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

Percentage Accurate: 99.9% → 99.9%

Time: 9.8s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 2: 99.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -1850000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.25:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (cos y)))))
   (if (<= z -1850000.0) t_0 (if (<= z 1.25) (+ z (+ x (sin y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z * cos(y));
	double tmp;
	if (z <= -1850000.0) {
		tmp = t_0;
	} else if (z <= 1.25) {
		tmp = z + (x + sin(y));
	} 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 = x + (z * cos(y))
    if (z <= (-1850000.0d0)) then
        tmp = t_0
    else if (z <= 1.25d0) then
        tmp = z + (x + sin(y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (z * Math.cos(y));
	double tmp;
	if (z <= -1850000.0) {
		tmp = t_0;
	} else if (z <= 1.25) {
		tmp = z + (x + Math.sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z * math.cos(y))
	tmp = 0
	if z <= -1850000.0:
		tmp = t_0
	elif z <= 1.25:
		tmp = z + (x + math.sin(y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(z * cos(y)))
	tmp = 0.0
	if (z <= -1850000.0)
		tmp = t_0;
	elseif (z <= 1.25)
		tmp = Float64(z + Float64(x + sin(y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (z * cos(y));
	tmp = 0.0;
	if (z <= -1850000.0)
		tmp = t_0;
	elseif (z <= 1.25)
		tmp = z + (x + sin(y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1850000.0], t$95$0, If[LessEqual[z, 1.25], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e6 or 1.25 < 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

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 99.1%

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

   if -1.85e6 < z < 1.25

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \color{blue}{z}\right) \]
   4. Step-by-step derivation

   5. Simplified 99.6%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850000:\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{elif}\;z \leq 1.25:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-17}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (cos y)))))
   (if (<= z -7.5e-38) t_0 (if (<= z 1.85e-17) (+ x (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z * cos(y));
	double tmp;
	if (z <= -7.5e-38) {
		tmp = t_0;
	} else if (z <= 1.85e-17) {
		tmp = x + sin(y);
	} 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 = x + (z * cos(y))
    if (z <= (-7.5d-38)) then
        tmp = t_0
    else if (z <= 1.85d-17) then
        tmp = x + sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (z * Math.cos(y));
	double tmp;
	if (z <= -7.5e-38) {
		tmp = t_0;
	} else if (z <= 1.85e-17) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z * math.cos(y))
	tmp = 0
	if z <= -7.5e-38:
		tmp = t_0
	elif z <= 1.85e-17:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(z * cos(y)))
	tmp = 0.0
	if (z <= -7.5e-38)
		tmp = t_0;
	elseif (z <= 1.85e-17)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (z * cos(y));
	tmp = 0.0;
	if (z <= -7.5e-38)
		tmp = t_0;
	elseif (z <= 1.85e-17)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-38], t$95$0, If[LessEqual[z, 1.85e-17], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e-38 or 1.8499999999999999e-17 < 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

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 97.9%

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

   if -7.5e-38 < z < 1.8499999999999999e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 95.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 95.8%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-38}:\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-17}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -190000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 128000:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -190000000.0) t_0 (if (<= z 128000.0) (+ x (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -190000000.0) {
		tmp = t_0;
	} else if (z <= 128000.0) {
		tmp = x + sin(y);
	} 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 <= (-190000000.0d0)) then
        tmp = t_0
    else if (z <= 128000.0d0) then
        tmp = x + sin(y)
    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 <= -190000000.0) {
		tmp = t_0;
	} else if (z <= 128000.0) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -190000000.0:
		tmp = t_0
	elif z <= 128000.0:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -190000000.0)
		tmp = t_0;
	elseif (z <= 128000.0)
		tmp = Float64(x + sin(y));
	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 <= -190000000.0)
		tmp = t_0;
	elseif (z <= 128000.0)
		tmp = x + sin(y);
	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, -190000000.0], t$95$0, If[LessEqual[z, 128000.0], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e8 or 128000 < 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

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right) \]

      2. cos-lowering-cos.f64 76.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right) \]

   5. Simplified 76.8%

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

   if -1.9e8 < z < 128000

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 93.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 93.3%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -190000000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 128000:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-53}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.4e-53) (+ x z) (if (<= x 1.95e-7) (* z (cos y)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e-53) {
		tmp = x + z;
	} else if (x <= 1.95e-7) {
		tmp = z * cos(y);
	} else {
		tmp = x + z;
	}
	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 <= (-2.4d-53)) then
        tmp = x + z
    else if (x <= 1.95d-7) then
        tmp = z * cos(y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e-53) {
		tmp = x + z;
	} else if (x <= 1.95e-7) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.4e-53:
		tmp = x + z
	elif x <= 1.95e-7:
		tmp = z * math.cos(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.4e-53)
		tmp = Float64(x + z);
	elseif (x <= 1.95e-7)
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.4e-53)
		tmp = x + z;
	elseif (x <= 1.95e-7)
		tmp = z * cos(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.4e-53], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.95e-7], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.40000000000000007e-53 or 1.95000000000000012e-7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 87.1%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 87.1%

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

   if -2.40000000000000007e-53 < x < 1.95000000000000012e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right) \]

      2. cos-lowering-cos.f64 62.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right) \]

   5. Simplified 62.2%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-53}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -215000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 0.0115:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 + y \cdot \left(y \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -215000000.0)
   (+ x z)
   (if (<= y 0.0115) (+ (+ x y) (* z (+ 1.0 (* y (* y -0.5))))) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -215000000.0) {
		tmp = x + z;
	} else if (y <= 0.0115) {
		tmp = (x + y) + (z * (1.0 + (y * (y * -0.5))));
	} else {
		tmp = x + z;
	}
	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 <= (-215000000.0d0)) then
        tmp = x + z
    else if (y <= 0.0115d0) then
        tmp = (x + y) + (z * (1.0d0 + (y * (y * (-0.5d0)))))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -215000000.0) {
		tmp = x + z;
	} else if (y <= 0.0115) {
		tmp = (x + y) + (z * (1.0 + (y * (y * -0.5))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -215000000.0:
		tmp = x + z
	elif y <= 0.0115:
		tmp = (x + y) + (z * (1.0 + (y * (y * -0.5))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -215000000.0)
		tmp = Float64(x + z);
	elseif (y <= 0.0115)
		tmp = Float64(Float64(x + y) + Float64(z * Float64(1.0 + Float64(y * Float64(y * -0.5)))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -215000000.0)
		tmp = x + z;
	elseif (y <= 0.0115)
		tmp = (x + y) + (z * (1.0 + (y * (y * -0.5))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -215000000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 0.0115], N[(N[(x + y), $MachinePrecision] + N[(z * N[(1.0 + N[(y * N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15e8 or 0.0115 < 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

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 38.1%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 38.1%

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

   if -2.15e8 < y < 0.0115

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto x + \left(z + \left(1 \cdot y + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) \cdot y}\right)\right) \]

      2. *-lft-identity N/A

         \[\leadsto x + \left(z + \left(y + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right)} \cdot y\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto x + \left(\left(z + y\right) + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) \cdot y}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(y + z\right) + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right)} \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(y + z\right) + \left(\frac{-1}{2} \cdot \left(z \cdot y\right)\right) \cdot y\right) \]

      6. associate-*r* N/A

         \[\leadsto x + \left(\left(y + z\right) + \left(\left(\frac{-1}{2} \cdot z\right) \cdot y\right) \cdot y\right) \]

      7. associate-*r* N/A

         \[\leadsto x + \left(\left(y + z\right) + \left(\frac{-1}{2} \cdot z\right) \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      8. unpow2 N/A

         \[\leadsto x + \left(\left(y + z\right) + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{\color{blue}{2}}\right) \]

      9. associate-+r+ N/A

         \[\leadsto x + \left(y + \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(x + y\right) + \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)} \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)}\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y + x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \left({y}^{2} \cdot \color{blue}{z}\right)\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(1 \cdot z + \color{blue}{\frac{-1}{2}} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(1 \cdot z + \left(\frac{-1}{2} \cdot {y}^{2}\right) \cdot \color{blue}{z}\right)\right) \]

      18. distribute-rgt-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z \cdot \color{blue}{\left(1 + \frac{-1}{2} \cdot {y}^{2}\right)}\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 + \frac{-1}{2} \cdot {y}^{2}\right)}\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{2} \cdot {y}^{2}\right)}\right)\right)\right) \]

      21. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \left(\frac{-1}{2} \cdot \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

   5. Simplified 98.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -215000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 0.0115:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 + y \cdot \left(y \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.0% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+21}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 0.000125:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.6e+21) (+ x z) (if (<= y 0.000125) (+ z (+ x y)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.6e+21) {
		tmp = x + z;
	} else if (y <= 0.000125) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	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 <= (-7.6d+21)) then
        tmp = x + z
    else if (y <= 0.000125d0) then
        tmp = z + (x + y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.6e+21) {
		tmp = x + z;
	} else if (y <= 0.000125) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.6e+21:
		tmp = x + z
	elif y <= 0.000125:
		tmp = z + (x + y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.6e+21)
		tmp = Float64(x + z);
	elseif (y <= 0.000125)
		tmp = Float64(z + Float64(x + y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.6e+21)
		tmp = x + z;
	elseif (y <= 0.000125)
		tmp = z + (x + y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.6e+21], N[(x + z), $MachinePrecision], If[LessEqual[y, 0.000125], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.6e21 or 1.25e-4 < 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

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 37.2%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 37.2%

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

   if -7.6e21 < y < 1.25e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + y\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(y + \color{blue}{x}\right)\right) \]

      5. +-lowering-+.f64 97.4%

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 97.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+21}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 0.000125:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.2% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-161}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-54}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.75e-161) (+ x z) (if (<= x 4.5e-54) (+ y z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e-161) {
		tmp = x + z;
	} else if (x <= 4.5e-54) {
		tmp = y + z;
	} else {
		tmp = x + z;
	}
	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 <= (-1.75d-161)) then
        tmp = x + z
    else if (x <= 4.5d-54) then
        tmp = y + z
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e-161) {
		tmp = x + z;
	} else if (x <= 4.5e-54) {
		tmp = y + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.75e-161:
		tmp = x + z
	elif x <= 4.5e-54:
		tmp = y + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.75e-161)
		tmp = Float64(x + z);
	elseif (x <= 4.5e-54)
		tmp = Float64(y + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.75e-161)
		tmp = x + z;
	elseif (x <= 4.5e-54)
		tmp = y + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.75e-161], N[(x + z), $MachinePrecision], If[LessEqual[x, 4.5e-54], N[(y + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7500000000000001e-161 or 4.4999999999999998e-54 < 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

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 76.1%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 76.1%

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

   if -1.7500000000000001e-161 < x < 4.4999999999999998e-54

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{\left(z \cdot \cos y\right)}\right) \]

      2. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \left(\color{blue}{z} \cdot \cos y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right)\right) \]

      4. cos-lowering-cos.f64 98.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 52.3%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{y}\right) \]

   8. Simplified 52.3%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-161}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-54}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.0% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -420:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-66}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -420.0) x (if (<= x 1.5e-66) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -420.0) {
		tmp = x;
	} else if (x <= 1.5e-66) {
		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 <= (-420.0d0)) then
        tmp = x
    else if (x <= 1.5d-66) 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 <= -420.0) {
		tmp = x;
	} else if (x <= 1.5e-66) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -420.0:
		tmp = x
	elif x <= 1.5e-66:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -420.0)
		tmp = x;
	elseif (x <= 1.5e-66)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -420.0)
		tmp = x;
	elseif (x <= 1.5e-66)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -420.0], x, If[LessEqual[x, 1.5e-66], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -420 or 1.5000000000000001e-66 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 71.1%

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

   if -420 < x < 1.5000000000000001e-66

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{\left(z \cdot \cos y\right)}\right) \]

      2. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \left(\color{blue}{z} \cdot \cos y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right)\right) \]

      4. cos-lowering-cos.f64 94.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   5. Simplified 94.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 34.4%

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

Alternative 10: 44.7% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-64}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.2e-162) x (if (<= x 5.5e-64) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.2e-162) {
		tmp = x;
	} else if (x <= 5.5e-64) {
		tmp = 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 <= (-6.2d-162)) then
        tmp = x
    else if (x <= 5.5d-64) then
        tmp = 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 <= -6.2e-162) {
		tmp = x;
	} else if (x <= 5.5e-64) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.2e-162:
		tmp = x
	elif x <= 5.5e-64:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.2e-162)
		tmp = x;
	elseif (x <= 5.5e-64)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.2e-162)
		tmp = x;
	elseif (x <= 5.5e-64)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.2e-162], x, If[LessEqual[x, 5.5e-64], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999997e-162 or 5.4999999999999999e-64 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 61.8%

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

   if -6.1999999999999997e-162 < x < 5.4999999999999999e-64

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto x + \left(z + \left(1 \cdot y + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) \cdot y}\right)\right) \]

      2. *-lft-identity N/A

         \[\leadsto x + \left(z + \left(y + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right)} \cdot y\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto x + \left(\left(z + y\right) + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) \cdot y}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(y + z\right) + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right)} \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(y + z\right) + \left(\frac{-1}{2} \cdot \left(z \cdot y\right)\right) \cdot y\right) \]

      6. associate-*r* N/A

         \[\leadsto x + \left(\left(y + z\right) + \left(\left(\frac{-1}{2} \cdot z\right) \cdot y\right) \cdot y\right) \]

      7. associate-*r* N/A

         \[\leadsto x + \left(\left(y + z\right) + \left(\frac{-1}{2} \cdot z\right) \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      8. unpow2 N/A

         \[\leadsto x + \left(\left(y + z\right) + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{\color{blue}{2}}\right) \]

      9. associate-+r+ N/A

         \[\leadsto x + \left(y + \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(x + y\right) + \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)} \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)}\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y + x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \left({y}^{2} \cdot \color{blue}{z}\right)\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(1 \cdot z + \color{blue}{\frac{-1}{2}} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(1 \cdot z + \left(\frac{-1}{2} \cdot {y}^{2}\right) \cdot \color{blue}{z}\right)\right) \]

      18. distribute-rgt-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z \cdot \color{blue}{\left(1 + \frac{-1}{2} \cdot {y}^{2}\right)}\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 + \frac{-1}{2} \cdot {y}^{2}\right)}\right)\right) \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{2} \cdot {y}^{2}\right)}\right)\right)\right) \]

      21. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \left(\frac{-1}{2} \cdot \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

   5. Simplified 54.4%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{{y}^{2} \cdot \left(\frac{-1}{2} \cdot z + \frac{1}{y}\right)} \]
   7. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \left(y \cdot y\right) \cdot \left(\color{blue}{\frac{-1}{2} \cdot z} + \frac{1}{y}\right) \]

      2. associate-*l* N/A

         \[\leadsto y \cdot \color{blue}{\left(y \cdot \left(\frac{-1}{2} \cdot z + \frac{1}{y}\right)\right)} \]

      3. distribute-lft-in N/A

         \[\leadsto y \cdot \left(y \cdot \left(\frac{-1}{2} \cdot z\right) + \color{blue}{y \cdot \frac{1}{y}}\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(y \cdot \left(z \cdot \frac{-1}{2}\right) + y \cdot \frac{1}{y}\right) \]

      5. associate-*r* N/A

         \[\leadsto y \cdot \left(\left(y \cdot z\right) \cdot \frac{-1}{2} + \color{blue}{y} \cdot \frac{1}{y}\right) \]

      6. *-commutative N/A

         \[\leadsto y \cdot \left(\frac{-1}{2} \cdot \left(y \cdot z\right) + \color{blue}{y} \cdot \frac{1}{y}\right) \]

      7. rgt-mult-inverse N/A

         \[\leadsto y \cdot \left(\frac{-1}{2} \cdot \left(y \cdot z\right) + 1\right) \]

      8. +-commutative N/A

         \[\leadsto y \cdot \left(1 + \color{blue}{\frac{-1}{2} \cdot \left(y \cdot z\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \frac{-1}{2} \cdot \left(z \cdot \color{blue}{y}\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\frac{-1}{2} \cdot z\right) \cdot \color{blue}{y}\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(\left(\frac{-1}{2} \cdot z\right) \cdot y\right)}\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(\left(z \cdot \frac{-1}{2}\right) \cdot y\right)\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(z \cdot \color{blue}{\left(\frac{-1}{2} \cdot y\right)}\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{-1}{2} \cdot y\right)}\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(y \cdot \color{blue}{\frac{-1}{2}}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 19.1%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{\frac{-1}{2}}\right)\right)\right)\right) \]

   8. Simplified 19.1%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y} \]
   10. Step-by-step derivation

   11. Simplified 19.3%

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

Alternative 11: 66.5% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

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 + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 62.9%

      \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

5. Simplified 62.9%

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

6. Final simplification 62.9%

   \[\leadsto x + z \]
7. Add Preprocessing

Alternative 12: 42.5% 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 x around inf

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

5. Simplified 41.8%

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

Reproduce

herbie shell --seed 2024158 
(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))))