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

Percentage Accurate: 99.9% → 99.9%

Time: 8.8s

Alternatives: 11

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

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((z * cos(y)) + 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 = x + ((z * cos(y)) + sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + 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. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

   1. fma-undefine 99.9%

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

6. Applied egg-rr 99.9%

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

Alternative 2: 85.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+110}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-15}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-38}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+77}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -9.5e+110)
     t_0
     (if (<= z -1.85e-15)
       (+ x z)
       (if (<= z 5.5e-38) (+ x (sin y)) (if (<= z 8.2e+77) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -9.5e+110) {
		tmp = t_0;
	} else if (z <= -1.85e-15) {
		tmp = x + z;
	} else if (z <= 5.5e-38) {
		tmp = x + sin(y);
	} else if (z <= 8.2e+77) {
		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 <= (-9.5d+110)) then
        tmp = t_0
    else if (z <= (-1.85d-15)) then
        tmp = x + z
    else if (z <= 5.5d-38) then
        tmp = x + sin(y)
    else if (z <= 8.2d+77) 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 <= -9.5e+110) {
		tmp = t_0;
	} else if (z <= -1.85e-15) {
		tmp = x + z;
	} else if (z <= 5.5e-38) {
		tmp = x + Math.sin(y);
	} else if (z <= 8.2e+77) {
		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 <= -9.5e+110:
		tmp = t_0
	elif z <= -1.85e-15:
		tmp = x + z
	elif z <= 5.5e-38:
		tmp = x + math.sin(y)
	elif z <= 8.2e+77:
		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 <= -9.5e+110)
		tmp = t_0;
	elseif (z <= -1.85e-15)
		tmp = Float64(x + z);
	elseif (z <= 5.5e-38)
		tmp = Float64(x + sin(y));
	elseif (z <= 8.2e+77)
		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 <= -9.5e+110)
		tmp = t_0;
	elseif (z <= -1.85e-15)
		tmp = x + z;
	elseif (z <= 5.5e-38)
		tmp = x + sin(y);
	elseif (z <= 8.2e+77)
		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, -9.5e+110], t$95$0, If[LessEqual[z, -1.85e-15], N[(x + z), $MachinePrecision], If[LessEqual[z, 5.5e-38], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+77], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.49999999999999939e110 or 8.2000000000000002e77 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.5%

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

   if -9.49999999999999939e110 < z < -1.85000000000000008e-15 or 5.50000000000000005e-38 < z < 8.2000000000000002e77

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 84.1%

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

      1. +-commutative 84.1%

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

   7. Simplified 84.1%

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

   if -1.85000000000000008e-15 < z < 5.50000000000000005e-38

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 96.4%

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

      1. +-commutative 96.4%

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

   7. Simplified 96.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-15}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-38}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+77}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -58000000 \lor \neg \left(z \leq 0.0135\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -58000000.0) (not (<= z 0.0135)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -58000000.0) || !(z <= 0.0135)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = z + (x + sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-58000000.0d0)) .or. (.not. (z <= 0.0135d0))) then
        tmp = x + (z * cos(y))
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -58000000.0) || !(z <= 0.0135)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -58000000.0) or not (z <= 0.0135):
		tmp = x + (z * math.cos(y))
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -58000000.0) || !(z <= 0.0135))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -58000000.0) || ~((z <= 0.0135)))
		tmp = x + (z * cos(y));
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -58000000.0], N[Not[LessEqual[z, 0.0135]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e7 or 0.0134999999999999998 < z

   1. Initial program 99.9%

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

      1. log1p-expm1-u 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 99.8%

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

   if -5.8e7 < z < 0.0134999999999999998

   1. Initial program 100.0%

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

      1. expm1-log1p-u 100.0%

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

      2. expm1-undefine 100.0%

         \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\cos y\right)} - 1\right)} \]

   4. Applied egg-rr 100.0%

      \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\cos y\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-define 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 99.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -58000000 \lor \neg \left(z \leq 0.0135\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-15} \lor \neg \left(z \leq 5.3 \cdot 10^{-37}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e-15) (not (<= z 5.3e-37)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e-15) || !(z <= 5.3e-37)) {
		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 <= (-2.2d-15)) .or. (.not. (z <= 5.3d-37))) 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 <= -2.2e-15) || !(z <= 5.3e-37)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.2e-15) or not (z <= 5.3e-37):
		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 <= -2.2e-15) || !(z <= 5.3e-37))
		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 <= -2.2e-15) || ~((z <= 5.3e-37)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e-15], N[Not[LessEqual[z, 5.3e-37]], $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 < -2.19999999999999986e-15 or 5.29999999999999995e-37 < z

   1. Initial program 99.9%

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

      1. log1p-expm1-u 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 97.5%

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

   if -2.19999999999999986e-15 < z < 5.29999999999999995e-37

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 96.4%

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

      1. +-commutative 96.4%

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

   7. Simplified 96.4%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-15} \lor \neg \left(z \leq 5.3 \cdot 10^{-37}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00041 \lor \neg \left(x \leq 55\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.00041) (not (<= x 55.0))) (+ x z) (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.00041) || !(x <= 55.0)) {
		tmp = x + z;
	} else {
		tmp = 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 <= (-0.00041d0)) .or. (.not. (x <= 55.0d0))) then
        tmp = x + z
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.00041) || !(x <= 55.0)) {
		tmp = x + z;
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.00041) or not (x <= 55.0):
		tmp = x + z
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.00041) || !(x <= 55.0))
		tmp = Float64(x + z);
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.00041) || ~((x <= 55.0)))
		tmp = x + z;
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.00041], N[Not[LessEqual[x, 55.0]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0999999999999999e-4 or 55 < x

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 85.7%

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

      1. +-commutative 85.7%

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

   7. Simplified 85.7%

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

   if -4.0999999999999999e-4 < x < 55

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 56.5%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00041 \lor \neg \left(x \leq 55\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.0% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+20} \lor \neg \left(y \leq 3.4 \cdot 10^{+14}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.42e+20) (not (<= y 3.4e+14)))
   (+ x z)
   (+ (+ x z) (* y (+ 1.0 (* -0.5 (* z y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.42e+20) || !(y <= 3.4e+14)) {
		tmp = x + z;
	} else {
		tmp = (x + z) + (y * (1.0 + (-0.5 * (z * 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 <= (-1.42d+20)) .or. (.not. (y <= 3.4d+14))) then
        tmp = x + z
    else
        tmp = (x + z) + (y * (1.0d0 + ((-0.5d0) * (z * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.42e+20) || !(y <= 3.4e+14)) {
		tmp = x + z;
	} else {
		tmp = (x + z) + (y * (1.0 + (-0.5 * (z * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.42e+20) or not (y <= 3.4e+14):
		tmp = x + z
	else:
		tmp = (x + z) + (y * (1.0 + (-0.5 * (z * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.42e+20) || !(y <= 3.4e+14))
		tmp = Float64(x + z);
	else
		tmp = Float64(Float64(x + z) + Float64(y * Float64(1.0 + Float64(-0.5 * Float64(z * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.42e+20) || ~((y <= 3.4e+14)))
		tmp = x + z;
	else
		tmp = (x + z) + (y * (1.0 + (-0.5 * (z * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.42e+20], N[Not[LessEqual[y, 3.4e+14]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[(y * N[(1.0 + N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.42e20 or 3.4e14 < y

   1. Initial program 99.8%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 38.3%

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

      1. +-commutative 38.3%

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

   7. Simplified 38.3%

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

   if -1.42e20 < y < 3.4e14

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 96.4%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 96.4%

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

      2. +-commutative 96.4%

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

   7. Simplified 96.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+20} \lor \neg \left(y \leq 3.4 \cdot 10^{+14}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.9% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+20} \lor \neg \left(y \leq 8 \cdot 10^{+16}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6e+20) (not (<= y 8e+16))) (+ x z) (+ y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e+20) || !(y <= 8e+16)) {
		tmp = x + z;
	} else {
		tmp = y + (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 <= (-6d+20)) .or. (.not. (y <= 8d+16))) then
        tmp = x + z
    else
        tmp = y + (x + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e+20) || !(y <= 8e+16)) {
		tmp = x + z;
	} else {
		tmp = y + (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6e+20) or not (y <= 8e+16):
		tmp = x + z
	else:
		tmp = y + (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6e+20) || !(y <= 8e+16))
		tmp = Float64(x + z);
	else
		tmp = Float64(y + Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6e+20) || ~((y <= 8e+16)))
		tmp = x + z;
	else
		tmp = y + (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6e+20], N[Not[LessEqual[y, 8e+16]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6e20 or 8e16 < y

   1. Initial program 99.8%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 38.3%

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

      1. +-commutative 38.3%

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

   7. Simplified 38.3%

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

   if -6e20 < y < 8e16

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 96.3%

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

      1. +-commutative 96.3%

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

      2. associate-+l+ 96.3%

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

   7. Simplified 96.3%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+20} \lor \neg \left(y \leq 8 \cdot 10^{+16}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.6% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-96} \lor \neg \left(x \leq 1.35 \cdot 10^{-180}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e-96) (not (<= x 1.35e-180))) (+ x z) (+ z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-96) || !(x <= 1.35e-180)) {
		tmp = x + z;
	} else {
		tmp = z + 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 <= (-7d-96)) .or. (.not. (x <= 1.35d-180))) then
        tmp = x + z
    else
        tmp = z + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-96) || !(x <= 1.35e-180)) {
		tmp = x + z;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e-96) or not (x <= 1.35e-180):
		tmp = x + z
	else:
		tmp = z + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e-96) || !(x <= 1.35e-180))
		tmp = Float64(x + z);
	else
		tmp = Float64(z + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e-96) || ~((x <= 1.35e-180)))
		tmp = x + z;
	else
		tmp = z + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e-96], N[Not[LessEqual[x, 1.35e-180]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.9999999999999998e-96 or 1.35000000000000007e-180 < x

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 72.2%

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

      1. +-commutative 72.2%

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

   7. Simplified 72.2%

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

   if -6.9999999999999998e-96 < x < 1.35000000000000007e-180

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.9%

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

   6. Taylor expanded in y around 0 45.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-96} \lor \neg \left(x \leq 1.35 \cdot 10^{-180}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.2% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00085:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 41000:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.00085) x (if (<= x 41000.0) (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.00085) {
		tmp = x;
	} else if (x <= 41000.0) {
		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 <= (-0.00085d0)) then
        tmp = x
    else if (x <= 41000.0d0) 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 <= -0.00085) {
		tmp = x;
	} else if (x <= 41000.0) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.00085:
		tmp = x
	elif x <= 41000.0:
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.00085)
		tmp = x;
	elseif (x <= 41000.0)
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.00085)
		tmp = x;
	elseif (x <= 41000.0)
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.00085], x, If[LessEqual[x, 41000.0], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999953e-4 or 41000 < x

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 74.4%

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

   if -8.49999999999999953e-4 < x < 41000

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 95.0%

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

   6. Taylor expanded in y around 0 43.3%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00085:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 41000:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.9% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00085:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 48000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.00085) x (if (<= x 48000.0) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.00085) {
		tmp = x;
	} else if (x <= 48000.0) {
		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 <= (-0.00085d0)) then
        tmp = x
    else if (x <= 48000.0d0) 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 <= -0.00085) {
		tmp = x;
	} else if (x <= 48000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.00085:
		tmp = x
	elif x <= 48000.0:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.00085)
		tmp = x;
	elseif (x <= 48000.0)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.00085)
		tmp = x;
	elseif (x <= 48000.0)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.00085], x, If[LessEqual[x, 48000.0], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999953e-4 or 48000 < x

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 74.4%

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

   if -8.49999999999999953e-4 < x < 48000

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 38.7%

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

      1. +-commutative 38.7%

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

   7. Simplified 38.7%

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

   8. Taylor expanded in z around inf 35.7%

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

Alternative 11: 43.5% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 38.8%

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

Reproduce

herbie shell --seed 2024146 
(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))))