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

Percentage Accurate: 99.9% → 99.9%

Time: 8.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z, \cos y, \sin y\right) + x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (fma z (cos y) (sin y)) x))

C

double code(double x, double y, double z) {
	return fma(z, cos(y), sin(y)) + x;
}

Julia

function code(x, y, z)
	return Float64(fma(z, cos(y), sin(y)) + x)
end

Wolfram

code[x_, y_, z_] := N[(N[(z * N[Cos[y], $MachinePrecision] + N[Sin[y], $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

   2. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(x + \sin y\right)} + z \cdot \cos y \]

   3. associate-+l+ N/A

      \[\leadsto \color{blue}{x + \left(\sin y + z \cdot \cos y\right)} \]

   4. +-commutative N/A

      \[\leadsto \color{blue}{\left(\sin y + z \cdot \cos y\right) + x} \]

   5. lower-+.f64 N/A

      \[\leadsto \color{blue}{\left(\sin y + z \cdot \cos y\right) + x} \]

   6. +-commutative N/A

      \[\leadsto \color{blue}{\left(z \cdot \cos y + \sin y\right)} + x \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\color{blue}{z \cdot \cos y} + \sin y\right) + x \]

   8. lower-fma.f64 100.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, \sin y\right)} + x \]

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, \sin y\right) + x} \]
5. Add Preprocessing

Alternative 2: 80.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y + \left(\sin y + x\right)\\ \mathbf{if}\;t\_0 \leq -1000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t\_0 \leq -2 \cdot 10^{-5}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-19}:\\ \;\;\;\;x + \left(z + y\right)\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (cos y)) (+ (sin y) x))))
   (if (<= t_0 -1000000.0)
     (+ z x)
     (if (<= t_0 -2e-5)
       (sin y)
       (if (<= t_0 2e-19) (+ x (+ z y)) (if (<= t_0 1.0) (sin y) (+ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * cos(y)) + (sin(y) + x);
	double tmp;
	if (t_0 <= -1000000.0) {
		tmp = z + x;
	} else if (t_0 <= -2e-5) {
		tmp = sin(y);
	} else if (t_0 <= 2e-19) {
		tmp = x + (z + y);
	} else if (t_0 <= 1.0) {
		tmp = sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * cos(y)) + (sin(y) + x)
    if (t_0 <= (-1000000.0d0)) then
        tmp = z + x
    else if (t_0 <= (-2d-5)) then
        tmp = sin(y)
    else if (t_0 <= 2d-19) then
        tmp = x + (z + y)
    else if (t_0 <= 1.0d0) then
        tmp = sin(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * Math.cos(y)) + (Math.sin(y) + x);
	double tmp;
	if (t_0 <= -1000000.0) {
		tmp = z + x;
	} else if (t_0 <= -2e-5) {
		tmp = Math.sin(y);
	} else if (t_0 <= 2e-19) {
		tmp = x + (z + y);
	} else if (t_0 <= 1.0) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * math.cos(y)) + (math.sin(y) + x)
	tmp = 0
	if t_0 <= -1000000.0:
		tmp = z + x
	elif t_0 <= -2e-5:
		tmp = math.sin(y)
	elif t_0 <= 2e-19:
		tmp = x + (z + y)
	elif t_0 <= 1.0:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * cos(y)) + Float64(sin(y) + x))
	tmp = 0.0
	if (t_0 <= -1000000.0)
		tmp = Float64(z + x);
	elseif (t_0 <= -2e-5)
		tmp = sin(y);
	elseif (t_0 <= 2e-19)
		tmp = Float64(x + Float64(z + y));
	elseif (t_0 <= 1.0)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * cos(y)) + (sin(y) + x);
	tmp = 0.0;
	if (t_0 <= -1000000.0)
		tmp = z + x;
	elseif (t_0 <= -2e-5)
		tmp = sin(y);
	elseif (t_0 <= 2e-19)
		tmp = x + (z + y);
	elseif (t_0 <= 1.0)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1000000.0], N[(z + x), $MachinePrecision], If[LessEqual[t$95$0, -2e-5], N[Sin[y], $MachinePrecision], If[LessEqual[t$95$0, 2e-19], N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -1e6 or 1 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + z} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{z + x} \]

      2. lower-+.f64 75.9

         \[\leadsto \color{blue}{z + x} \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{z + x} \]

   if -1e6 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -2.00000000000000016e-5 or 2e-19 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 1

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \sin y} \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, \sin y\right)} \]

      3. lower-cos.f64 N/A

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\cos y}, \sin y\right) \]

      4. lower-sin.f64 93.7

         \[\leadsto \mathsf{fma}\left(z, \cos y, \color{blue}{\sin y}\right) \]

   5. Applied rewrites 93.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, \sin y\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \sin y \]
   7. Step-by-step derivation

   8. Applied rewrites 86.9%

      \[\leadsto \sin y \]

   if -2.00000000000000016e-5 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 2e-19

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right)} + z \cdot \cos y \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{x + \left(\sin y + z \cdot \cos y\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\sin y + z \cdot \cos y\right) + x} \]

      5. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(\sin y + z \cdot \cos y\right) + x} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot \cos y + \sin y\right)} + x \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{z \cdot \cos y} + \sin y\right) + x \]

      8. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, \sin y\right)} + x \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, \sin y\right) + x} \]

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(y + z\right)} + x \]
   6. Step-by-step derivation

      1. lower-+.f64 99.9

         \[\leadsto \color{blue}{\left(y + z\right)} + x \]

   7. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\left(y + z\right)} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \cos y + \left(\sin y + x\right) \leq -1000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \cdot \cos y + \left(\sin y + x\right) \leq -2 \cdot 10^{-5}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \cdot \cos y + \left(\sin y + x\right) \leq 2 \cdot 10^{-19}:\\ \;\;\;\;x + \left(z + y\right)\\ \mathbf{elif}\;z \cdot \cos y + \left(\sin y + x\right) \leq 1:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024228 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))