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

Percentage Accurate: 99.9% → 99.9%

Time: 15.1s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(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 + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(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 + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + \cos y\right) - z \cdot \sin y \]

2. Taylor expanded in z around 0 100.0%

   \[\leadsto \color{blue}{x + \left(\cos y + -1 \cdot \left(z \cdot \sin y\right)\right)} \]
3. Step-by-step derivation

   1. associate-+r+ 100.0%

      \[\leadsto \color{blue}{\left(x + \cos y\right) + -1 \cdot \left(z \cdot \sin y\right)} \]

   2. mul-1-neg 100.0%

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

   3. distribute-rgt-neg-out 100.0%

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

   4. +-commutative 100.0%

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

   5. fma-def 100.0%

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

   6. +-commutative 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -118:\\ \;\;\;\;\cos y + x\\ \mathbf{elif}\;x \leq 16200000:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -118.0)
   (+ (cos y) x)
   (if (<= x 16200000.0) (- (cos y) (* z (sin y))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -118.0) {
		tmp = cos(y) + x;
	} else if (x <= 16200000.0) {
		tmp = cos(y) - (z * sin(y));
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (x <= (-118.0d0)) then
        tmp = cos(y) + x
    else if (x <= 16200000.0d0) then
        tmp = cos(y) - (z * sin(y))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -118.0) {
		tmp = Math.cos(y) + x;
	} else if (x <= 16200000.0) {
		tmp = Math.cos(y) - (z * Math.sin(y));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -118.0:
		tmp = math.cos(y) + x
	elif x <= 16200000.0:
		tmp = math.cos(y) - (z * math.sin(y))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -118.0)
		tmp = Float64(cos(y) + x);
	elseif (x <= 16200000.0)
		tmp = Float64(cos(y) - Float64(z * sin(y)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -118.0)
		tmp = cos(y) + x;
	elseif (x <= 16200000.0)
		tmp = cos(y) - (z * sin(y));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -118.0], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], If[LessEqual[x, 16200000.0], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -118

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in z around 0 89.0%

      \[\leadsto \color{blue}{x + \cos y} \]
   3. Step-by-step derivation

      1. +-commutative 89.0%

         \[\leadsto \color{blue}{\cos y + x} \]

   4. Simplified 89.0%

      \[\leadsto \color{blue}{\cos y + x} \]

   if -118 < x < 1.62e7

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around 0 99.0%

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

   if 1.62e7 < x

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0 85.8%

      \[\leadsto \color{blue}{1 + x} \]
   3. Step-by-step derivation

      1. +-commutative 85.8%

         \[\leadsto \color{blue}{x + 1} \]

   4. Simplified 85.8%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -118:\\ \;\;\;\;\cos y + x\\ \mathbf{elif}\;x \leq 16200000:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (cos(y) + x) - (z * sin(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 = (cos(y) + x) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + \cos y\right) - z \cdot \sin y \]

2. Final simplification 100.0%

   \[\leadsto \left(\cos y + x\right) - z \cdot \sin y \]

Alternative 4: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-5} \lor \neg \left(y \leq 0.32\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e-5) (not (<= y 0.32))) (+ (cos y) x) (+ x (- 1.0 (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e-5) || !(y <= 0.32)) {
		tmp = cos(y) + x;
	} else {
		tmp = x + (1.0 - (z * y));
	}
	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) :: tmp
    if ((y <= (-5d-5)) .or. (.not. (y <= 0.32d0))) then
        tmp = cos(y) + x
    else
        tmp = x + (1.0d0 - (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e-5) || !(y <= 0.32)) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = x + (1.0 - (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e-5) or not (y <= 0.32):
		tmp = math.cos(y) + x
	else:
		tmp = x + (1.0 - (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e-5) || !(y <= 0.32))
		tmp = Float64(cos(y) + x);
	else
		tmp = Float64(x + Float64(1.0 - Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5e-5) || ~((y <= 0.32)))
		tmp = cos(y) + x;
	else
		tmp = x + (1.0 - (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e-5], N[Not[LessEqual[y, 0.32]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(x + N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000024e-5 or 0.320000000000000007 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in z around 0 65.4%

      \[\leadsto \color{blue}{x + \cos y} \]
   3. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto \color{blue}{\cos y + x} \]

   4. Simplified 65.4%

      \[\leadsto \color{blue}{\cos y + x} \]

   if -5.00000000000000024e-5 < y < 0.320000000000000007

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0 99.2%

      \[\leadsto \color{blue}{1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 99.2%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(y \cdot z\right)\right) + 1} \]

      2. associate-+l+ 99.2%

         \[\leadsto \color{blue}{x + \left(-1 \cdot \left(y \cdot z\right) + 1\right)} \]

      3. +-commutative 99.2%

         \[\leadsto x + \color{blue}{\left(1 + -1 \cdot \left(y \cdot z\right)\right)} \]

      4. mul-1-neg 99.2%

         \[\leadsto x + \left(1 + \color{blue}{\left(-y \cdot z\right)}\right) \]

      5. neg-sub0 99.2%

         \[\leadsto x + \left(1 + \color{blue}{\left(0 - y \cdot z\right)}\right) \]

      6. associate-+r- 99.2%

         \[\leadsto x + \color{blue}{\left(\left(1 + 0\right) - y \cdot z\right)} \]

      7. metadata-eval 99.2%

         \[\leadsto x + \left(\color{blue}{1} - y \cdot z\right) \]

   4. Simplified 99.2%

      \[\leadsto \color{blue}{x + \left(1 - y \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-5} \lor \neg \left(y \leq 0.32\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - z \cdot y\right)\\ \end{array} \]

Alternative 5: 80.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+91}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.5e+69)
   (* z (- (sin y)))
   (if (<= z 2.15e+91) (+ (cos y) x) (+ x (- 1.0 (* z y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+69) {
		tmp = z * -sin(y);
	} else if (z <= 2.15e+91) {
		tmp = cos(y) + x;
	} else {
		tmp = x + (1.0 - (z * y));
	}
	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) :: tmp
    if (z <= (-4.5d+69)) then
        tmp = z * -sin(y)
    else if (z <= 2.15d+91) then
        tmp = cos(y) + x
    else
        tmp = x + (1.0d0 - (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+69) {
		tmp = z * -Math.sin(y);
	} else if (z <= 2.15e+91) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = x + (1.0 - (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.5e+69:
		tmp = z * -math.sin(y)
	elif z <= 2.15e+91:
		tmp = math.cos(y) + x
	else:
		tmp = x + (1.0 - (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.5e+69)
		tmp = Float64(z * Float64(-sin(y)));
	elseif (z <= 2.15e+91)
		tmp = Float64(cos(y) + x);
	else
		tmp = Float64(x + Float64(1.0 - Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.5e+69)
		tmp = z * -sin(y);
	elseif (z <= 2.15e+91)
		tmp = cos(y) + x;
	else
		tmp = x + (1.0 - (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.5e+69], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 2.15e+91], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(x + N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4999999999999999e69

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in z around inf 74.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 74.0%

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

      2. distribute-rgt-neg-out 74.0%

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

   4. Simplified 74.0%

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

   if -4.4999999999999999e69 < z < 2.15e91

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in z around 0 94.6%

      \[\leadsto \color{blue}{x + \cos y} \]
   3. Step-by-step derivation

      1. +-commutative 94.6%

         \[\leadsto \color{blue}{\cos y + x} \]

   4. Simplified 94.6%

      \[\leadsto \color{blue}{\cos y + x} \]

   if 2.15e91 < z

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0 68.4%

      \[\leadsto \color{blue}{1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 68.4%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(y \cdot z\right)\right) + 1} \]

      2. associate-+l+ 68.4%

         \[\leadsto \color{blue}{x + \left(-1 \cdot \left(y \cdot z\right) + 1\right)} \]

      3. +-commutative 68.4%

         \[\leadsto x + \color{blue}{\left(1 + -1 \cdot \left(y \cdot z\right)\right)} \]

      4. mul-1-neg 68.4%

         \[\leadsto x + \left(1 + \color{blue}{\left(-y \cdot z\right)}\right) \]

      5. neg-sub0 68.4%

         \[\leadsto x + \left(1 + \color{blue}{\left(0 - y \cdot z\right)}\right) \]

      6. associate-+r- 68.4%

         \[\leadsto x + \color{blue}{\left(\left(1 + 0\right) - y \cdot z\right)} \]

      7. metadata-eval 68.4%

         \[\leadsto x + \left(\color{blue}{1} - y \cdot z\right) \]

   4. Simplified 68.4%

      \[\leadsto \color{blue}{x + \left(1 - y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+91}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - z \cdot y\right)\\ \end{array} \]

Alternative 6: 65.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-138} \lor \neg \left(x \leq 3 \cdot 10^{-212}\right):\\ \;\;\;\;x + \left(1 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.7e-138) (not (<= x 3e-212))) (+ x (- 1.0 (* z y))) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e-138) || !(x <= 3e-212)) {
		tmp = x + (1.0 - (z * y));
	} else {
		tmp = cos(y);
	}
	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) :: tmp
    if ((x <= (-3.7d-138)) .or. (.not. (x <= 3d-212))) then
        tmp = x + (1.0d0 - (z * y))
    else
        tmp = cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e-138) || !(x <= 3e-212)) {
		tmp = x + (1.0 - (z * y));
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.7e-138) or not (x <= 3e-212):
		tmp = x + (1.0 - (z * y))
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.7e-138) || !(x <= 3e-212))
		tmp = Float64(x + Float64(1.0 - Float64(z * y)));
	else
		tmp = cos(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.7e-138) || ~((x <= 3e-212)))
		tmp = x + (1.0 - (z * y));
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.7e-138], N[Not[LessEqual[x, 3e-212]], $MachinePrecision]], N[(x + N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.69999999999999991e-138 or 3.0000000000000003e-212 < x

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0 78.0%

      \[\leadsto \color{blue}{1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 78.0%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(y \cdot z\right)\right) + 1} \]

      2. associate-+l+ 78.0%

         \[\leadsto \color{blue}{x + \left(-1 \cdot \left(y \cdot z\right) + 1\right)} \]

      3. +-commutative 78.0%

         \[\leadsto x + \color{blue}{\left(1 + -1 \cdot \left(y \cdot z\right)\right)} \]

      4. mul-1-neg 78.0%

         \[\leadsto x + \left(1 + \color{blue}{\left(-y \cdot z\right)}\right) \]

      5. neg-sub0 78.0%

         \[\leadsto x + \left(1 + \color{blue}{\left(0 - y \cdot z\right)}\right) \]

      6. associate-+r- 78.0%

         \[\leadsto x + \color{blue}{\left(\left(1 + 0\right) - y \cdot z\right)} \]

      7. metadata-eval 78.0%

         \[\leadsto x + \left(\color{blue}{1} - y \cdot z\right) \]

   4. Simplified 78.0%

      \[\leadsto \color{blue}{x + \left(1 - y \cdot z\right)} \]

   if -3.69999999999999991e-138 < x < 3.0000000000000003e-212

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in z around 0 67.4%

      \[\leadsto \color{blue}{\cos y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-138} \lor \neg \left(x \leq 3 \cdot 10^{-212}\right):\\ \;\;\;\;x + \left(1 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]

Alternative 7: 66.1% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -19 \lor \neg \left(x \leq 15000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -19.0) (not (<= x 15000000.0))) (+ x 1.0) (- 1.0 (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -19.0) || !(x <= 15000000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (z * y);
	}
	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) :: tmp
    if ((x <= (-19.0d0)) .or. (.not. (x <= 15000000.0d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -19.0) || !(x <= 15000000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -19.0) or not (x <= 15000000.0):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -19.0) || !(x <= 15000000.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -19.0) || ~((x <= 15000000.0)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -19.0], N[Not[LessEqual[x, 15000000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -19 or 1.5e7 < x

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0 86.2%

      \[\leadsto \color{blue}{1 + x} \]
   3. Step-by-step derivation

      1. +-commutative 86.2%

         \[\leadsto \color{blue}{x + 1} \]

   4. Simplified 86.2%

      \[\leadsto \color{blue}{x + 1} \]

   if -19 < x < 1.5e7

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around 0 99.0%

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

   3. Taylor expanded in y around 0 59.1%

      \[\leadsto \color{blue}{1 + -1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.1%

         \[\leadsto 1 + \color{blue}{\left(-y \cdot z\right)} \]

      2. unsub-neg 59.1%

         \[\leadsto \color{blue}{1 - y \cdot z} \]

   5. Simplified 59.1%

      \[\leadsto \color{blue}{1 - y \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -19 \lor \neg \left(x \leq 15000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot y\\ \end{array} \]

Alternative 8: 65.8% accurate, 22.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.46 \cdot 10^{+113}:\\ \;\;\;\;x + \left(1 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.46e+113) (+ x (- 1.0 (* z y))) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.46e+113) {
		tmp = x + (1.0 - (z * y));
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (y <= 1.46d+113) then
        tmp = x + (1.0d0 - (z * y))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.46e+113) {
		tmp = x + (1.0 - (z * y));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.46e+113:
		tmp = x + (1.0 - (z * y))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.46e+113)
		tmp = Float64(x + Float64(1.0 - Float64(z * y)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.46e+113)
		tmp = x + (1.0 - (z * y));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.46e+113], N[(x + N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.46e113

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0 76.8%

      \[\leadsto \color{blue}{1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 76.8%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(y \cdot z\right)\right) + 1} \]

      2. associate-+l+ 76.8%

         \[\leadsto \color{blue}{x + \left(-1 \cdot \left(y \cdot z\right) + 1\right)} \]

      3. +-commutative 76.8%

         \[\leadsto x + \color{blue}{\left(1 + -1 \cdot \left(y \cdot z\right)\right)} \]

      4. mul-1-neg 76.8%

         \[\leadsto x + \left(1 + \color{blue}{\left(-y \cdot z\right)}\right) \]

      5. neg-sub0 76.8%

         \[\leadsto x + \left(1 + \color{blue}{\left(0 - y \cdot z\right)}\right) \]

      6. associate-+r- 76.8%

         \[\leadsto x + \color{blue}{\left(\left(1 + 0\right) - y \cdot z\right)} \]

      7. metadata-eval 76.8%

         \[\leadsto x + \left(\color{blue}{1} - y \cdot z\right) \]

   4. Simplified 76.8%

      \[\leadsto \color{blue}{x + \left(1 - y \cdot z\right)} \]

   if 1.46e113 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0 56.5%

      \[\leadsto \color{blue}{1 + x} \]
   3. Step-by-step derivation

      1. +-commutative 56.5%

         \[\leadsto \color{blue}{x + 1} \]

   4. Simplified 56.5%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.46 \cdot 10^{+113}:\\ \;\;\;\;x + \left(1 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9: 61.5% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+229}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.8e+229) (* z (- y)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e+229) {
		tmp = z * -y;
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (z <= (-7.8d+229)) then
        tmp = z * -y
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e+229) {
		tmp = z * -y;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.8e+229:
		tmp = z * -y
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.8e+229)
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.8e+229)
		tmp = z * -y;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.8e+229], N[(z * (-y)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.7999999999999996e229

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0 59.1%

      \[\leadsto \color{blue}{1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 59.1%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(y \cdot z\right)\right) + 1} \]

      2. associate-+l+ 59.1%

         \[\leadsto \color{blue}{x + \left(-1 \cdot \left(y \cdot z\right) + 1\right)} \]

      3. +-commutative 59.1%

         \[\leadsto x + \color{blue}{\left(1 + -1 \cdot \left(y \cdot z\right)\right)} \]

      4. mul-1-neg 59.1%

         \[\leadsto x + \left(1 + \color{blue}{\left(-y \cdot z\right)}\right) \]

      5. neg-sub0 59.1%

         \[\leadsto x + \left(1 + \color{blue}{\left(0 - y \cdot z\right)}\right) \]

      6. associate-+r- 59.1%

         \[\leadsto x + \color{blue}{\left(\left(1 + 0\right) - y \cdot z\right)} \]

      7. metadata-eval 59.1%

         \[\leadsto x + \left(\color{blue}{1} - y \cdot z\right) \]

   4. Simplified 59.1%

      \[\leadsto \color{blue}{x + \left(1 - y \cdot z\right)} \]

   5. Taylor expanded in y around inf 45.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 45.8%

         \[\leadsto \color{blue}{-y \cdot z} \]

   7. Simplified 45.8%

      \[\leadsto \color{blue}{-y \cdot z} \]

   if -7.7999999999999996e229 < z

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0 70.6%

      \[\leadsto \color{blue}{1 + x} \]
   3. Step-by-step derivation

      1. +-commutative 70.6%

         \[\leadsto \color{blue}{x + 1} \]

   4. Simplified 70.6%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+229}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 10: 59.8% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -19:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -19.0) x (if (<= x 1.25) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -19.0) {
		tmp = x;
	} else if (x <= 1.25) {
		tmp = 1.0;
	} else {
		tmp = 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) :: tmp
    if (x <= (-19.0d0)) then
        tmp = x
    else if (x <= 1.25d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -19.0) {
		tmp = x;
	} else if (x <= 1.25) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -19.0:
		tmp = x
	elif x <= 1.25:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -19.0)
		tmp = x;
	elseif (x <= 1.25)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -19.0)
		tmp = x;
	elseif (x <= 1.25)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -19.0], x, If[LessEqual[x, 1.25], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -19 or 1.25 < x

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around inf 83.9%

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

   if -19 < x < 1.25

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around 0 99.6%

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

   3. Taylor expanded in y around 0 46.1%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -19:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 60.5% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

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 + 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + \cos y\right) - z \cdot \sin y \]

2. Taylor expanded in y around 0 65.8%

   \[\leadsto \color{blue}{1 + x} \]
3. Step-by-step derivation

   1. +-commutative 65.8%

      \[\leadsto \color{blue}{x + 1} \]

4. Simplified 65.8%

   \[\leadsto \color{blue}{x + 1} \]

5. Final simplification 65.8%

   \[\leadsto x + 1 \]

Alternative 12: 21.2% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

   \[\left(x + \cos y\right) - z \cdot \sin y \]

2. Taylor expanded in x around 0 57.7%

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

3. Taylor expanded in y around 0 24.2%

   \[\leadsto \color{blue}{1} \]

4. Final simplification 24.2%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))