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

Percentage Accurate: 99.9% → 99.9%

Time: 12.0s

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: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, x\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-40}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.6e+32)
   (fma z (cos y) x)
   (if (<= z 9e-40) (+ z (+ x (sin y))) (+ x (* z (cos y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+32) {
		tmp = fma(z, cos(y), x);
	} else if (z <= 9e-40) {
		tmp = z + (x + sin(y));
	} else {
		tmp = x + (z * cos(y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.6e+32)
		tmp = fma(z, cos(y), x);
	elseif (z <= 9e-40)
		tmp = Float64(z + Float64(x + sin(y)));
	else
		tmp = Float64(x + Float64(z * cos(y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.6e+32], N[(z * N[Cos[y], $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 9e-40], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5999999999999997e32

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.7%

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

   if -3.5999999999999997e32 < z < 9.0000000000000002e-40

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.6%

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

   if 9.0000000000000002e-40 < 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 97.0%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, x\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-40}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \cos y\\ \end{array} \]
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: 73.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+167}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-258}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-223}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-204}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+115}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.65e+167)
     t_0
     (if (<= z -3.4e-258)
       (+ z x)
       (if (<= z 1.6e-223)
         (+ z (+ y x))
         (if (<= z 1.15e-204) (sin y) (if (<= z 7.2e+115) (+ z x) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.65e+167) {
		tmp = t_0;
	} else if (z <= -3.4e-258) {
		tmp = z + x;
	} else if (z <= 1.6e-223) {
		tmp = z + (y + x);
	} else if (z <= 1.15e-204) {
		tmp = sin(y);
	} else if (z <= 7.2e+115) {
		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 <= (-1.65d+167)) then
        tmp = t_0
    else if (z <= (-3.4d-258)) then
        tmp = z + x
    else if (z <= 1.6d-223) then
        tmp = z + (y + x)
    else if (z <= 1.15d-204) then
        tmp = sin(y)
    else if (z <= 7.2d+115) 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 <= -1.65e+167) {
		tmp = t_0;
	} else if (z <= -3.4e-258) {
		tmp = z + x;
	} else if (z <= 1.6e-223) {
		tmp = z + (y + x);
	} else if (z <= 1.15e-204) {
		tmp = Math.sin(y);
	} else if (z <= 7.2e+115) {
		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 <= -1.65e+167:
		tmp = t_0
	elif z <= -3.4e-258:
		tmp = z + x
	elif z <= 1.6e-223:
		tmp = z + (y + x)
	elif z <= 1.15e-204:
		tmp = math.sin(y)
	elif z <= 7.2e+115:
		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 <= -1.65e+167)
		tmp = t_0;
	elseif (z <= -3.4e-258)
		tmp = Float64(z + x);
	elseif (z <= 1.6e-223)
		tmp = Float64(z + Float64(y + x));
	elseif (z <= 1.15e-204)
		tmp = sin(y);
	elseif (z <= 7.2e+115)
		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 <= -1.65e+167)
		tmp = t_0;
	elseif (z <= -3.4e-258)
		tmp = z + x;
	elseif (z <= 1.6e-223)
		tmp = z + (y + x);
	elseif (z <= 1.15e-204)
		tmp = sin(y);
	elseif (z <= 7.2e+115)
		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, -1.65e+167], t$95$0, If[LessEqual[z, -3.4e-258], N[(z + x), $MachinePrecision], If[LessEqual[z, 1.6e-223], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-204], N[Sin[y], $MachinePrecision], If[LessEqual[z, 7.2e+115], N[(z + x), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.65000000000000009e167 or 7.2000000000000001e115 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 85.8%

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

   if -1.65000000000000009e167 < z < -3.3999999999999998e-258 or 1.15e-204 < z < 7.2000000000000001e115

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.1%

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

      1. +-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -3.3999999999999998e-258 < z < 1.6e-223

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. +-commutative 78.5%

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

      3. associate-+l+ 78.5%

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

   5. Simplified 78.5%

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

   if 1.6e-223 < z < 1.15e-204

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.4%

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

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in x around 0 84.3%

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

Alternative 5: 85.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.000245:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-39}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+118}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.7e+35)
     t_0
     (if (<= z -0.000245)
       (+ z x)
       (if (<= z 2.3e-39) (+ x (sin y)) (if (<= z 9.5e+118) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.7e+35) {
		tmp = t_0;
	} else if (z <= -0.000245) {
		tmp = z + x;
	} else if (z <= 2.3e-39) {
		tmp = x + sin(y);
	} else if (z <= 9.5e+118) {
		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 <= (-1.7d+35)) then
        tmp = t_0
    else if (z <= (-0.000245d0)) then
        tmp = z + x
    else if (z <= 2.3d-39) then
        tmp = x + sin(y)
    else if (z <= 9.5d+118) 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 <= -1.7e+35) {
		tmp = t_0;
	} else if (z <= -0.000245) {
		tmp = z + x;
	} else if (z <= 2.3e-39) {
		tmp = x + Math.sin(y);
	} else if (z <= 9.5e+118) {
		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 <= -1.7e+35:
		tmp = t_0
	elif z <= -0.000245:
		tmp = z + x
	elif z <= 2.3e-39:
		tmp = x + math.sin(y)
	elif z <= 9.5e+118:
		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 <= -1.7e+35)
		tmp = t_0;
	elseif (z <= -0.000245)
		tmp = Float64(z + x);
	elseif (z <= 2.3e-39)
		tmp = Float64(x + sin(y));
	elseif (z <= 9.5e+118)
		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 <= -1.7e+35)
		tmp = t_0;
	elseif (z <= -0.000245)
		tmp = z + x;
	elseif (z <= 2.3e-39)
		tmp = x + sin(y);
	elseif (z <= 9.5e+118)
		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, -1.7e+35], t$95$0, If[LessEqual[z, -0.000245], N[(z + x), $MachinePrecision], If[LessEqual[z, 2.3e-39], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+118], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7000000000000001e35 or 9.49999999999999974e118 < 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 82.0%

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

   if -1.7000000000000001e35 < z < -2.4499999999999999e-4 or 2.30000000000000008e-39 < z < 9.49999999999999974e118

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 83.7%

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

      1. +-commutative 83.7%

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

   5. Simplified 83.7%

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

   if -2.4499999999999999e-4 < z < 2.30000000000000008e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.3%

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

      1. +-commutative 92.3%

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

   5. Simplified 92.3%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -0.000245:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-39}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+118}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-263}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-223}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-209}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5e-263)
   (+ z x)
   (if (<= z 2.25e-223) (+ z (+ y x)) (if (<= z 2.05e-209) (sin y) (+ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e-263) {
		tmp = z + x;
	} else if (z <= 2.25e-223) {
		tmp = z + (y + x);
	} else if (z <= 2.05e-209) {
		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 (z <= (-9.5d-263)) then
        tmp = z + x
    else if (z <= 2.25d-223) then
        tmp = z + (y + x)
    else if (z <= 2.05d-209) 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 (z <= -9.5e-263) {
		tmp = z + x;
	} else if (z <= 2.25e-223) {
		tmp = z + (y + x);
	} else if (z <= 2.05e-209) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.5e-263:
		tmp = z + x
	elif z <= 2.25e-223:
		tmp = z + (y + x)
	elif z <= 2.05e-209:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5e-263)
		tmp = Float64(z + x);
	elseif (z <= 2.25e-223)
		tmp = Float64(z + Float64(y + x));
	elseif (z <= 2.05e-209)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.5e-263)
		tmp = z + x;
	elseif (z <= 2.25e-223)
		tmp = z + (y + x);
	elseif (z <= 2.05e-209)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.5e-263], N[(z + x), $MachinePrecision], If[LessEqual[z, 2.25e-223], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-209], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000005e-263 or 2.04999999999999989e-209 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 65.0%

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

      1. +-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -9.5000000000000005e-263 < z < 2.24999999999999984e-223

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. +-commutative 78.5%

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

      3. associate-+l+ 78.5%

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

   5. Simplified 78.5%

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

   if 2.24999999999999984e-223 < z < 2.04999999999999989e-209

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.4%

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

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in x around 0 84.3%

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

Alternative 7: 98.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+32} \lor \neg \left(z \leq 9 \cdot 10^{-40}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.6e+32) (not (<= z 9e-40)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e+32) || !(z <= 9e-40)) {
		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 <= (-3.6d+32)) .or. (.not. (z <= 9d-40))) 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 <= -3.6e+32) || !(z <= 9e-40)) {
		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 <= -3.6e+32) or not (z <= 9e-40):
		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 <= -3.6e+32) || !(z <= 9e-40))
		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 <= -3.6e+32) || ~((z <= 9e-40)))
		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, -3.6e+32], N[Not[LessEqual[z, 9e-40]], $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 < -3.5999999999999997e32 or 9.0000000000000002e-40 < 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 98.3%

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

   if -3.5999999999999997e32 < z < 9.0000000000000002e-40

   1. Initial program 100.0%

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

   3. 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 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+32} \lor \neg \left(z \leq 9 \cdot 10^{-40}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-19} \lor \neg \left(z \leq 1.26 \cdot 10^{-39}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.2e-19) (not (<= z 1.26e-39)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.2e-19) || !(z <= 1.26e-39)) {
		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 <= (-8.2d-19)) .or. (.not. (z <= 1.26d-39))) 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 <= -8.2e-19) || !(z <= 1.26e-39)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.2e-19) or not (z <= 1.26e-39):
		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 <= -8.2e-19) || !(z <= 1.26e-39))
		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 <= -8.2e-19) || ~((z <= 1.26e-39)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.2e-19], N[Not[LessEqual[z, 1.26e-39]], $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 < -8.1999999999999997e-19 or 1.26e-39 < 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 98.5%

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

   if -8.1999999999999997e-19 < z < 1.26e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 93.2%

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

      1. +-commutative 93.2%

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

   5. Simplified 93.2%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-19} \lor \neg \left(z \leq 1.26 \cdot 10^{-39}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.1% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+62} \lor \neg \left(y \leq 4.1 \cdot 10^{-63}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.75e+62) (not (<= y 4.1e-63))) (+ z x) (+ z (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.75e+62) || !(y <= 4.1e-63)) {
		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 <= (-1.75d+62)) .or. (.not. (y <= 4.1d-63))) 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 <= -1.75e+62) || !(y <= 4.1e-63)) {
		tmp = z + x;
	} else {
		tmp = z + (y + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.75e+62) or not (y <= 4.1e-63):
		tmp = z + x
	else:
		tmp = z + (y + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.75e+62) || !(y <= 4.1e-63))
		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 <= -1.75e+62) || ~((y <= 4.1e-63)))
		tmp = z + x;
	else
		tmp = z + (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.75e+62], N[Not[LessEqual[y, 4.1e-63]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.74999999999999992e62 or 4.0999999999999998e-63 < 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 40.9%

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

      1. +-commutative 40.9%

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

   5. Simplified 40.9%

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

   if -1.74999999999999992e62 < y < 4.0999999999999998e-63

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.4%

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

      1. +-commutative 92.4%

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

      2. +-commutative 92.4%

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

      3. associate-+l+ 92.4%

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

   5. Simplified 92.4%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+62} \lor \neg \left(y \leq 4.1 \cdot 10^{-63}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.9% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-67}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e+60) x (if (<= x 2.9e-67) (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e+60) {
		tmp = x;
	} else if (x <= 2.9e-67) {
		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 <= (-1.25d+60)) then
        tmp = x
    else if (x <= 2.9d-67) 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 <= -1.25e+60) {
		tmp = x;
	} else if (x <= 2.9e-67) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e+60:
		tmp = x
	elif x <= 2.9e-67:
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e+60)
		tmp = x;
	elseif (x <= 2.9e-67)
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.25e+60)
		tmp = x;
	elseif (x <= 2.9e-67)
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e+60], x, If[LessEqual[x, 2.9e-67], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.24999999999999994e60 or 2.90000000000000005e-67 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.7%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.7%

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

      5. pow2 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 75.4%

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

   if -1.24999999999999994e60 < x < 2.90000000000000005e-67

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 93.1%

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

   4. Taylor expanded in y around 0 45.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-67}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.8% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.1 \cdot 10^{-84}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e+60) x (if (<= x 8.1e-84) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+60) {
		tmp = x;
	} else if (x <= 8.1e-84) {
		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 <= (-2.1d+60)) then
        tmp = x
    else if (x <= 8.1d-84) 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 <= -2.1e+60) {
		tmp = x;
	} else if (x <= 8.1e-84) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e+60:
		tmp = x
	elif x <= 8.1e-84:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e+60)
		tmp = x;
	elseif (x <= 8.1e-84)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e+60)
		tmp = x;
	elseif (x <= 8.1e-84)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e+60], x, If[LessEqual[x, 8.1e-84], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e60 or 8.0999999999999997e-84 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.7%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.7%

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

      5. pow2 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 74.2%

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

   if -2.1000000000000001e60 < x < 8.0999999999999997e-84

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.4%

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

      3. associate-*r* 99.4%

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

      4. fma-define 99.4%

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

      5. pow2 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in z around inf 62.2%

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

      1. *-commutative 62.2%

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

   7. Simplified 62.2%

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

   8. Taylor expanded in y around 0 39.1%

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

Alternative 12: 66.6% 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 63.5%

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

   1. +-commutative 63.5%

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

5. Simplified 63.5%

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

Alternative 13: 42.2% 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. add-cube-cbrt 99.6%

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

   3. associate-*r* 99.5%

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

   4. fma-define 99.5%

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

   5. pow2 99.5%

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

4. Applied egg-rr 99.5%

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

5. Taylor expanded in x around inf 40.4%

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

Reproduce

herbie shell --seed 2024107 
(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))))