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

Percentage Accurate: 75.9% → 99.5%

Time: 14.7s

Alternatives: 6

Speedup: 3.0×

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: 75.9% 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: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(\frac{x}{2}\right)\\ \frac{t\_0}{\frac{\frac{\sin x}{t\_0}}{2.6666666666666665}} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (/ x 2.0)))) (/ t_0 (/ (/ (sin x) t_0) 2.6666666666666665))))

C

double code(double x) {
	double t_0 = sin((x / 2.0));
	return t_0 / ((sin(x) / t_0) / 2.6666666666666665);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x / 2.0d0))
    code = t_0 / ((sin(x) / t_0) / 2.6666666666666665d0)
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x / 2.0));
	return t_0 / ((Math.sin(x) / t_0) / 2.6666666666666665);
}

Python

def code(x):
	t_0 = math.sin((x / 2.0))
	return t_0 / ((math.sin(x) / t_0) / 2.6666666666666665)

Julia

function code(x)
	t_0 = sin(Float64(x / 2.0))
	return Float64(t_0 / Float64(Float64(sin(x) / t_0) / 2.6666666666666665))
end

MATLAB

function tmp = code(x)
	t_0 = sin((x / 2.0));
	tmp = t_0 / ((sin(x) / t_0) / 2.6666666666666665);
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x / 2.0), $MachinePrecision]], $MachinePrecision]}, N[(t$95$0 / N[(N[(N[Sin[x], $MachinePrecision] / t$95$0), $MachinePrecision] / 2.6666666666666665), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 78.7%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

8. Applied egg-rr 0

   \[\leadsto expr\]
9. Add Preprocessing

Alternative 2: 99.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \tan \left(\frac{x}{2}\right) \cdot 1.3333333333333333 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (tan (/ x 2.0)) 1.3333333333333333))

C

double code(double x) {
	return tan((x / 2.0)) * 1.3333333333333333;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = tan((x / 2.0d0)) * 1.3333333333333333d0
end function

Java

public static double code(double x) {
	return Math.tan((x / 2.0)) * 1.3333333333333333;
}

Python

def code(x):
	return math.tan((x / 2.0)) * 1.3333333333333333

Julia

function code(x)
	return Float64(tan(Float64(x / 2.0)) * 1.3333333333333333)
end

MATLAB

function tmp = code(x)
	tmp = tan((x / 2.0)) * 1.3333333333333333;
end

Wolfram

code[x_] := N[(N[Tan[N[(x / 2.0), $MachinePrecision]], $MachinePrecision] * 1.3333333333333333), $MachinePrecision]

Derivation

1. Initial program 78.7%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

8. Applied egg-rr 0

   \[\leadsto expr\]
9. Add Preprocessing

Alternative 3: 52.6% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{1.5 + \left(x \cdot x\right) \cdot -0.125}{x}} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 1.0 (/ (+ 1.5 (* (* x x) -0.125)) x)))

C

double code(double x) {
	return 1.0 / ((1.5 + ((x * x) * -0.125)) / x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / ((1.5d0 + ((x * x) * (-0.125d0))) / x)
end function

Java

public static double code(double x) {
	return 1.0 / ((1.5 + ((x * x) * -0.125)) / x);
}

Python

def code(x):
	return 1.0 / ((1.5 + ((x * x) * -0.125)) / x)

Julia

function code(x)
	return Float64(1.0 / Float64(Float64(1.5 + Float64(Float64(x * x) * -0.125)) / x))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 / ((1.5 + ((x * x) * -0.125)) / x);
end

Wolfram

code[x_] := N[(1.0 / N[(N[(1.5 + N[(N[(x * x), $MachinePrecision] * -0.125), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.7%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

8. Applied egg-rr 0

   \[\leadsto expr\]

9. Taylor expanded in x around 0 0

   \[\leadsto expr\]

11. Simplified 0

    \[\leadsto expr\]
12. Add Preprocessing

Alternative 4: 52.0% accurate, 62.6× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{1.5}{x}} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 1.0 (/ 1.5 x)))

C

double code(double x) {
	return 1.0 / (1.5 / x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / (1.5d0 / x)
end function

Java

public static double code(double x) {
	return 1.0 / (1.5 / x);
}

Python

def code(x):
	return 1.0 / (1.5 / x)

Julia

function code(x)
	return Float64(1.0 / Float64(1.5 / x))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 / (1.5 / x);
end

Wolfram

code[x_] := N[(1.0 / N[(1.5 / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.7%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

8. Applied egg-rr 0

   \[\leadsto expr\]

9. Taylor expanded in x around 0 0

   \[\leadsto expr\]

11. Simplified 0

    \[\leadsto expr\]
12. Add Preprocessing

Alternative 5: 51.9% accurate, 62.6× speedup

Math

\[\begin{array}{l} \\ \frac{0.6666666666666666}{\frac{1}{x}} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 0.6666666666666666 (/ 1.0 x)))

C

double code(double x) {
	return 0.6666666666666666 / (1.0 / x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.6666666666666666d0 / (1.0d0 / x)
end function

Java

public static double code(double x) {
	return 0.6666666666666666 / (1.0 / x);
}

Python

def code(x):
	return 0.6666666666666666 / (1.0 / x)

Julia

function code(x)
	return Float64(0.6666666666666666 / Float64(1.0 / x))
end

MATLAB

function tmp = code(x)
	tmp = 0.6666666666666666 / (1.0 / x);
end

Wolfram

code[x_] := N[(0.6666666666666666 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.7%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

7. Taylor expanded in x around 0 0

   \[\leadsto expr\]

9. Simplified 0

   \[\leadsto expr\]

10. Taylor expanded in x around 0 0

    \[\leadsto expr\]

12. Simplified 0

    \[\leadsto expr\]

14. Applied egg-rr 0

    \[\leadsto expr\]
15. Add Preprocessing

Alternative 6: 51.9% accurate, 104.3× 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 78.7%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in x around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Developer target: 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 2024110 
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"
  :precision binary64

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

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