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

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 13

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-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6500:\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{elif}\;z \leq 0.75:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6500.0)
   (+ x (* z (cos y)))
   (if (<= z 0.75) (+ z (+ x (sin y))) (fma z (cos y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6500.0) {
		tmp = x + (z * cos(y));
	} else if (z <= 0.75) {
		tmp = z + (x + sin(y));
	} else {
		tmp = fma(z, cos(y), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6500.0)
		tmp = Float64(x + Float64(z * cos(y)));
	elseif (z <= 0.75)
		tmp = Float64(z + Float64(x + sin(y)));
	else
		tmp = fma(z, cos(y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6500.0], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.75], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6500

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 98.7%

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

   if -6500 < z < 0.75

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.7%

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

   if 0.75 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 99.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500:\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{elif}\;z \leq 0.75:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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]

Derivation

1. Initial program 99.9%

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

Alternative 4: 84.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+99}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-132}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+165}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.8e+99)
     t_0
     (if (<= z -3.2e-44)
       (+ z x)
       (if (<= z 4.2e-132) (+ x (sin y)) (if (<= z 3.5e+165) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.8e+99) {
		tmp = t_0;
	} else if (z <= -3.2e-44) {
		tmp = z + x;
	} else if (z <= 4.2e-132) {
		tmp = x + sin(y);
	} else if (z <= 3.5e+165) {
		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 <= (-2.8d+99)) then
        tmp = t_0
    else if (z <= (-3.2d-44)) then
        tmp = z + x
    else if (z <= 4.2d-132) then
        tmp = x + sin(y)
    else if (z <= 3.5d+165) 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 <= -2.8e+99) {
		tmp = t_0;
	} else if (z <= -3.2e-44) {
		tmp = z + x;
	} else if (z <= 4.2e-132) {
		tmp = x + Math.sin(y);
	} else if (z <= 3.5e+165) {
		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 <= -2.8e+99:
		tmp = t_0
	elif z <= -3.2e-44:
		tmp = z + x
	elif z <= 4.2e-132:
		tmp = x + math.sin(y)
	elif z <= 3.5e+165:
		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 <= -2.8e+99)
		tmp = t_0;
	elseif (z <= -3.2e-44)
		tmp = Float64(z + x);
	elseif (z <= 4.2e-132)
		tmp = Float64(x + sin(y));
	elseif (z <= 3.5e+165)
		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 <= -2.8e+99)
		tmp = t_0;
	elseif (z <= -3.2e-44)
		tmp = z + x;
	elseif (z <= 4.2e-132)
		tmp = x + sin(y);
	elseif (z <= 3.5e+165)
		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, -2.8e+99], t$95$0, If[LessEqual[z, -3.2e-44], N[(z + x), $MachinePrecision], If[LessEqual[z, 4.2e-132], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+165], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e99 or 3.49999999999999996e165 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 86.5%

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

   if -2.8e99 < z < -3.19999999999999995e-44 or 4.2000000000000002e-132 < z < 3.49999999999999996e165

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.0%

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

      1. +-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -3.19999999999999995e-44 < z < 4.2000000000000002e-132

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.8%

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

      1. +-commutative 94.8%

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

   5. Simplified 94.8%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-132}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+165}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-16}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-106}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-58}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.4e-16)
   (+ z x)
   (if (<= x 6.2e-106) (* z (cos y)) (if (<= x 2.5e-58) (sin y) (+ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.4e-16) {
		tmp = z + x;
	} else if (x <= 6.2e-106) {
		tmp = z * cos(y);
	} else if (x <= 2.5e-58) {
		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 (x <= (-7.4d-16)) then
        tmp = z + x
    else if (x <= 6.2d-106) then
        tmp = z * cos(y)
    else if (x <= 2.5d-58) 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 (x <= -7.4e-16) {
		tmp = z + x;
	} else if (x <= 6.2e-106) {
		tmp = z * Math.cos(y);
	} else if (x <= 2.5e-58) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.4e-16:
		tmp = z + x
	elif x <= 6.2e-106:
		tmp = z * math.cos(y)
	elif x <= 2.5e-58:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.4e-16)
		tmp = Float64(z + x);
	elseif (x <= 6.2e-106)
		tmp = Float64(z * cos(y));
	elseif (x <= 2.5e-58)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.4e-16)
		tmp = z + x;
	elseif (x <= 6.2e-106)
		tmp = z * cos(y);
	elseif (x <= 2.5e-58)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.4e-16], N[(z + x), $MachinePrecision], If[LessEqual[x, 6.2e-106], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-58], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.3999999999999999e-16 or 2.49999999999999989e-58 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 85.6%

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

      1. +-commutative 85.6%

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

   5. Simplified 85.6%

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

   if -7.3999999999999999e-16 < x < 6.19999999999999971e-106

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 68.0%

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

   if 6.19999999999999971e-106 < x < 2.49999999999999989e-58

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in z around 0 74.0%

      \[\leadsto \color{blue}{\sin y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 69.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+14}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-113}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-58}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.85e+14)
   (+ z x)
   (if (<= x 2e-113) (+ z (+ y x)) (if (<= x 4.3e-58) (sin y) (+ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.85e+14) {
		tmp = z + x;
	} else if (x <= 2e-113) {
		tmp = z + (y + x);
	} else if (x <= 4.3e-58) {
		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 (x <= (-1.85d+14)) then
        tmp = z + x
    else if (x <= 2d-113) then
        tmp = z + (y + x)
    else if (x <= 4.3d-58) 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 (x <= -1.85e+14) {
		tmp = z + x;
	} else if (x <= 2e-113) {
		tmp = z + (y + x);
	} else if (x <= 4.3e-58) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.85e+14:
		tmp = z + x
	elif x <= 2e-113:
		tmp = z + (y + x)
	elif x <= 4.3e-58:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.85e+14)
		tmp = Float64(z + x);
	elseif (x <= 2e-113)
		tmp = Float64(z + Float64(y + x));
	elseif (x <= 4.3e-58)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.85e+14)
		tmp = z + x;
	elseif (x <= 2e-113)
		tmp = z + (y + x);
	elseif (x <= 4.3e-58)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.85e+14], N[(z + x), $MachinePrecision], If[LessEqual[x, 2e-113], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e-58], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85e14 or 4.2999999999999999e-58 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 85.1%

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

      1. +-commutative 85.1%

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

   5. Simplified 85.1%

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

   if -1.85e14 < x < 1.99999999999999996e-113

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 52.2%

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

      1. +-commutative 52.2%

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

      2. +-commutative 52.2%

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

      3. associate-+l+ 52.2%

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

   5. Simplified 52.2%

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

   if 1.99999999999999996e-113 < x < 4.2999999999999999e-58

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in z around 0 68.2%

      \[\leadsto \color{blue}{\sin y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 99.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6500 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6500.0) (not (<= z 0.65)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6500.0) || !(z <= 0.65)) {
		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 <= (-6500.0d0)) .or. (.not. (z <= 0.65d0))) 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 <= -6500.0) || !(z <= 0.65)) {
		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 <= -6500.0) or not (z <= 0.65):
		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 <= -6500.0) || !(z <= 0.65))
		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 <= -6500.0) || ~((z <= 0.65)))
		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, -6500.0], N[Not[LessEqual[z, 0.65]], $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 < -6500 or 0.650000000000000022 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.2%

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

   if -6500 < z < 0.650000000000000022

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-38} \lor \neg \left(z \leq 1.46 \cdot 10^{-137}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.6e-38) (not (<= z 1.46e-137)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e-38) || !(z <= 1.46e-137)) {
		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 <= (-4.6d-38)) .or. (.not. (z <= 1.46d-137))) 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 <= -4.6e-38) || !(z <= 1.46e-137)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.6e-38) or not (z <= 1.46e-137):
		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 <= -4.6e-38) || !(z <= 1.46e-137))
		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 <= -4.6e-38) || ~((z <= 1.46e-137)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.6e-38], N[Not[LessEqual[z, 1.46e-137]], $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 < -4.60000000000000003e-38 or 1.46e-137 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 94.1%

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

   if -4.60000000000000003e-38 < z < 1.46e-137

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.8%

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

      1. +-commutative 94.8%

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

   5. Simplified 94.8%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-38} \lor \neg \left(z \leq 1.46 \cdot 10^{-137}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+16} \lor \neg \left(y \leq 1900000000000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e+16) (not (<= y 1900000000000.0)))
   (+ z x)
   (+ (+ z x) (* y (+ 1.0 (* -0.5 (* z y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+16) || !(y <= 1900000000000.0)) {
		tmp = z + x;
	} else {
		tmp = (z + x) + (y * (1.0 + (-0.5 * (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 <= (-3d+16)) .or. (.not. (y <= 1900000000000.0d0))) then
        tmp = z + x
    else
        tmp = (z + x) + (y * (1.0d0 + ((-0.5d0) * (z * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+16) || !(y <= 1900000000000.0)) {
		tmp = z + x;
	} else {
		tmp = (z + x) + (y * (1.0 + (-0.5 * (z * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e+16) or not (y <= 1900000000000.0):
		tmp = z + x
	else:
		tmp = (z + x) + (y * (1.0 + (-0.5 * (z * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e+16) || !(y <= 1900000000000.0))
		tmp = Float64(z + x);
	else
		tmp = Float64(Float64(z + x) + Float64(y * Float64(1.0 + Float64(-0.5 * Float64(z * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3e+16) || ~((y <= 1900000000000.0)))
		tmp = z + x;
	else
		tmp = (z + x) + (y * (1.0 + (-0.5 * (z * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e+16], N[Not[LessEqual[y, 1900000000000.0]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + N[(y * N[(1.0 + N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e16 or 1.9e12 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 37.4%

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

      1. +-commutative 37.4%

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

   5. Simplified 37.4%

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

   if -3e16 < y < 1.9e12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ 97.3%

         \[\leadsto \color{blue}{\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)} \]

      2. +-commutative 97.3%

         \[\leadsto \color{blue}{\left(z + x\right)} + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right) \]

      3. *-commutative 97.3%

         \[\leadsto \left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \color{blue}{\left(z \cdot y\right)}\right) \]

   5. Simplified 97.3%

      \[\leadsto \color{blue}{\left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+16} \lor \neg \left(y \leq 1900000000000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.1% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+31} \lor \neg \left(y \leq 8.2 \cdot 10^{+15}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.55e+31) (not (<= y 8.2e+15))) (+ z x) (+ z (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.55e+31) || !(y <= 8.2e+15)) {
		tmp = z + x;
	} else {
		tmp = z + (y + 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 <= (-3.55d+31)) .or. (.not. (y <= 8.2d+15))) then
        tmp = z + x
    else
        tmp = z + (y + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.55e+31) || !(y <= 8.2e+15)) {
		tmp = z + x;
	} else {
		tmp = z + (y + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.55e+31) or not (y <= 8.2e+15):
		tmp = z + x
	else:
		tmp = z + (y + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.55e+31) || !(y <= 8.2e+15))
		tmp = Float64(z + x);
	else
		tmp = Float64(z + Float64(y + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.55e+31) || ~((y <= 8.2e+15)))
		tmp = z + x;
	else
		tmp = z + (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.55e+31], N[Not[LessEqual[y, 8.2e+15]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5499999999999998e31 or 8.2e15 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 37.9%

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

      1. +-commutative 37.9%

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

   5. Simplified 37.9%

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

   if -3.5499999999999998e31 < y < 8.2e15

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.9%

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

      1. +-commutative 93.9%

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

      2. +-commutative 93.9%

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

      3. associate-+l+ 93.9%

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

   5. Simplified 93.9%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+31} \lor \neg \left(y \leq 8.2 \cdot 10^{+15}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.1% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.18:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.6e-40) x (if (<= x 0.18) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.6e-40) {
		tmp = x;
	} else if (x <= 0.18) {
		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 <= (-5.6d-40)) then
        tmp = x
    else if (x <= 0.18d0) 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 <= -5.6e-40) {
		tmp = x;
	} else if (x <= 0.18) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.6e-40:
		tmp = x
	elif x <= 0.18:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.6e-40)
		tmp = x;
	elseif (x <= 0.18)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.6e-40)
		tmp = x;
	elseif (x <= 0.18)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.6e-40], x, If[LessEqual[x, 0.18], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5999999999999999e-40 or 0.17999999999999999 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. distribute-rgt-neg-in 80.7%

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

      3. distribute-lft-out 80.7%

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

      4. mul-1-neg 80.7%

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

      5. remove-double-neg 80.7%

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

      6. +-commutative 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in x around inf 80.2%

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

   if -5.5999999999999999e-40 < x < 0.17999999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 45.4%

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

      1. +-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in z around inf 39.8%

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

Alternative 12: 67.0% 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. Add Preprocessing

3. Taylor expanded in y around 0 64.2%

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

   1. +-commutative 64.2%

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

5. Simplified 64.2%

   \[\leadsto \color{blue}{z + x} \]
6. Add Preprocessing

Alternative 13: 43.9% 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. Add Preprocessing

3. Taylor expanded in z around -inf 91.0%

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

   1. mul-1-neg 91.0%

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

   2. distribute-rgt-neg-in 91.0%

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

   3. distribute-lft-out 91.0%

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

   4. mul-1-neg 91.0%

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

   5. remove-double-neg 91.0%

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

   6. +-commutative 91.0%

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

5. Simplified 91.0%

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

6. Taylor expanded in x around inf 41.2%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024116 
(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))))