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

Percentage Accurate: 76.9% → 99.8%

Time: 10.0s

Alternatives: 5

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: 76.9% 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, 2.9× speedup

Math

\[\begin{array}{l} \\ \frac{\tan \left(x \cdot 0.5\right)}{0.75} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (tan (* x 0.5)) 0.75))

C

double code(double x) {
	return tan((x * 0.5)) / 0.75;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = tan((x * 0.5d0)) / 0.75d0
end function

Java

public static double code(double x) {
	return Math.tan((x * 0.5)) / 0.75;
}

Python

def code(x):
	return math.tan((x * 0.5)) / 0.75

Julia

function code(x)
	return Float64(tan(Float64(x * 0.5)) / 0.75)
end

MATLAB

function tmp = code(x)
	tmp = tan((x * 0.5)) / 0.75;
end

Wolfram

code[x_] := N[(N[Tan[N[(x * 0.5), $MachinePrecision]], $MachinePrecision] / 0.75), $MachinePrecision]

Derivation

1. Initial program 77.4%

   \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]
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. clear-num N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. associate-/r* N/A

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

   7. clear-num N/A

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

   8. lift-sin.f64 N/A

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

   9. lift-sin.f64 N/A

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

   10. sin-mult N/A

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

   11. div-inv N/A

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

   12. metadata-eval N/A

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

   13. associate-/l* N/A

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

4. Applied rewrites 54.2%

   \[\leadsto \color{blue}{\left(1 - \cos x\right) \cdot \frac{0.5}{0.375 \cdot \sin x}} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. frac-2neg N/A

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

   4. metadata-eval N/A

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

   5. associate-*r/ N/A

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

   6. *-commutative N/A

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

   7. lift--.f64 N/A

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

   8. sub-neg N/A

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

   9. distribute-rgt-in N/A

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

   10. metadata-eval N/A

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

   11. metadata-eval N/A

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

   12. distribute-lft-neg-in N/A

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

   13. distribute-neg-in N/A

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

   14. +-commutative N/A

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

   15. lift-fma.f64 N/A

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

   16. frac-2neg N/A

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

   17. lift-*.f64 N/A

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

   18. associate-/l/ N/A

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

   19. lift-/.f64 N/A

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

   20. lift-/.f64 54.2

       \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\cos x, -0.5, 0.5\right)}{\sin x}}{0.375}} \]

6. Applied rewrites 99.8%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. metadata-eval N/A

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

   5. metadata-eval N/A

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

   6. div-inv N/A

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

   7. lower-/.f64 99.8

      \[\leadsto \color{blue}{\frac{\tan \left(\frac{x}{2}\right)}{0.75}} \]

   8. lift-/.f64 N/A

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

   9. clear-num N/A

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

   10. associate-/r/ N/A

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

   11. metadata-eval N/A

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

   12. lower-*.f64 99.8

       \[\leadsto \frac{\tan \color{blue}{\left(0.5 \cdot x\right)}}{0.75} \]

8. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\frac{\tan \left(0.5 \cdot x\right)}{0.75}} \]

9. Final simplification 99.8%

   \[\leadsto \frac{\tan \left(x \cdot 0.5\right)}{0.75} \]
10. Add Preprocessing

Alternative 2: 99.5% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.9%

   \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]
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. clear-num N/A

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

   3. associate-/r/ N/A

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

   4. remove-double-neg N/A

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

   5. lift-*.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. associate-*l* N/A

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

   8. distribute-rgt-neg-in N/A

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

   9. distribute-lft-neg-in N/A

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

   10. associate-*r* N/A

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

   11. lower-*.f64 N/A

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

4. Applied rewrites 52.7%

   \[\leadsto \color{blue}{\left(\frac{1}{\sin x} \cdot -2.6666666666666665\right) \cdot \left(\left(1 - \cos x\right) \cdot -0.5\right)} \]

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. Final simplification 99.5%

   \[\leadsto 1.3333333333333333 \cdot \tan \left(x \cdot 0.5\right) \]
9. 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 2024230 
(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)))