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

Percentage Accurate: 99.9% → 99.9%

Time: 8.5s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(x + N[(z * N[Cos[y], $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. Add Preprocessing

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 3: 83.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-58}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+22}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.5e+73)
     t_0
     (if (<= z -3.5e-58) (+ x z) (if (<= z 1.75e+22) (+ x (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.5e+73) {
		tmp = t_0;
	} else if (z <= -3.5e-58) {
		tmp = x + z;
	} else if (z <= 1.75e+22) {
		tmp = x + sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-2.5d+73)) then
        tmp = t_0
    else if (z <= (-3.5d-58)) then
        tmp = x + z
    else if (z <= 1.75d+22) then
        tmp = x + sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -2.5e+73) {
		tmp = t_0;
	} else if (z <= -3.5e-58) {
		tmp = x + z;
	} else if (z <= 1.75e+22) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -2.5e+73:
		tmp = t_0
	elif z <= -3.5e-58:
		tmp = x + z
	elif z <= 1.75e+22:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -2.5e+73)
		tmp = t_0;
	elseif (z <= -3.5e-58)
		tmp = Float64(x + z);
	elseif (z <= 1.75e+22)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -2.5e+73)
		tmp = t_0;
	elseif (z <= -3.5e-58)
		tmp = x + z;
	elseif (z <= 1.75e+22)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+73], t$95$0, If[LessEqual[z, -3.5e-58], N[(x + z), $MachinePrecision], If[LessEqual[z, 1.75e+22], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999988e73 or 1.75e22 < 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 x around inf 74.9%

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

      1. associate-+r+ 74.9%

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

      2. associate-/l* 74.7%

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

   7. Simplified 74.7%

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

   8. Taylor expanded in z around inf 83.1%

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

   if -2.49999999999999988e73 < z < -3.4999999999999999e-58

   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 83.1%

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

      1. +-commutative 83.1%

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

   7. Simplified 83.1%

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

   if -3.4999999999999999e-58 < z < 1.75e22

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   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 93.2%

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

      1. +-commutative 93.2%

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

   7. Simplified 93.2%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-58}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+22}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+33} \lor \neg \left(z \leq 0.86\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.14e+33) (not (<= z 0.86)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.14e+33) || !(z <= 0.86)) {
		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 <= (-1.14d+33)) .or. (.not. (z <= 0.86d0))) 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 <= -1.14e+33) || !(z <= 0.86)) {
		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 <= -1.14e+33) or not (z <= 0.86):
		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 <= -1.14e+33) || !(z <= 0.86))
		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 <= -1.14e+33) || ~((z <= 0.86)))
		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, -1.14e+33], N[Not[LessEqual[z, 0.86]], $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 < -1.14e33 or 0.859999999999999987 < 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 99.9%

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

   if -1.14e33 < z < 0.859999999999999987

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.4%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+33} \lor \neg \left(z \leq 0.86\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-57} \lor \neg \left(z \leq 1.95 \cdot 10^{-33}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.9e-57) (not (<= z 1.95e-33)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.9e-57) || !(z <= 1.95e-33)) {
		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 <= (-3.9d-57)) .or. (.not. (z <= 1.95d-33))) 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 <= -3.9e-57) || !(z <= 1.95e-33)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.9e-57) or not (z <= 1.95e-33):
		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 <= -3.9e-57) || !(z <= 1.95e-33))
		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 <= -3.9e-57) || ~((z <= 1.95e-33)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.9e-57], N[Not[LessEqual[z, 1.95e-33]], $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 < -3.90000000000000006e-57 or 1.94999999999999987e-33 < 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 96.9%

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

   if -3.90000000000000006e-57 < z < 1.94999999999999987e-33

   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 95.1%

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

      1. +-commutative 95.1%

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

   7. Simplified 95.1%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-57} \lor \neg \left(z \leq 1.95 \cdot 10^{-33}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+73} \lor \neg \left(z \leq 8.2 \cdot 10^{+88}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4e+73) (not (<= z 8.2e+88))) (* z (cos y)) (+ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4e+73) || !(z <= 8.2e+88)) {
		tmp = z * cos(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.4d+73)) .or. (.not. (z <= 8.2d+88))) then
        tmp = z * cos(y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4e+73) || !(z <= 8.2e+88)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4e+73) or not (z <= 8.2e+88):
		tmp = z * math.cos(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.4e+73) || !(z <= 8.2e+88))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.4e+73) || ~((z <= 8.2e+88)))
		tmp = z * cos(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4e+73], N[Not[LessEqual[z, 8.2e+88]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3999999999999998e73 or 8.20000000000000055e88 < 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 x around inf 71.4%

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

      1. associate-+r+ 71.4%

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

      2. associate-/l* 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in z around inf 87.3%

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

   if -5.3999999999999998e73 < z < 8.20000000000000055e88

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   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 64.0%

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

      1. +-commutative 64.0%

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

   7. Simplified 64.0%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+73} \lor \neg \left(z \leq 8.2 \cdot 10^{+88}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.6% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2550000 \lor \neg \left(y \leq 42000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2550000.0) (not (<= y 42000.0)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2550000.0) || !(y <= 42000.0)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	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 <= (-2550000.0d0)) .or. (.not. (y <= 42000.0d0))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2550000.0) || !(y <= 42000.0)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2550000.0) or not (y <= 42000.0):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2550000.0) || !(y <= 42000.0))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2550000.0) || ~((y <= 42000.0)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2550000.0], N[Not[LessEqual[y, 42000.0]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55e6 or 42000 < y

   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 38.9%

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

      1. +-commutative 38.9%

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

   7. Simplified 38.9%

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

   if -2.55e6 < y < 42000

   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 97.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2550000 \lor \neg \left(y \leq 42000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -600000 \lor \neg \left(y \leq 9 \cdot 10^{-74}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -600000.0) (not (<= y 9e-74)))
   (+ x z)
   (+ (+ x z) (* y (+ 1.0 (* -0.5 (* z y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -600000.0) || !(y <= 9e-74)) {
		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 <= (-600000.0d0)) .or. (.not. (y <= 9d-74))) 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 <= -600000.0) || !(y <= 9e-74)) {
		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 <= -600000.0) or not (y <= 9e-74):
		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 <= -600000.0) || !(y <= 9e-74))
		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 <= -600000.0) || ~((y <= 9e-74)))
		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, -600000.0], N[Not[LessEqual[y, 9e-74]], $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 < -6e5 or 8.9999999999999998e-74 < y

   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 42.6%

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

      1. +-commutative 42.6%

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

   7. Simplified 42.6%

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

   if -6e5 < y < 8.9999999999999998e-74

   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 97.5%

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

      1. associate-+r+ 97.5%

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

      2. +-commutative 97.5%

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

      3. *-commutative 97.5%

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

   7. Simplified 97.5%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -600000 \lor \neg \left(y \leq 9 \cdot 10^{-74}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.3% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+41} \lor \neg \left(y \leq 5 \cdot 10^{-74}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.42e+41) (not (<= y 5e-74))) (+ x z) (+ x (+ z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.42e+41) || !(y <= 5e-74)) {
		tmp = x + z;
	} else {
		tmp = x + (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+41)) .or. (.not. (y <= 5d-74))) then
        tmp = x + z
    else
        tmp = x + (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+41) || !(y <= 5e-74)) {
		tmp = x + z;
	} else {
		tmp = x + (z + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.42e+41) or not (y <= 5e-74):
		tmp = x + z
	else:
		tmp = x + (z + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.42e+41) || !(y <= 5e-74))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.42e+41) || ~((y <= 5e-74)))
		tmp = x + z;
	else
		tmp = x + (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.42e+41], N[Not[LessEqual[y, 5e-74]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.42000000000000007e41 or 4.99999999999999998e-74 < y

   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 41.4%

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

      1. +-commutative 41.4%

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

   7. Simplified 41.4%

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

   if -1.42000000000000007e41 < y < 4.99999999999999998e-74

   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 92.6%

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

      1. +-commutative 92.6%

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

      2. +-commutative 92.6%

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

   7. Simplified 92.6%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+41} \lor \neg \left(y \leq 5 \cdot 10^{-74}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-9}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.5e+99) x (if (<= x 4.4e-9) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e+99) {
		tmp = x;
	} else if (x <= 4.4e-9) {
		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 <= (-2.5d+99)) then
        tmp = x
    else if (x <= 4.4d-9) 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 <= -2.5e+99) {
		tmp = x;
	} else if (x <= 4.4e-9) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.5e+99:
		tmp = x
	elif x <= 4.4e-9:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e+99)
		tmp = x;
	elseif (x <= 4.4e-9)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.5e+99)
		tmp = x;
	elseif (x <= 4.4e-9)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e+99], x, If[LessEqual[x, 4.4e-9], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.50000000000000004e99 or 4.3999999999999997e-9 < x

   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 x around inf 99.1%

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

      1. associate-+r+ 99.1%

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

      2. associate-/l* 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in x around inf 72.5%

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

   if -2.50000000000000004e99 < x < 4.3999999999999997e-9

   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 47.1%

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

      1. +-commutative 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in z around inf 38.7%

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

Alternative 11: 66.0% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]
2. 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 62.6%

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

   1. +-commutative 62.6%

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

7. Simplified 62.6%

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

8. Final simplification 62.6%

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

Alternative 12: 43.1% 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 87.8%

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

   1. associate-+r+ 87.8%

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

   2. associate-/l* 87.6%

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

7. Simplified 87.6%

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

8. Taylor expanded in x around inf 34.0%

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

Reproduce

herbie shell --seed 2024113 
(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))))