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

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-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: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-19} \lor \neg \left(x \leq 1.45 \cdot 10^{-77}\right):\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.3e-19) (not (<= x 1.45e-77)))
   (+ z (+ x (sin y)))
   (+ (sin y) (* z (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.3e-19) || !(x <= 1.45e-77)) {
		tmp = z + (x + sin(y));
	} else {
		tmp = sin(y) + (z * cos(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 ((x <= (-2.3d-19)) .or. (.not. (x <= 1.45d-77))) then
        tmp = z + (x + sin(y))
    else
        tmp = sin(y) + (z * cos(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.3e-19) || !(x <= 1.45e-77)) {
		tmp = z + (x + Math.sin(y));
	} else {
		tmp = Math.sin(y) + (z * Math.cos(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.3e-19) or not (x <= 1.45e-77):
		tmp = z + (x + math.sin(y))
	else:
		tmp = math.sin(y) + (z * math.cos(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.3e-19) || !(x <= 1.45e-77))
		tmp = Float64(z + Float64(x + sin(y)));
	else
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.3e-19) || ~((x <= 1.45e-77)))
		tmp = z + (x + sin(y));
	else
		tmp = sin(y) + (z * cos(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.3e-19], N[Not[LessEqual[x, 1.45e-77]], $MachinePrecision]], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998e-19 or 1.4499999999999999e-77 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.8%

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

   if -2.2999999999999998e-19 < x < 1.4499999999999999e-77

   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 91.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-19} \lor \neg \left(x \leq 1.45 \cdot 10^{-77}\right):\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 89.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ t_1 := t_0 + \left(y + x\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+55}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+151} \lor \neg \left(z \leq 4.3 \cdot 10^{+251}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))) (t_1 (+ t_0 (+ y x))))
   (if (<= z -5.4e+137)
     t_1
     (if (<= z 2.05e+55)
       (+ z (+ x (sin y)))
       (if (or (<= z 2.5e+151) (not (<= z 4.3e+251))) t_0 t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double t_1 = t_0 + (y + x);
	double tmp;
	if (z <= -5.4e+137) {
		tmp = t_1;
	} else if (z <= 2.05e+55) {
		tmp = z + (x + sin(y));
	} else if ((z <= 2.5e+151) || !(z <= 4.3e+251)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = z * cos(y)
    t_1 = t_0 + (y + x)
    if (z <= (-5.4d+137)) then
        tmp = t_1
    else if (z <= 2.05d+55) then
        tmp = z + (x + sin(y))
    else if ((z <= 2.5d+151) .or. (.not. (z <= 4.3d+251))) then
        tmp = t_0
    else
        tmp = t_1
    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 t_1 = t_0 + (y + x);
	double tmp;
	if (z <= -5.4e+137) {
		tmp = t_1;
	} else if (z <= 2.05e+55) {
		tmp = z + (x + Math.sin(y));
	} else if ((z <= 2.5e+151) || !(z <= 4.3e+251)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	t_1 = t_0 + (y + x)
	tmp = 0
	if z <= -5.4e+137:
		tmp = t_1
	elif z <= 2.05e+55:
		tmp = z + (x + math.sin(y))
	elif (z <= 2.5e+151) or not (z <= 4.3e+251):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	t_1 = Float64(t_0 + Float64(y + x))
	tmp = 0.0
	if (z <= -5.4e+137)
		tmp = t_1;
	elseif (z <= 2.05e+55)
		tmp = Float64(z + Float64(x + sin(y)));
	elseif ((z <= 2.5e+151) || !(z <= 4.3e+251))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	t_1 = t_0 + (y + x);
	tmp = 0.0;
	if (z <= -5.4e+137)
		tmp = t_1;
	elseif (z <= 2.05e+55)
		tmp = z + (x + sin(y));
	elseif ((z <= 2.5e+151) || ~((z <= 4.3e+251)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+137], t$95$1, If[LessEqual[z, 2.05e+55], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.5e+151], N[Not[LessEqual[z, 4.3e+251]], $MachinePrecision]], t$95$0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.40000000000000034e137 or 2.5000000000000001e151 < z < 4.3e251

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 89.5%

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

   if -5.40000000000000034e137 < z < 2.04999999999999991e55

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.2%

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

   if 2.04999999999999991e55 < z < 2.5000000000000001e151 or 4.3e251 < z

   1. Initial program 99.7%

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

      1. log1p-expm1-u 99.7%

         \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)}\right) + z \cdot \cos y \]

   3. Applied egg-rr 99.7%

      \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)}\right) + z \cdot \cos y \]

   4. Taylor expanded in z around inf 81.0%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \cos y + \left(y + x\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+55}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+151} \lor \neg \left(z \leq 4.3 \cdot 10^{+251}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y + \left(y + x\right)\\ \end{array} \]

Alternative 5: 88.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+232} \lor \neg \left(z \leq 1.95 \cdot 10^{+55}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.2e+232) (not (<= z 1.95e+55)))
   (* z (cos y))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.2e+232) || !(z <= 1.95e+55)) {
		tmp = z * cos(y);
	} else {
		tmp = z + (x + sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-9.2d+232)) .or. (.not. (z <= 1.95d+55))) then
        tmp = z * cos(y)
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.2e+232) || !(z <= 1.95e+55)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.2e+232) or not (z <= 1.95e+55):
		tmp = z * math.cos(y)
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.2e+232) || !(z <= 1.95e+55))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.2e+232) || ~((z <= 1.95e+55)))
		tmp = z * cos(y);
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.2e+232], N[Not[LessEqual[z, 1.95e+55]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.20000000000000024e232 or 1.95000000000000014e55 < z

   1. Initial program 99.8%

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

      1. log1p-expm1-u 99.8%

         \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)}\right) + z \cdot \cos y \]

   3. Applied egg-rr 99.8%

      \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)}\right) + z \cdot \cos y \]

   4. Taylor expanded in z around inf 80.3%

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

   if -9.20000000000000024e232 < z < 1.95000000000000014e55

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 92.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+232} \lor \neg \left(z \leq 1.95 \cdot 10^{+55}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 6: 71.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+232} \lor \neg \left(z \leq 2 \cdot 10^{+55}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.2e+232) (not (<= z 2e+55))) (* z (cos y)) (+ z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.2e+232) || !(z <= 2e+55)) {
		tmp = z * cos(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-9.2d+232)) .or. (.not. (z <= 2d+55))) then
        tmp = z * cos(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.2e+232) || !(z <= 2e+55)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.2e+232) or not (z <= 2e+55):
		tmp = z * math.cos(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.2e+232) || !(z <= 2e+55))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.2e+232) || ~((z <= 2e+55)))
		tmp = z * cos(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.2e+232], N[Not[LessEqual[z, 2e+55]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.20000000000000024e232 or 2.00000000000000002e55 < z

   1. Initial program 99.8%

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

      1. log1p-expm1-u 99.8%

         \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)}\right) + z \cdot \cos y \]

   3. Applied egg-rr 99.8%

      \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)}\right) + z \cdot \cos y \]

   4. Taylor expanded in z around inf 80.3%

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

   if -9.20000000000000024e232 < z < 2.00000000000000002e55

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 72.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+232} \lor \neg \left(z \leq 2 \cdot 10^{+55}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 7: 80.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.061 \lor \neg \left(y \leq 7000\right):\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + \left(y + z \cdot \left(y \cdot \left(y \cdot -0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.061) (not (<= y 7000.0)))
   (+ x (sin y))
   (+ (+ z x) (+ y (* z (* y (* y -0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.061) || !(y <= 7000.0)) {
		tmp = x + sin(y);
	} else {
		tmp = (z + x) + (y + (z * (y * (y * -0.5))));
	}
	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 <= (-0.061d0)) .or. (.not. (y <= 7000.0d0))) then
        tmp = x + sin(y)
    else
        tmp = (z + x) + (y + (z * (y * (y * (-0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.061) || !(y <= 7000.0)) {
		tmp = x + Math.sin(y);
	} else {
		tmp = (z + x) + (y + (z * (y * (y * -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.061) or not (y <= 7000.0):
		tmp = x + math.sin(y)
	else:
		tmp = (z + x) + (y + (z * (y * (y * -0.5))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.061) || !(y <= 7000.0))
		tmp = Float64(x + sin(y));
	else
		tmp = Float64(Float64(z + x) + Float64(y + Float64(z * Float64(y * Float64(y * -0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.061) || ~((y <= 7000.0)))
		tmp = x + sin(y);
	else
		tmp = (z + x) + (y + (z * (y * (y * -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.061], N[Not[LessEqual[y, 7000.0]], $MachinePrecision]], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + N[(y + N[(z * N[(y * N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.060999999999999999 or 7e3 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 65.2%

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

   if -0.060999999999999999 < y < 7e3

   1. Initial program 100.0%

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

      1. log1p-expm1-u 100.0%

         \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)}\right) + z \cdot \cos y \]

   3. Applied egg-rr 100.0%

      \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)}\right) + z \cdot \cos y \]

   4. Taylor expanded in y around 0 99.2%

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

      1. associate-+r+ 99.2%

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

      2. +-commutative 99.2%

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

      3. +-commutative 99.2%

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

      4. +-commutative 99.2%

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

      5. associate-*r* 99.2%

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

      6. fma-def 99.2%

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

      7. *-commutative 99.2%

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

      8. unpow2 99.2%

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

   6. Simplified 99.2%

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

      1. fma-udef 99.2%

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

      2. associate-*l* 99.2%

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

   8. Applied egg-rr 99.2%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.061 \lor \neg \left(y \leq 7000\right):\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + \left(y + z \cdot \left(y \cdot \left(y \cdot -0.5\right)\right)\right)\\ \end{array} \]

Alternative 8: 69.9% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 10000:\\ \;\;\;\;\left(z + x\right) + \left(y + z \cdot \left(y \cdot \left(y \cdot -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e+14)
   (+ z x)
   (if (<= y 10000.0) (+ (+ z x) (+ y (* z (* y (* y -0.5))))) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+14) {
		tmp = z + x;
	} else if (y <= 10000.0) {
		tmp = (z + x) + (y + (z * (y * (y * -0.5))));
	} 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 <= (-7.5d+14)) then
        tmp = z + x
    else if (y <= 10000.0d0) then
        tmp = (z + x) + (y + (z * (y * (y * (-0.5d0)))))
    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 <= -7.5e+14) {
		tmp = z + x;
	} else if (y <= 10000.0) {
		tmp = (z + x) + (y + (z * (y * (y * -0.5))));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e+14:
		tmp = z + x
	elif y <= 10000.0:
		tmp = (z + x) + (y + (z * (y * (y * -0.5))))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e+14)
		tmp = Float64(z + x);
	elseif (y <= 10000.0)
		tmp = Float64(Float64(z + x) + Float64(y + Float64(z * Float64(y * Float64(y * -0.5)))));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.5e+14)
		tmp = z + x;
	elseif (y <= 10000.0)
		tmp = (z + x) + (y + (z * (y * (y * -0.5))));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e+14], N[(z + x), $MachinePrecision], If[LessEqual[y, 10000.0], N[(N[(z + x), $MachinePrecision] + N[(y + N[(z * N[(y * N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e14 or 1e4 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 43.0%

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

   if -7.5e14 < y < 1e4

   1. Initial program 100.0%

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

      1. log1p-expm1-u 100.0%

         \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)}\right) + z \cdot \cos y \]

   3. Applied egg-rr 100.0%

      \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin y\right)\right)}\right) + z \cdot \cos y \]

   4. Taylor expanded in y around 0 97.8%

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

      1. associate-+r+ 97.8%

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

      2. +-commutative 97.8%

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

      3. +-commutative 97.8%

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

      4. +-commutative 97.8%

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

      5. associate-*r* 97.8%

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

      6. fma-def 97.8%

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

      7. *-commutative 97.8%

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

      8. unpow2 97.8%

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

   6. Simplified 97.8%

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

      1. fma-udef 97.8%

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

      2. associate-*l* 97.8%

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

   8. Applied egg-rr 97.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 10000:\\ \;\;\;\;\left(z + x\right) + \left(y + z \cdot \left(y \cdot \left(y \cdot -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 9: 69.7% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -440 \lor \neg \left(y \leq 9.5 \cdot 10^{+60}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -440.0) (not (<= y 9.5e+60))) (+ z x) (+ z (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -440.0) || !(y <= 9.5e+60)) {
		tmp = z + x;
	} else {
		tmp = z + (y + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-440.0d0)) .or. (.not. (y <= 9.5d+60))) then
        tmp = z + x
    else
        tmp = z + (y + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -440.0) || !(y <= 9.5e+60)) {
		tmp = z + x;
	} else {
		tmp = z + (y + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -440.0) or not (y <= 9.5e+60):
		tmp = z + x
	else:
		tmp = z + (y + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -440.0) || !(y <= 9.5e+60))
		tmp = Float64(z + x);
	else
		tmp = Float64(z + Float64(y + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -440.0) || ~((y <= 9.5e+60)))
		tmp = z + x;
	else
		tmp = z + (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -440.0], N[Not[LessEqual[y, 9.5e+60]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -440 or 9.49999999999999988e60 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 42.2%

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

   if -440 < y < 9.49999999999999988e60

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.2%

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

      1. +-commutative 95.2%

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

      2. associate-+l+ 95.2%

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

      3. +-commutative 95.2%

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

   4. Simplified 95.2%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -440 \lor \neg \left(y \leq 9.5 \cdot 10^{+60}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \]

Alternative 10: 58.1% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-28}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e-53) x (if (<= x 1.6e-28) (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-53) {
		tmp = x;
	} else if (x <= 1.6e-28) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.4d-53)) then
        tmp = x
    else if (x <= 1.6d-28) then
        tmp = z + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-53) {
		tmp = x;
	} else if (x <= 1.6e-28) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e-53:
		tmp = x
	elif x <= 1.6e-28:
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e-53)
		tmp = x;
	elseif (x <= 1.6e-28)
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.4e-53)
		tmp = x;
	elseif (x <= 1.6e-28)
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e-53], x, If[LessEqual[x, 1.6e-28], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999993e-53 or 1.59999999999999991e-28 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 71.3%

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

   if -1.39999999999999993e-53 < x < 1.59999999999999991e-28

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.1%

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

   3. Taylor expanded in y around 0 56.3%

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

   4. Taylor expanded in x around 0 46.1%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-28}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 54.1% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-28}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.5e-102) x (if (<= x 1.35e-28) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e-102) {
		tmp = x;
	} else if (x <= 1.35e-28) {
		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 <= (-6.5d-102)) then
        tmp = x
    else if (x <= 1.35d-28) 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 <= -6.5e-102) {
		tmp = x;
	} else if (x <= 1.35e-28) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.5e-102:
		tmp = x
	elif x <= 1.35e-28:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.5e-102)
		tmp = x;
	elseif (x <= 1.35e-28)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.5e-102)
		tmp = x;
	elseif (x <= 1.35e-28)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.5e-102], x, If[LessEqual[x, 1.35e-28], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5000000000000003e-102 or 1.3499999999999999e-28 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 67.4%

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

   if -6.5000000000000003e-102 < x < 1.3499999999999999e-28

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.2%

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

   3. Taylor expanded in z around inf 41.9%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-28}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 65.6% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 68.4%

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

3. Final simplification 68.4%

   \[\leadsto z + x \]

Alternative 13: 41.8% 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. Taylor expanded in x around inf 47.2%

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

3. Final simplification 47.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023240 
(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))))