{\sin x} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5)))) (/ (* (* (/ 8.0 3.0) t_0) t_0) (sin x))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	return (((8.0 / 3.0) * t_0) * t_0) / sin(x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x * 0.5d0))
    code = (((8.0d0 / 3.0d0) * t_0) * t_0) / sin(x)
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	return (((8.0 / 3.0) * t_0) * t_0) / Math.sin(x);
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	return (((8.0 / 3.0) * t_0) * t_0) / math.sin(x)

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	return Float64(Float64(Float64(Float64(8.0 / 3.0) * t_0) * t_0) / sin(x))
end

MATLAB

function tmp = code(x)
	t_0 = sin((x * 0.5));
	tmp = (((8.0 / 3.0) * t_0) * t_0) / sin(x);
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(N[(N[(N[(8.0 / 3.0), $MachinePrecision] * t$95$0), $MachinePrecision] * t$95$0), $MachinePrecision] / N[Sin[x], $MachinePrecision]), $MachinePrecision]]

Initial Program: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \frac{\left(\frac{8}{3} \cdot t\_0\right) \cdot t\_0}{\sin x} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5)))) (/ (* (* (/ 8.0 3.0) t_0) t_0) (sin x))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	return (((8.0 / 3.0) * t_0) * t_0) / sin(x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x * 0.5d0))
    code = (((8.0d0 / 3.0d0) * t_0) * t_0) / sin(x)
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	return (((8.0 / 3.0) * t_0) * t_0) / Math.sin(x);
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	return (((8.0 / 3.0) * t_0) * t_0) / math.sin(x)

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	return Float64(Float64(Float64(Float64(8.0 / 3.0) * t_0) * t_0) / sin(x))
end

MATLAB

function tmp = code(x)
	t_0 = sin((x * 0.5));
	tmp = (((8.0 / 3.0) * t_0) * t_0) / sin(x);
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(N[(N[(N[(8.0 / 3.0), $MachinePrecision] * t$95$0), $MachinePrecision] * t$95$0), $MachinePrecision] / N[Sin[x], $MachinePrecision]), $MachinePrecision]]

Alternative 1: 99.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \frac{\tan \left(0.5 \cdot x\right) \cdot 0.5}{0.375} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (* (tan (* 0.5 x)) 0.5) 0.375))

C

double code(double x) {
	return (tan((0.5 * x)) * 0.5) / 0.375;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (tan((0.5d0 * x)) * 0.5d0) / 0.375d0
end function

Java

public static double code(double x) {
	return (Math.tan((0.5 * x)) * 0.5) / 0.375;
}

Python

def code(x):
	return (math.tan((0.5 * x)) * 0.5) / 0.375

Julia

function code(x)
	return Float64(Float64(tan(Float64(0.5 * x)) * 0.5) / 0.375)
end

MATLAB

function tmp = code(x)
	tmp = (tan((0.5 * x)) * 0.5) / 0.375;
end

Wolfram

code[x_] := N[(N[(N[Tan[N[(0.5 * x), $MachinePrecision]], $MachinePrecision] * 0.5), $MachinePrecision] / 0.375), $MachinePrecision]

Derivation

1. Initial program 78.5%

   \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]
2. Add Preprocessing
3. Step-by-step derivation

4. Applied rewrites 53.4%

   \[\leadsto \color{blue}{\frac{\left(1 - \cos x\right) \cdot 1.3333333333333333}{\sin x}} \]

6. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\frac{0.5 \cdot \tan \left(\frac{x}{2}\right)}{0.375}} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \tan \left(\frac{x}{2}\right)}}{\frac{3}{8}} \]

   2. *-commutative N/A

      \[\leadsto \frac{\color{blue}{\tan \left(\frac{x}{2}\right) \cdot \frac{1}{2}}}{\frac{3}{8}} \]

   3. lower-*.f64 99.8

      \[\leadsto \frac{\color{blue}{\tan \left(\frac{x}{2}\right) \cdot 0.5}}{0.375} \]

   4. lift-/.f64 N/A

      \[\leadsto \frac{\tan \color{blue}{\left(\frac{x}{2}\right)} \cdot \frac{1}{2}}{\frac{3}{8}} \]

   5. div-inv N/A

      \[\leadsto \frac{\tan \color{blue}{\left(x \cdot \frac{1}{2}\right)} \cdot \frac{1}{2}}{\frac{3}{8}} \]

   6. metadata-eval N/A

      \[\leadsto \frac{\tan \left(x \cdot \color{blue}{\frac{1}{2}}\right) \cdot \frac{1}{2}}{\frac{3}{8}} \]

   7. lower-*.f64 99.8

      \[\leadsto \frac{\tan \color{blue}{\left(x \cdot 0.5\right)} \cdot 0.5}{0.375} \]

8. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\frac{\tan \left(x \cdot 0.5\right) \cdot 0.5}{0.375}} \]

9. Final simplification 99.8%

   \[\leadsto \frac{\tan \left(0.5 \cdot x\right) \cdot 0.5}{0.375} \]
10. Add Preprocessing

Alternative 2: 99.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \tan \left(0.5 \cdot x\right) \cdot 1.3333333333333333 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (tan (* 0.5 x)) 1.3333333333333333))

C

double code(double x) {
	return tan((0.5 * x)) * 1.3333333333333333;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = tan((0.5d0 * x)) * 1.3333333333333333d0
end function

Java

public static double code(double x) {
	return Math.tan((0.5 * x)) * 1.3333333333333333;
}

Python

def code(x):
	return math.tan((0.5 * x)) * 1.3333333333333333

Julia

function code(x)
	return Float64(tan(Float64(0.5 * x)) * 1.3333333333333333)
end

MATLAB

function tmp = code(x)
	tmp = tan((0.5 * x)) * 1.3333333333333333;
end

Wolfram

code[x_] := N[(N[Tan[N[(0.5 * x), $MachinePrecision]], $MachinePrecision] * 1.3333333333333333), $MachinePrecision]

Derivation

1. Initial program 78.5%

   \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]
2. Add Preprocessing
3. Step-by-step derivation

4. Applied rewrites 53.4%

   \[\leadsto \color{blue}{\frac{\left(1 - \cos x\right) \cdot 1.3333333333333333}{\sin x}} \]

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{4}{3} \cdot \frac{1 - \cos x}{\sin x}} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\frac{1 - \cos x}{\sin x} \cdot \frac{4}{3}} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{1 - \cos x}{\sin x} \cdot \frac{4}{3}} \]

   3. hang-p0-tan N/A

      \[\leadsto \color{blue}{\tan \left(\frac{x}{2}\right)} \cdot \frac{4}{3} \]

   4. *-rgt-identity N/A

      \[\leadsto \tan \left(\frac{\color{blue}{x \cdot 1}}{2}\right) \cdot \frac{4}{3} \]

   5. associate-/l* N/A

      \[\leadsto \tan \color{blue}{\left(x \cdot \frac{1}{2}\right)} \cdot \frac{4}{3} \]

   6. metadata-eval N/A

      \[\leadsto \tan \left(x \cdot \color{blue}{\frac{1}{2}}\right) \cdot \frac{4}{3} \]

   7. *-commutative N/A

      \[\leadsto \tan \color{blue}{\left(\frac{1}{2} \cdot x\right)} \cdot \frac{4}{3} \]

   8. lower-tan.f64 N/A

      \[\leadsto \color{blue}{\tan \left(\frac{1}{2} \cdot x\right)} \cdot \frac{4}{3} \]

   9. lower-*.f64 99.5

      \[\leadsto \tan \color{blue}{\left(0.5 \cdot x\right)} \cdot 1.3333333333333333 \]

7. Applied rewrites 99.5%

   \[\leadsto \color{blue}{\tan \left(0.5 \cdot x\right) \cdot 1.3333333333333333} \]
8. Add Preprocessing

Alternative 3: 49.9% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \frac{2.6666666666666665}{\frac{\mathsf{fma}\left(-0.3333333333333333, x \cdot x, 4\right)}{x}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ 2.6666666666666665 (/ (fma -0.3333333333333333 (* x x) 4.0) x)))

C

double code(double x) {
	return 2.6666666666666665 / (fma(-0.3333333333333333, (x * x), 4.0) / x);
}

Julia

function code(x)
	return Float64(2.6666666666666665 / Float64(fma(-0.3333333333333333, Float64(x * x), 4.0) / x))
end

Wolfram

code[x_] := N[(2.6666666666666665 / N[(N[(-0.3333333333333333 * N[(x * x), $MachinePrecision] + 4.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.5%

   \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot \frac{1}{2}\right)\right) \cdot \sin \left(x \cdot \frac{1}{2}\right)}{\sin x}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{\left(\frac{8}{3} \cdot \sin \left(x \cdot \frac{1}{2}\right)\right) \cdot \sin \left(x \cdot \frac{1}{2}\right)}}{\sin x} \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{\left(\frac{8}{3} \cdot \sin \left(x \cdot \frac{1}{2}\right)\right)} \cdot \sin \left(x \cdot \frac{1}{2}\right)}{\sin x} \]

   4. associate-*l* N/A

      \[\leadsto \frac{\color{blue}{\frac{8}{3} \cdot \left(\sin \left(x \cdot \frac{1}{2}\right) \cdot \sin \left(x \cdot \frac{1}{2}\right)\right)}}{\sin x} \]

   5. *-commutative N/A

      \[\leadsto \frac{\color{blue}{\left(\sin \left(x \cdot \frac{1}{2}\right) \cdot \sin \left(x \cdot \frac{1}{2}\right)\right) \cdot \frac{8}{3}}}{\sin x} \]

   6. associate-/l* N/A

      \[\leadsto \color{blue}{\left(\sin \left(x \cdot \frac{1}{2}\right) \cdot \sin \left(x \cdot \frac{1}{2}\right)\right) \cdot \frac{\frac{8}{3}}{\sin x}} \]

   7. lift-sin.f64 N/A

      \[\leadsto \left(\color{blue}{\sin \left(x \cdot \frac{1}{2}\right)} \cdot \sin \left(x \cdot \frac{1}{2}\right)\right) \cdot \frac{\frac{8}{3}}{\sin x} \]

   8. lift-sin.f64 N/A

      \[\leadsto \left(\sin \left(x \cdot \frac{1}{2}\right) \cdot \color{blue}{\sin \left(x \cdot \frac{1}{2}\right)}\right) \cdot \frac{\frac{8}{3}}{\sin x} \]

   9. sin-mult N/A

      \[\leadsto \color{blue}{\frac{\cos \left(x \cdot \frac{1}{2} - x \cdot \frac{1}{2}\right) - \cos \left(x \cdot \frac{1}{2} + x \cdot \frac{1}{2}\right)}{2}} \cdot \frac{\frac{8}{3}}{\sin x} \]

   10. clear-num N/A

       \[\leadsto \color{blue}{\frac{1}{\frac{2}{\cos \left(x \cdot \frac{1}{2} - x \cdot \frac{1}{2}\right) - \cos \left(x \cdot \frac{1}{2} + x \cdot \frac{1}{2}\right)}}} \cdot \frac{\frac{8}{3}}{\sin x} \]

   11. frac-times N/A

       \[\leadsto \color{blue}{\frac{1 \cdot \frac{8}{3}}{\frac{2}{\cos \left(x \cdot \frac{1}{2} - x \cdot \frac{1}{2}\right) - \cos \left(x \cdot \frac{1}{2} + x \cdot \frac{1}{2}\right)} \cdot \sin x}} \]

   12. lift-/.f64 N/A

       \[\leadsto \frac{1 \cdot \color{blue}{\frac{8}{3}}}{\frac{2}{\cos \left(x \cdot \frac{1}{2} - x \cdot \frac{1}{2}\right) - \cos \left(x \cdot \frac{1}{2} + x \cdot \frac{1}{2}\right)} \cdot \sin x} \]

   13. metadata-eval N/A

       \[\leadsto \frac{1 \cdot \color{blue}{\frac{8}{3}}}{\frac{2}{\cos \left(x \cdot \frac{1}{2} - x \cdot \frac{1}{2}\right) - \cos \left(x \cdot \frac{1}{2} + x \cdot \frac{1}{2}\right)} \cdot \sin x} \]

   14. metadata-eval N/A

       \[\leadsto \frac{\color{blue}{\frac{8}{3}}}{\frac{2}{\cos \left(x \cdot \frac{1}{2} - x \cdot \frac{1}{2}\right) - \cos \left(x \cdot \frac{1}{2} + x \cdot \frac{1}{2}\right)} \cdot \sin x} \]

   15. metadata-eval N/A

       \[\leadsto \frac{\color{blue}{\frac{8}{3}}}{\frac{2}{\cos \left(x \cdot \frac{1}{2} - x \cdot \frac{1}{2}\right) - \cos \left(x \cdot \frac{1}{2} + x \cdot \frac{1}{2}\right)} \cdot \sin x} \]

   16. lift-/.f64 N/A

       \[\leadsto \frac{\color{blue}{\frac{8}{3}}}{\frac{2}{\cos \left(x \cdot \frac{1}{2} - x \cdot \frac{1}{2}\right) - \cos \left(x \cdot \frac{1}{2} + x \cdot \frac{1}{2}\right)} \cdot \sin x} \]

4. Applied rewrites 53.5%

   \[\leadsto \color{blue}{\frac{2.6666666666666665}{\frac{2}{1 - \cos x} \cdot \sin x}} \]

5. Taylor expanded in x around 0

   \[\leadsto \frac{\frac{8}{3}}{\color{blue}{\frac{4 + \frac{-1}{3} \cdot {x}^{2}}{x}}} \]
6. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{\frac{8}{3}}{\color{blue}{\frac{4 + \frac{-1}{3} \cdot {x}^{2}}{x}}} \]

   2. +-commutative N/A

      \[\leadsto \frac{\frac{8}{3}}{\frac{\color{blue}{\frac{-1}{3} \cdot {x}^{2} + 4}}{x}} \]

   3. lower-fma.f64 N/A

      \[\leadsto \frac{\frac{8}{3}}{\frac{\color{blue}{\mathsf{fma}\left(\frac{-1}{3}, {x}^{2}, 4\right)}}{x}} \]

   4. unpow2 N/A

      \[\leadsto \frac{\frac{8}{3}}{\frac{\mathsf{fma}\left(\frac{-1}{3}, \color{blue}{x \cdot x}, 4\right)}{x}} \]

   5. lower-*.f64 50.6

      \[\leadsto \frac{2.6666666666666665}{\frac{\mathsf{fma}\left(-0.3333333333333333, \color{blue}{x \cdot x}, 4\right)}{x}} \]

7. Applied rewrites 50.6%

   \[\leadsto \frac{2.6666666666666665}{\color{blue}{\frac{\mathsf{fma}\left(-0.3333333333333333, x \cdot x, 4\right)}{x}}} \]
8. Add Preprocessing

Alternative 4: 49.7% accurate, 20.2× speedup

Math

\[\begin{array}{l} \\ \frac{0.25 \cdot x}{0.375} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (* 0.25 x) 0.375))

C

double code(double x) {
	return (0.25 * x) / 0.375;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (0.25d0 * x) / 0.375d0
end function

Java

public static double code(double x) {
	return (0.25 * x) / 0.375;
}

Python

def code(x):
	return (0.25 * x) / 0.375

Julia

function code(x)
	return Float64(Float64(0.25 * x) / 0.375)
end

MATLAB

function tmp = code(x)
	tmp = (0.25 * x) / 0.375;
end

Wolfram

code[x_] := N[(N[(0.25 * x), $MachinePrecision] / 0.375), $MachinePrecision]

Derivation

1. Initial program 78.5%

   \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]
2. Add Preprocessing
3. Step-by-step derivation

4. Applied rewrites 53.4%

   \[\leadsto \color{blue}{\frac{\left(1 - \cos x\right) \cdot 1.3333333333333333}{\sin x}} \]

6. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\frac{0.5 \cdot \tan \left(\frac{x}{2}\right)}{0.375}} \]

7. Taylor expanded in x around 0

   \[\leadsto \frac{\color{blue}{\frac{1}{4} \cdot x}}{\frac{3}{8}} \]
8. Step-by-step derivation

   1. lower-*.f64 50.1

      \[\leadsto \frac{\color{blue}{0.25 \cdot x}}{0.375} \]

9. Applied rewrites 50.1%

   \[\leadsto \frac{\color{blue}{0.25 \cdot x}}{0.375} \]
10. Add Preprocessing

Alternative 5: 49.5% accurate, 31.2× speedup

Math

\[\begin{array}{l} \\ \left(0.25 \cdot x\right) \cdot 2.6666666666666665 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (* 0.25 x) 2.6666666666666665))

C

double code(double x) {
	return (0.25 * x) * 2.6666666666666665;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (0.25d0 * x) * 2.6666666666666665d0
end function

Java

public static double code(double x) {
	return (0.25 * x) * 2.6666666666666665;
}

Python

def code(x):
	return (0.25 * x) * 2.6666666666666665

Julia

function code(x)
	return Float64(Float64(0.25 * x) * 2.6666666666666665)
end

MATLAB

function tmp = code(x)
	tmp = (0.25 * x) * 2.6666666666666665;
end

Wolfram

code[x_] := N[(N[(0.25 * x), $MachinePrecision] * 2.6666666666666665), $MachinePrecision]

Derivation

1. Initial program 78.5%

   \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]
2. Add Preprocessing
3. Step-by-step derivation

4. Applied rewrites 53.4%

   \[\leadsto \color{blue}{\frac{\left(1 - \cos x\right) \cdot 1.3333333333333333}{\sin x}} \]

6. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\frac{0.5 \cdot \tan \left(\frac{x}{2}\right)}{0.375}} \]

7. Taylor expanded in x around 0

   \[\leadsto \frac{\color{blue}{\frac{1}{4} \cdot x}}{\frac{3}{8}} \]
8. Step-by-step derivation

   1. lower-*.f64 50.1

      \[\leadsto \frac{\color{blue}{0.25 \cdot x}}{0.375} \]

9. Applied rewrites 50.1%

   \[\leadsto \frac{\color{blue}{0.25 \cdot x}}{0.375} \]
10. Step-by-step derivation

    1. lift-/.f64 N/A

       \[\leadsto \color{blue}{\frac{\frac{1}{4} \cdot x}{\frac{3}{8}}} \]

    2. div-inv N/A

       \[\leadsto \color{blue}{\left(\frac{1}{4} \cdot x\right) \cdot \frac{1}{\frac{3}{8}}} \]

    3. metadata-eval N/A

       \[\leadsto \left(\frac{1}{4} \cdot x\right) \cdot \color{blue}{\frac{8}{3}} \]

    4. lower-*.f64 49.8

       \[\leadsto \color{blue}{\left(0.25 \cdot x\right) \cdot 2.6666666666666665} \]

11. Applied rewrites 49.8%

    \[\leadsto \color{blue}{\left(0.25 \cdot x\right) \cdot 2.6666666666666665} \]
12. Add Preprocessing

Alternative 6: 49.5% accurate, 57.2× speedup

Math

\[\begin{array}{l} \\ 0.6666666666666666 \cdot x \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 0.6666666666666666 x))

C

double code(double x) {
	return 0.6666666666666666 * x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.6666666666666666d0 * x
end function

Java

public static double code(double x) {
	return 0.6666666666666666 * x;
}

Python

def code(x):
	return 0.6666666666666666 * x

Julia

function code(x)
	return Float64(0.6666666666666666 * x)
end

MATLAB

function tmp = code(x)
	tmp = 0.6666666666666666 * x;
end

Wolfram

code[x_] := N[(0.6666666666666666 * x), $MachinePrecision]

Derivation

1. Initial program 78.5%

   \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{2}{3} \cdot x} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{x \cdot \frac{2}{3}} \]

   2. lower-*.f64 49.8

      \[\leadsto \color{blue}{x \cdot 0.6666666666666666} \]

5. Applied rewrites 49.8%

   \[\leadsto \color{blue}{x \cdot 0.6666666666666666} \]

6. Final simplification 49.8%

   \[\leadsto 0.6666666666666666 \cdot x \]
7. Add Preprocessing

Developer Target 1: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \frac{\frac{8 \cdot t\_0}{3}}{\frac{\sin x}{t\_0}} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5)))) (/ (/ (* 8.0 t_0) 3.0) (/ (sin x) t_0))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	return ((8.0 * t_0) / 3.0) / (sin(x) / t_0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x * 0.5d0))
    code = ((8.0d0 * t_0) / 3.0d0) / (sin(x) / t_0)
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	return ((8.0 * t_0) / 3.0) / (Math.sin(x) / t_0);
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	return ((8.0 * t_0) / 3.0) / (math.sin(x) / t_0)

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	return Float64(Float64(Float64(8.0 * t_0) / 3.0) / Float64(sin(x) / t_0))
end

MATLAB

function tmp = code(x)
	t_0 = sin((x * 0.5));
	tmp = ((8.0 * t_0) / 3.0) / (sin(x) / t_0);
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(N[(N[(8.0 * t$95$0), $MachinePrecision] / 3.0), $MachinePrecision] / N[(N[Sin[x], $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024270 
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (/ (* 8 (sin (* x 1/2))) 3) (/ (sin x) (sin (* x 1/2)))))

  (/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))