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

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

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

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

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 2: 83.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-40}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+165}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -7.2e+41)
     t_0
     (if (<= z 1.85e-40) (+ x (sin y)) (if (<= z 3.3e+165) (+ x z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -7.2e+41) {
		tmp = t_0;
	} else if (z <= 1.85e-40) {
		tmp = x + sin(y);
	} else if (z <= 3.3e+165) {
		tmp = x + z;
	} 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 <= (-7.2d+41)) then
        tmp = t_0
    else if (z <= 1.85d-40) then
        tmp = x + sin(y)
    else if (z <= 3.3d+165) then
        tmp = x + z
    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 <= -7.2e+41) {
		tmp = t_0;
	} else if (z <= 1.85e-40) {
		tmp = x + Math.sin(y);
	} else if (z <= 3.3e+165) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -7.2e+41:
		tmp = t_0
	elif z <= 1.85e-40:
		tmp = x + math.sin(y)
	elif z <= 3.3e+165:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -7.2e+41)
		tmp = t_0;
	elseif (z <= 1.85e-40)
		tmp = Float64(x + sin(y));
	elseif (z <= 3.3e+165)
		tmp = Float64(x + z);
	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 <= -7.2e+41)
		tmp = t_0;
	elseif (z <= 1.85e-40)
		tmp = x + sin(y);
	elseif (z <= 3.3e+165)
		tmp = x + z;
	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, -7.2e+41], t$95$0, If[LessEqual[z, 1.85e-40], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+165], N[(x + z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.20000000000000051e41 or 3.2999999999999999e165 < z

   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 83.9%

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

   5. Simplified 83.9%

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

   if -7.20000000000000051e41 < z < 1.84999999999999999e-40

   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 88.6%

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

   5. Simplified 88.6%

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

   if 1.84999999999999999e-40 < z < 3.2999999999999999e165

   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 80.9%

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

   5. Simplified 80.9%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-40}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+165}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -4 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-162}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+164}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -4e+43)
     t_0
     (if (<= z -7.8e-162) (+ x z) (if (<= z 4.5e+164) (+ y (+ x z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -4e+43) {
		tmp = t_0;
	} else if (z <= -7.8e-162) {
		tmp = x + z;
	} else if (z <= 4.5e+164) {
		tmp = y + (x + z);
	} 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 <= (-4d+43)) then
        tmp = t_0
    else if (z <= (-7.8d-162)) then
        tmp = x + z
    else if (z <= 4.5d+164) then
        tmp = y + (x + z)
    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 <= -4e+43) {
		tmp = t_0;
	} else if (z <= -7.8e-162) {
		tmp = x + z;
	} else if (z <= 4.5e+164) {
		tmp = y + (x + z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -4e+43:
		tmp = t_0
	elif z <= -7.8e-162:
		tmp = x + z
	elif z <= 4.5e+164:
		tmp = y + (x + z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -4e+43)
		tmp = t_0;
	elseif (z <= -7.8e-162)
		tmp = Float64(x + z);
	elseif (z <= 4.5e+164)
		tmp = Float64(y + Float64(x + z));
	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 <= -4e+43)
		tmp = t_0;
	elseif (z <= -7.8e-162)
		tmp = x + z;
	elseif (z <= 4.5e+164)
		tmp = y + (x + z);
	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, -4e+43], t$95$0, If[LessEqual[z, -7.8e-162], N[(x + z), $MachinePrecision], If[LessEqual[z, 4.5e+164], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000006e43 or 4.49999999999999975e164 < z

   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 83.9%

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

   5. Simplified 83.9%

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

   if -4.00000000000000006e43 < z < -7.7999999999999999e-162

   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 76.0%

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

   5. Simplified 76.0%

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

   if -7.7999999999999999e-162 < z < 4.49999999999999975e164

   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. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

      5. +-commutative N/A

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

      6. +-lowering-+.f64 75.5%

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

   5. Simplified 75.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-162}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+164}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -0.8:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.75:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (cos y)))))
   (if (<= z -0.8) t_0 (if (<= z 0.75) (+ (+ x (sin y)) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z * cos(y));
	double tmp;
	if (z <= -0.8) {
		tmp = t_0;
	} else if (z <= 0.75) {
		tmp = (x + sin(y)) + z;
	} 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 <= (-0.8d0)) then
        tmp = t_0
    else if (z <= 0.75d0) then
        tmp = (x + sin(y)) + z
    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 <= -0.8) {
		tmp = t_0;
	} else if (z <= 0.75) {
		tmp = (x + Math.sin(y)) + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z * math.cos(y))
	tmp = 0
	if z <= -0.8:
		tmp = t_0
	elif z <= 0.75:
		tmp = (x + math.sin(y)) + z
	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 <= -0.8)
		tmp = t_0;
	elseif (z <= 0.75)
		tmp = Float64(Float64(x + sin(y)) + z);
	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 <= -0.8)
		tmp = t_0;
	elseif (z <= 0.75)
		tmp = (x + sin(y)) + z;
	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, -0.8], t$95$0, If[LessEqual[z, 0.75], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.80000000000000004 or 0.75 < 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 98.6%

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

   if -0.80000000000000004 < 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

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

   5. Simplified 99.2%

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

Alternative 5: 94.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-97}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-44}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (cos y)))))
   (if (<= z -4.6e-97) t_0 (if (<= z 8e-44) (+ 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 <= -4.6e-97) {
		tmp = t_0;
	} else if (z <= 8e-44) {
		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 <= (-4.6d-97)) then
        tmp = t_0
    else if (z <= 8d-44) 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 <= -4.6e-97) {
		tmp = t_0;
	} else if (z <= 8e-44) {
		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 <= -4.6e-97:
		tmp = t_0
	elif z <= 8e-44:
		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 <= -4.6e-97)
		tmp = t_0;
	elseif (z <= 8e-44)
		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 <= -4.6e-97)
		tmp = t_0;
	elseif (z <= 8e-44)
		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, -4.6e-97], t$95$0, If[LessEqual[z, 8e-44], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.59999999999999988e-97 or 7.99999999999999962e-44 < 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 95.1%

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

   if -4.59999999999999988e-97 < z < 7.99999999999999962e-44

   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 93.1%

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

   5. Simplified 93.1%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-97}:\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-44}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.4% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.8:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.3e+26)
   (+ x z)
   (if (<= y 4.8)
     (+ (+ x z) (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666))))))
     (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+26) {
		tmp = x + z;
	} else if (y <= 4.8) {
		tmp = (x + z) + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666)))));
	} 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 <= (-1.3d+26)) then
        tmp = x + z
    else if (y <= 4.8d0) then
        tmp = (x + z) + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0))))))
    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 <= -1.3e+26) {
		tmp = x + z;
	} else if (y <= 4.8) {
		tmp = (x + z) + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3e+26:
		tmp = x + z
	elif y <= 4.8:
		tmp = (x + z) + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666)))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e+26)
		tmp = Float64(x + z);
	elseif (y <= 4.8)
		tmp = Float64(Float64(x + z) + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666))))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.3e+26)
		tmp = x + z;
	elseif (y <= 4.8)
		tmp = (x + z) + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666)))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3e+26], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.8], N[(N[(x + z), $MachinePrecision] + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.30000000000000001e26 or 4.79999999999999982 < y

   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 41.8%

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

   5. Simplified 41.8%

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

   if -1.30000000000000001e26 < y < 4.79999999999999982

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + z\right) + \color{blue}{y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x + z\right), \color{blue}{\left(y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z + x\right), \left(\color{blue}{y} \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\color{blue}{y} \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \color{blue}{\left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-1}{2} \cdot z\right), \color{blue}{\left(\frac{-1}{6} \cdot y\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \frac{-1}{2}\right), \left(\color{blue}{\frac{-1}{6}} \cdot y\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \left(\color{blue}{\frac{-1}{6}} \cdot y\right)\right)\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \left(y \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 98.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \mathsf{*.f64}\left(y, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   5. Simplified 98.7%

      \[\leadsto \color{blue}{\left(z + x\right) + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.8:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.4% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+46}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 340:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+46) (+ x z) (if (<= y 340.0) (+ y (+ x z)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+46) {
		tmp = x + z;
	} else if (y <= 340.0) {
		tmp = y + (x + 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 (y <= (-5.8d+46)) then
        tmp = x + z
    else if (y <= 340.0d0) then
        tmp = y + (x + 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 (y <= -5.8e+46) {
		tmp = x + z;
	} else if (y <= 340.0) {
		tmp = y + (x + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+46:
		tmp = x + z
	elif y <= 340.0:
		tmp = y + (x + z)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+46)
		tmp = Float64(x + z);
	elseif (y <= 340.0)
		tmp = Float64(y + Float64(x + z));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.8e+46)
		tmp = x + z;
	elseif (y <= 340.0)
		tmp = y + (x + z);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+46], N[(x + z), $MachinePrecision], If[LessEqual[y, 340.0], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000004e46 or 340 < y

   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 43.1%

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

   5. Simplified 43.1%

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

   if -5.8000000000000004e46 < y < 340

   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. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

      5. +-commutative N/A

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

      6. +-lowering-+.f64 95.6%

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

   5. Simplified 95.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+46}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 340:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.5% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-189}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-61}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e-189) (+ x z) (if (<= x 8.2e-61) (+ y z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e-189) {
		tmp = x + z;
	} else if (x <= 8.2e-61) {
		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 <= (-3.4d-189)) then
        tmp = x + z
    else if (x <= 8.2d-61) 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 <= -3.4e-189) {
		tmp = x + z;
	} else if (x <= 8.2e-61) {
		tmp = y + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.4e-189:
		tmp = x + z
	elif x <= 8.2e-61:
		tmp = y + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e-189)
		tmp = Float64(x + z);
	elseif (x <= 8.2e-61)
		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 <= -3.4e-189)
		tmp = x + z;
	elseif (x <= 8.2e-61)
		tmp = y + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.4e-189], N[(x + z), $MachinePrecision], If[LessEqual[x, 8.2e-61], N[(y + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4000000000000001e-189 or 8.19999999999999998e-61 < 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 78.8%

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

   5. Simplified 78.8%

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

   if -3.4000000000000001e-189 < x < 8.19999999999999998e-61

   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 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in y around 0

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

      1. +-lowering-+.f64 52.9%

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

   8. Simplified 52.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-189}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-61}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3100000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-42}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3100000000000.0) x (if (<= x 2.5e-42) (+ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3100000000000.0) {
		tmp = x;
	} else if (x <= 2.5e-42) {
		tmp = y + 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 <= (-3100000000000.0d0)) then
        tmp = x
    else if (x <= 2.5d-42) then
        tmp = y + 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 <= -3100000000000.0) {
		tmp = x;
	} else if (x <= 2.5e-42) {
		tmp = y + z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3100000000000.0:
		tmp = x
	elif x <= 2.5e-42:
		tmp = y + z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3100000000000.0)
		tmp = x;
	elseif (x <= 2.5e-42)
		tmp = Float64(y + z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3100000000000.0)
		tmp = x;
	elseif (x <= 2.5e-42)
		tmp = y + z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3100000000000.0], x, If[LessEqual[x, 2.5e-42], N[(y + z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e12 or 2.50000000000000001e-42 < 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 80.3%

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

   if -3.1e12 < x < 2.50000000000000001e-42

   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 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in y around 0

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

      1. +-lowering-+.f64 48.2%

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

   8. Simplified 48.2%

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

Alternative 10: 55.0% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-43}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.55e+14) x (if (<= x 4e-43) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.55e+14) {
		tmp = x;
	} else if (x <= 4e-43) {
		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 <= (-2.55d+14)) then
        tmp = x
    else if (x <= 4d-43) 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 <= -2.55e+14) {
		tmp = x;
	} else if (x <= 4e-43) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.55e+14:
		tmp = x
	elif x <= 4e-43:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.55e+14)
		tmp = x;
	elseif (x <= 4e-43)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.55e+14)
		tmp = x;
	elseif (x <= 4e-43)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.55e+14], x, If[LessEqual[x, 4e-43], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.55e14 or 4.00000000000000031e-43 < 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 80.9%

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

   if -2.55e14 < x < 4.00000000000000031e-43

   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 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 38.7%

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

Alternative 11: 44.2% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-44}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e-132) x (if (<= x 2.05e-44) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e-132) {
		tmp = x;
	} else if (x <= 2.05e-44) {
		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 <= (-7.5d-132)) then
        tmp = x
    else if (x <= 2.05d-44) 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 <= -7.5e-132) {
		tmp = x;
	} else if (x <= 2.05e-44) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e-132:
		tmp = x
	elif x <= 2.05e-44:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e-132)
		tmp = x;
	elseif (x <= 2.05e-44)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.5e-132)
		tmp = x;
	elseif (x <= 2.05e-44)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e-132], x, If[LessEqual[x, 2.05e-44], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.49999999999999989e-132 or 2.04999999999999996e-44 < 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 67.2%

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

   if -7.49999999999999989e-132 < x < 2.04999999999999996e-44

   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 47.9%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 17.4%

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

   8. Simplified 17.4%

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

   9. Taylor expanded in y around inf

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

   11. Simplified 16.9%

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

Alternative 12: 42.8% 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 46.1%

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

Reproduce

herbie shell --seed 2024138 
(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))))