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

Percentage Accurate: 99.9% → 99.9%

Time: 8.0s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 94.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{-65} \lor \neg \left(x \leq 5 \cdot 10^{-79}\right):\\ \;\;\;\;x + t_0\\ \mathbf{else}:\\ \;\;\;\;\sin y + t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (or (<= x -2.3e-65) (not (<= x 5e-79))) (+ x t_0) (+ (sin y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if ((x <= -2.3e-65) || !(x <= 5e-79)) {
		tmp = x + t_0;
	} else {
		tmp = sin(y) + 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 ((x <= (-2.3d-65)) .or. (.not. (x <= 5d-79))) then
        tmp = x + t_0
    else
        tmp = sin(y) + 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 ((x <= -2.3e-65) || !(x <= 5e-79)) {
		tmp = x + t_0;
	} else {
		tmp = Math.sin(y) + t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if (x <= -2.3e-65) or not (x <= 5e-79):
		tmp = x + t_0
	else:
		tmp = math.sin(y) + t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if ((x <= -2.3e-65) || !(x <= 5e-79))
		tmp = Float64(x + t_0);
	else
		tmp = Float64(sin(y) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if ((x <= -2.3e-65) || ~((x <= 5e-79)))
		tmp = x + t_0;
	else
		tmp = sin(y) + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2.3e-65], N[Not[LessEqual[x, 5e-79]], $MachinePrecision]], N[(x + t$95$0), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e-65 or 4.99999999999999999e-79 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.7%

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

   if -2.3e-65 < x < 4.99999999999999999e-79

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 96.9%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-65} \lor \neg \left(x \leq 5 \cdot 10^{-79}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 94.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-121} \lor \neg \left(z \leq 3.4 \cdot 10^{-66}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.52e-121) (not (<= z 3.4e-66)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.52e-121) || !(z <= 3.4e-66)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = x + sin(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.52d-121)) .or. (.not. (z <= 3.4d-66))) then
        tmp = x + (z * cos(y))
    else
        tmp = x + sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.52e-121) || !(z <= 3.4e-66)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.52e-121) or not (z <= 3.4e-66):
		tmp = x + (z * math.cos(y))
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.52e-121) || !(z <= 3.4e-66))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.52e-121) || ~((z <= 3.4e-66)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.52e-121], N[Not[LessEqual[z, 3.4e-66]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.52e-121 or 3.39999999999999997e-66 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 95.8%

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

   if -1.52e-121 < z < 3.39999999999999997e-66

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 96.6%

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

      1. +-commutative 96.6%

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

   6. Simplified 96.6%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-121} \lor \neg \left(z \leq 3.4 \cdot 10^{-66}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 5: 72.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-84}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-79}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.6e-84)
   (+ z x)
   (if (<= x 1.55e-138) (* z (cos y)) (if (<= x 3.3e-79) (sin y) (+ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.6e-84) {
		tmp = z + x;
	} else if (x <= 1.55e-138) {
		tmp = z * cos(y);
	} else if (x <= 3.3e-79) {
		tmp = sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.6d-84)) then
        tmp = z + x
    else if (x <= 1.55d-138) then
        tmp = z * cos(y)
    else if (x <= 3.3d-79) then
        tmp = sin(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.6e-84) {
		tmp = z + x;
	} else if (x <= 1.55e-138) {
		tmp = z * Math.cos(y);
	} else if (x <= 3.3e-79) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.6e-84:
		tmp = z + x
	elif x <= 1.55e-138:
		tmp = z * math.cos(y)
	elif x <= 3.3e-79:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.6e-84)
		tmp = Float64(z + x);
	elseif (x <= 1.55e-138)
		tmp = Float64(z * cos(y));
	elseif (x <= 3.3e-79)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.6e-84)
		tmp = z + x;
	elseif (x <= 1.55e-138)
		tmp = z * cos(y);
	elseif (x <= 3.3e-79)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.6e-84], N[(z + x), $MachinePrecision], If[LessEqual[x, 1.55e-138], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-79], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.59999999999999964e-84 or 3.2999999999999998e-79 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 85.9%

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

      1. +-commutative 85.9%

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

   6. Simplified 85.9%

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

   if -5.59999999999999964e-84 < x < 1.5499999999999999e-138

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 58.6%

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

   if 1.5499999999999999e-138 < x < 3.2999999999999998e-79

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 89.0%

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

   5. Taylor expanded in z around 0 78.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-84}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-79}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 6: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00052 \lor \neg \left(y \leq 2.85 \cdot 10^{-5}\right):\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(z + y\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00052) (not (<= y 2.85e-5)))
   (+ x (sin y))
   (+ x (+ (+ z y) (* -0.5 (* z (* y y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00052) || !(y <= 2.85e-5)) {
		tmp = x + sin(y);
	} else {
		tmp = x + ((z + y) + (-0.5 * (z * (y * y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-0.00052d0)) .or. (.not. (y <= 2.85d-5))) then
        tmp = x + sin(y)
    else
        tmp = x + ((z + y) + ((-0.5d0) * (z * (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00052) || !(y <= 2.85e-5)) {
		tmp = x + Math.sin(y);
	} else {
		tmp = x + ((z + y) + (-0.5 * (z * (y * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00052) or not (y <= 2.85e-5):
		tmp = x + math.sin(y)
	else:
		tmp = x + ((z + y) + (-0.5 * (z * (y * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00052) || !(y <= 2.85e-5))
		tmp = Float64(x + sin(y));
	else
		tmp = Float64(x + Float64(Float64(z + y) + Float64(-0.5 * Float64(z * Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00052) || ~((y <= 2.85e-5)))
		tmp = x + sin(y);
	else
		tmp = x + ((z + y) + (-0.5 * (z * (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00052], N[Not[LessEqual[y, 2.85e-5]], $MachinePrecision]], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z + y), $MachinePrecision] + N[(-0.5 * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999954e-4 or 2.8500000000000002e-5 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 64.8%

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

      1. +-commutative 64.8%

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

   6. Simplified 64.8%

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

   if -5.19999999999999954e-4 < y < 2.8500000000000002e-5

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{x + \left(y + \left(z + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 100.0%

         \[\leadsto x + \color{blue}{\left(\left(y + z\right) + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)} \]

      2. +-commutative 100.0%

         \[\leadsto x + \left(\color{blue}{\left(z + y\right)} + -0.5 \cdot \left({y}^{2} \cdot z\right)\right) \]

      3. *-commutative 100.0%

         \[\leadsto x + \left(\left(z + y\right) + -0.5 \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right) \]

      4. unpow2 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00052 \lor \neg \left(y \leq 2.85 \cdot 10^{-5}\right):\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(z + y\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 7: 67.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15.6:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+49}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -15.6) (+ z x) (if (<= y 9.5e+49) (+ z (+ y x)) (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -15.6) {
		tmp = z + x;
	} else if (y <= 9.5e+49) {
		tmp = z + (y + x);
	} else {
		tmp = sin(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-15.6d0)) then
        tmp = z + x
    else if (y <= 9.5d+49) then
        tmp = z + (y + x)
    else
        tmp = sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -15.6) {
		tmp = z + x;
	} else if (y <= 9.5e+49) {
		tmp = z + (y + x);
	} else {
		tmp = Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -15.6:
		tmp = z + x
	elif y <= 9.5e+49:
		tmp = z + (y + x)
	else:
		tmp = math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -15.6)
		tmp = Float64(z + x);
	elseif (y <= 9.5e+49)
		tmp = Float64(z + Float64(y + x));
	else
		tmp = sin(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -15.6)
		tmp = z + x;
	elseif (y <= 9.5e+49)
		tmp = z + (y + x);
	else
		tmp = sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -15.6], N[(z + x), $MachinePrecision], If[LessEqual[y, 9.5e+49], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], N[Sin[y], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -15.5999999999999996

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 40.2%

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

      1. +-commutative 40.2%

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

   6. Simplified 40.2%

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

   if -15.5999999999999996 < y < 9.49999999999999969e49

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.9%

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

      1. +-commutative 96.9%

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

      2. +-commutative 96.9%

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

      3. associate-+l+ 96.9%

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

   6. Simplified 96.9%

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

   if 9.49999999999999969e49 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 72.8%

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

   5. Taylor expanded in z around 0 33.1%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15.6:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+49}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y\\ \end{array} \]

Alternative 8: 71.1% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -450:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 14000:\\ \;\;\;\;x + \left(\left(z + y\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -450.0)
   (+ z x)
   (if (<= y 14000.0) (+ x (+ (+ z y) (* -0.5 (* z (* y y))))) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -450.0) {
		tmp = z + x;
	} else if (y <= 14000.0) {
		tmp = x + ((z + y) + (-0.5 * (z * (y * y))));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-450.0d0)) then
        tmp = z + x
    else if (y <= 14000.0d0) then
        tmp = x + ((z + y) + ((-0.5d0) * (z * (y * y))))
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -450.0) {
		tmp = z + x;
	} else if (y <= 14000.0) {
		tmp = x + ((z + y) + (-0.5 * (z * (y * y))));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -450.0:
		tmp = z + x
	elif y <= 14000.0:
		tmp = x + ((z + y) + (-0.5 * (z * (y * y))))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -450.0)
		tmp = Float64(z + x);
	elseif (y <= 14000.0)
		tmp = Float64(x + Float64(Float64(z + y) + Float64(-0.5 * Float64(z * Float64(y * y)))));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -450.0)
		tmp = z + x;
	elseif (y <= 14000.0)
		tmp = x + ((z + y) + (-0.5 * (z * (y * y))));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -450.0], N[(z + x), $MachinePrecision], If[LessEqual[y, 14000.0], N[(x + N[(N[(z + y), $MachinePrecision] + N[(-0.5 * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -450 or 14000 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 38.3%

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

      1. +-commutative 38.3%

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

   6. Simplified 38.3%

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

   if -450 < y < 14000

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.9%

      \[\leadsto \color{blue}{x + \left(y + \left(z + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 98.9%

         \[\leadsto x + \color{blue}{\left(\left(y + z\right) + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)} \]

      2. +-commutative 98.9%

         \[\leadsto x + \left(\color{blue}{\left(z + y\right)} + -0.5 \cdot \left({y}^{2} \cdot z\right)\right) \]

      3. *-commutative 98.9%

         \[\leadsto x + \left(\left(z + y\right) + -0.5 \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right) \]

      4. unpow2 98.9%

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

   6. Simplified 98.9%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -450:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 14000:\\ \;\;\;\;x + \left(\left(z + y\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 9: 70.9% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15.6:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2800:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -15.6) (+ z x) (if (<= y 2800.0) (+ z (+ y x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -15.6) {
		tmp = z + x;
	} else if (y <= 2800.0) {
		tmp = z + (y + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-15.6d0)) then
        tmp = z + x
    else if (y <= 2800.0d0) then
        tmp = z + (y + x)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -15.6) {
		tmp = z + x;
	} else if (y <= 2800.0) {
		tmp = z + (y + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -15.6:
		tmp = z + x
	elif y <= 2800.0:
		tmp = z + (y + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -15.6)
		tmp = Float64(z + x);
	elseif (y <= 2800.0)
		tmp = Float64(z + Float64(y + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -15.6)
		tmp = z + x;
	elseif (y <= 2800.0)
		tmp = z + (y + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -15.6], N[(z + x), $MachinePrecision], If[LessEqual[y, 2800.0], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -15.5999999999999996 or 2800 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 38.3%

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

      1. +-commutative 38.3%

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

   6. Simplified 38.3%

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

   if -15.5999999999999996 < y < 2800

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.9%

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

      1. +-commutative 98.9%

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

      2. +-commutative 98.9%

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

      3. associate-+l+ 98.9%

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

   6. Simplified 98.9%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15.6:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2800:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 10: 68.4% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-119}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-102}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.95e-119) (+ z x) (if (<= x 9e-102) (+ z y) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e-119) {
		tmp = z + x;
	} else if (x <= 9e-102) {
		tmp = z + y;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.95d-119)) then
        tmp = z + x
    else if (x <= 9d-102) then
        tmp = z + y
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e-119) {
		tmp = z + x;
	} else if (x <= 9e-102) {
		tmp = z + y;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.95e-119:
		tmp = z + x
	elif x <= 9e-102:
		tmp = z + y
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.95e-119)
		tmp = Float64(z + x);
	elseif (x <= 9e-102)
		tmp = Float64(z + y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.95e-119)
		tmp = z + x;
	elseif (x <= 9e-102)
		tmp = z + y;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.95e-119], N[(z + x), $MachinePrecision], If[LessEqual[x, 9e-102], N[(z + y), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.94999999999999995e-119 or 8.99999999999999999e-102 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 81.7%

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

      1. +-commutative 81.7%

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

   6. Simplified 81.7%

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

   if -1.94999999999999995e-119 < x < 8.99999999999999999e-102

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.7%

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

   5. Taylor expanded in y around 0 53.4%

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

      1. +-commutative 53.4%

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

   7. Simplified 53.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-119}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-102}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 11: 55.3% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-18}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.65e-65) x (if (<= x 6.6e-18) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.65e-65) {
		tmp = x;
	} else if (x <= 6.6e-18) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.65d-65)) then
        tmp = x
    else if (x <= 6.6d-18) 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 <= -2.65e-65) {
		tmp = x;
	} else if (x <= 6.6e-18) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.65e-65:
		tmp = x
	elif x <= 6.6e-18:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.65e-65)
		tmp = x;
	elseif (x <= 6.6e-18)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.65e-65)
		tmp = x;
	elseif (x <= 6.6e-18)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.65e-65], x, If[LessEqual[x, 6.6e-18], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.65000000000000019e-65 or 6.6000000000000003e-18 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 98.1%

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

   3. Taylor expanded in x around inf 70.8%

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

   if -2.65000000000000019e-65 < x < 6.6000000000000003e-18

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 58.5%

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

   5. Taylor expanded in y around 0 39.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-18}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 67.2% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 67.3%

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

   1. +-commutative 67.3%

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

6. Simplified 67.3%

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

7. Final simplification 67.3%

   \[\leadsto z + x \]

Alternative 13: 42.9% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around inf 81.7%

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

3. Taylor expanded in x around inf 41.5%

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

4. Final simplification 41.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023271 
(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))))