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

Percentage Accurate: 99.9% → 99.9%

Time: 8.7s

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 3: 85.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+120}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-14}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-26}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+111}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -4.4e+120)
     t_0
     (if (<= z -5.5e-14)
       (+ z x)
       (if (<= z 3.6e-26) (+ x (sin y)) (if (<= z 2.2e+111) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -4.4e+120) {
		tmp = t_0;
	} else if (z <= -5.5e-14) {
		tmp = z + x;
	} else if (z <= 3.6e-26) {
		tmp = x + sin(y);
	} else if (z <= 2.2e+111) {
		tmp = z + x;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-4.4d+120)) then
        tmp = t_0
    else if (z <= (-5.5d-14)) then
        tmp = z + x
    else if (z <= 3.6d-26) then
        tmp = x + sin(y)
    else if (z <= 2.2d+111) then
        tmp = z + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -4.4e+120) {
		tmp = t_0;
	} else if (z <= -5.5e-14) {
		tmp = z + x;
	} else if (z <= 3.6e-26) {
		tmp = x + Math.sin(y);
	} else if (z <= 2.2e+111) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -4.4e+120:
		tmp = t_0
	elif z <= -5.5e-14:
		tmp = z + x
	elif z <= 3.6e-26:
		tmp = x + math.sin(y)
	elif z <= 2.2e+111:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -4.4e+120)
		tmp = t_0;
	elseif (z <= -5.5e-14)
		tmp = Float64(z + x);
	elseif (z <= 3.6e-26)
		tmp = Float64(x + sin(y));
	elseif (z <= 2.2e+111)
		tmp = Float64(z + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -4.4e+120)
		tmp = t_0;
	elseif (z <= -5.5e-14)
		tmp = z + x;
	elseif (z <= 3.6e-26)
		tmp = x + sin(y);
	elseif (z <= 2.2e+111)
		tmp = z + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+120], t$95$0, If[LessEqual[z, -5.5e-14], N[(z + x), $MachinePrecision], If[LessEqual[z, 3.6e-26], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+111], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4000000000000003e120 or 2.19999999999999999e111 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 90.9%

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

   if -4.4000000000000003e120 < z < -5.49999999999999991e-14 or 3.6000000000000001e-26 < z < 2.19999999999999999e111

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.6%

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

      1. +-commutative 76.6%

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

   4. Simplified 76.6%

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

   if -5.49999999999999991e-14 < z < 3.6000000000000001e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 93.4%

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

      1. +-commutative 93.4%

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

   4. Simplified 93.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-14}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-26}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+111}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 4: 95.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-7} \lor \neg \left(z \leq 2.7 \cdot 10^{-26}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.3e-7) (not (<= z 2.7e-26)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e-7) || !(z <= 2.7e-26)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = x + sin(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 <= (-2.3d-7)) .or. (.not. (z <= 2.7d-26))) then
        tmp = x + (z * cos(y))
    else
        tmp = x + sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e-7) || !(z <= 2.7e-26)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.3e-7) or not (z <= 2.7e-26):
		tmp = x + (z * math.cos(y))
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.3e-7) || !(z <= 2.7e-26))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.3e-7) || ~((z <= 2.7e-26)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.3e-7], N[Not[LessEqual[z, 2.7e-26]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999995e-7 or 2.69999999999999982e-26 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 98.3%

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

   if -2.29999999999999995e-7 < z < 2.69999999999999982e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 93.4%

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

      1. +-commutative 93.4%

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

   4. Simplified 93.4%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-7} \lor \neg \left(z \leq 2.7 \cdot 10^{-26}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 5: 99.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \lor \neg \left(z \leq 0.05\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5) (not (<= z 0.05)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5) || !(z <= 0.05)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = z + (x + sin(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 <= (-1.5d0)) .or. (.not. (z <= 0.05d0))) then
        tmp = x + (z * cos(y))
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5) || !(z <= 0.05)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5) or not (z <= 0.05):
		tmp = x + (z * math.cos(y))
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5) || !(z <= 0.05))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.5) || ~((z <= 0.05)))
		tmp = x + (z * cos(y));
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5], N[Not[LessEqual[z, 0.05]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5 or 0.050000000000000003 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 98.9%

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

   if -1.5 < z < 0.050000000000000003

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \lor \neg \left(z \leq 0.05\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 6: 66.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+135}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+51}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+181}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.8e+135)
   (sin y)
   (if (<= y 2.8e+51) (+ y (+ z x)) (if (<= y 1.2e+181) (sin y) (+ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e+135) {
		tmp = sin(y);
	} else if (y <= 2.8e+51) {
		tmp = y + (z + x);
	} else if (y <= 1.2e+181) {
		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) :: tmp
    if (y <= (-9.8d+135)) then
        tmp = sin(y)
    else if (y <= 2.8d+51) then
        tmp = y + (z + x)
    else if (y <= 1.2d+181) 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 tmp;
	if (y <= -9.8e+135) {
		tmp = Math.sin(y);
	} else if (y <= 2.8e+51) {
		tmp = y + (z + x);
	} else if (y <= 1.2e+181) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.8e+135:
		tmp = math.sin(y)
	elif y <= 2.8e+51:
		tmp = y + (z + x)
	elif y <= 1.2e+181:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.8e+135)
		tmp = sin(y);
	elseif (y <= 2.8e+51)
		tmp = Float64(y + Float64(z + x));
	elseif (y <= 1.2e+181)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.8e+135)
		tmp = sin(y);
	elseif (y <= 2.8e+51)
		tmp = y + (z + x);
	elseif (y <= 1.2e+181)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.8e+135], N[Sin[y], $MachinePrecision], If[LessEqual[y, 2.8e+51], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+181], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.8000000000000002e135 or 2.80000000000000005e51 < y < 1.20000000000000001e181

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 59.2%

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

      1. +-commutative 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in x around 0 35.5%

      \[\leadsto \color{blue}{\sin y} \]

   if -9.8000000000000002e135 < y < 2.80000000000000005e51

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 84.6%

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

      1. +-commutative 84.6%

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

      2. associate-+l+ 84.6%

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

   4. Simplified 84.6%

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

   if 1.20000000000000001e181 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 41.8%

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

      1. +-commutative 41.8%

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

   4. Simplified 41.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+135}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+51}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+181}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 7: 73.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+121} \lor \neg \left(z \leq 7 \cdot 10^{+107}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e+121) (not (<= z 7e+107))) (* z (cos y)) (+ z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+121) || !(z <= 7e+107)) {
		tmp = z * cos(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) :: tmp
    if ((z <= (-1.5d+121)) .or. (.not. (z <= 7d+107))) then
        tmp = z * cos(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+121) || !(z <= 7e+107)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e+121) or not (z <= 7e+107):
		tmp = z * math.cos(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e+121) || !(z <= 7e+107))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.5e+121) || ~((z <= 7e+107)))
		tmp = z * cos(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e+121], N[Not[LessEqual[z, 7e+107]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5000000000000001e121 or 6.9999999999999995e107 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 90.9%

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

   if -1.5000000000000001e121 < z < 6.9999999999999995e107

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 68.1%

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

      1. +-commutative 68.1%

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

   4. Simplified 68.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+121} \lor \neg \left(z \leq 7 \cdot 10^{+107}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 8: 70.6% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+21} \lor \neg \left(y \leq 3.1\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;y + \left(z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.6e+21) (not (<= y 3.1))) (+ z x) (+ y (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e+21) || !(y <= 3.1)) {
		tmp = z + x;
	} else {
		tmp = y + (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) :: tmp
    if ((y <= (-6.6d+21)) .or. (.not. (y <= 3.1d0))) then
        tmp = z + x
    else
        tmp = y + (z + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e+21) || !(y <= 3.1)) {
		tmp = z + x;
	} else {
		tmp = y + (z + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.6e+21) or not (y <= 3.1):
		tmp = z + x
	else:
		tmp = y + (z + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.6e+21) || !(y <= 3.1))
		tmp = Float64(z + x);
	else
		tmp = Float64(y + Float64(z + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.6e+21) || ~((y <= 3.1)))
		tmp = z + x;
	else
		tmp = y + (z + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.6e+21], N[Not[LessEqual[y, 3.1]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6e21 or 3.10000000000000009 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 30.6%

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

      1. +-commutative 30.6%

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

   4. Simplified 30.6%

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

   if -6.6e21 < y < 3.10000000000000009

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-+l+ 96.6%

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

   4. Simplified 96.6%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+21} \lor \neg \left(y \leq 3.1\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;y + \left(z + x\right)\\ \end{array} \]

Alternative 9: 57.3% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+74}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7e-16) x (if (<= x 8e+74) (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e-16) {
		tmp = x;
	} else if (x <= 8e+74) {
		tmp = z + y;
	} 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 <= (-7d-16)) then
        tmp = x
    else if (x <= 8d+74) then
        tmp = z + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e-16) {
		tmp = x;
	} else if (x <= 8e+74) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7e-16:
		tmp = x
	elif x <= 8e+74:
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7e-16)
		tmp = x;
	elseif (x <= 8e+74)
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7e-16)
		tmp = x;
	elseif (x <= 8e+74)
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7e-16], x, If[LessEqual[x, 8e+74], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.00000000000000035e-16 or 7.99999999999999961e74 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.5%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \cdot \cos y + \left(x + \sin y\right) \]

      3. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \cos y\right)} + \left(x + \sin y\right) \]

      4. fma-def 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{z} \cdot \sqrt[3]{z}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right)} \]

      5. pow2 99.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right) \]

      6. +-commutative 99.5%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \cos y, \color{blue}{\sin y + x}\right) \]

   3. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \cos y, \sin y + x\right)} \]

   4. Taylor expanded in x around inf 75.2%

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

   if -7.00000000000000035e-16 < x < 7.99999999999999961e74

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.1%

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

   3. Taylor expanded in y around 0 42.2%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+74}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 53.9% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+74}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -6e-13) x (if (<= x 8e+74) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6e-13) {
		tmp = x;
	} else if (x <= 8e+74) {
		tmp = z;
	} 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 <= (-6d-13)) then
        tmp = x
    else if (x <= 8d+74) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6e-13) {
		tmp = x;
	} else if (x <= 8e+74) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6e-13:
		tmp = x
	elif x <= 8e+74:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6e-13)
		tmp = x;
	elseif (x <= 8e+74)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6e-13)
		tmp = x;
	elseif (x <= 8e+74)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6e-13], x, If[LessEqual[x, 8e+74], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.99999999999999968e-13 or 7.99999999999999961e74 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.5%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \cdot \cos y + \left(x + \sin y\right) \]

      3. associate-*l* 99.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \cos y\right)} + \left(x + \sin y\right) \]

      4. fma-def 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{z} \cdot \sqrt[3]{z}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right)} \]

      5. pow2 99.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right) \]

      6. +-commutative 99.5%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \cos y, \color{blue}{\sin y + x}\right) \]

   3. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \cos y, \sin y + x\right)} \]

   4. Taylor expanded in x around inf 75.8%

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

   if -5.99999999999999968e-13 < x < 7.99999999999999961e74

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.1%

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

   3. Taylor expanded in y around 0 37.6%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+74}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 66.3% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 62.8%

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

   1. +-commutative 62.8%

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

4. Simplified 62.8%

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

5. Final simplification 62.8%

   \[\leadsto z + x \]

Alternative 12: 43.0% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. add-cube-cbrt 99.0%

      \[\leadsto \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \cdot \cos y + \left(x + \sin y\right) \]

   3. associate-*l* 99.0%

      \[\leadsto \color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \cos y\right)} + \left(x + \sin y\right) \]

   4. fma-def 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{z} \cdot \sqrt[3]{z}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right)} \]

   5. pow2 99.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right) \]

   6. +-commutative 99.0%

      \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \cos y, \color{blue}{\sin y + x}\right) \]

3. Applied egg-rr 99.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \cos y, \sin y + x\right)} \]

4. Taylor expanded in x around inf 39.4%

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

5. Final simplification 39.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023320 
(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))))