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

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 81.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+233}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+215}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+95}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.65 \cdot 10^{+61} \lor \neg \left(z \leq 6.5 \cdot 10^{+178}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (sin y)))))
   (if (<= z -2.9e+233)
     t_0
     (if (<= z -4.6e+215)
       x
       (if (<= z -7.8e+154)
         t_0
         (if (<= z -4.2e+95)
           (+ 1.0 (- x (* y z)))
           (if (or (<= z -4.65e+61) (not (<= z 6.5e+178)))
             t_0
             (+ x (cos y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -sin(y);
	double tmp;
	if (z <= -2.9e+233) {
		tmp = t_0;
	} else if (z <= -4.6e+215) {
		tmp = x;
	} else if (z <= -7.8e+154) {
		tmp = t_0;
	} else if (z <= -4.2e+95) {
		tmp = 1.0 + (x - (y * z));
	} else if ((z <= -4.65e+61) || !(z <= 6.5e+178)) {
		tmp = t_0;
	} else {
		tmp = x + 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) :: t_0
    real(8) :: tmp
    t_0 = z * -sin(y)
    if (z <= (-2.9d+233)) then
        tmp = t_0
    else if (z <= (-4.6d+215)) then
        tmp = x
    else if (z <= (-7.8d+154)) then
        tmp = t_0
    else if (z <= (-4.2d+95)) then
        tmp = 1.0d0 + (x - (y * z))
    else if ((z <= (-4.65d+61)) .or. (.not. (z <= 6.5d+178))) then
        tmp = t_0
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -Math.sin(y);
	double tmp;
	if (z <= -2.9e+233) {
		tmp = t_0;
	} else if (z <= -4.6e+215) {
		tmp = x;
	} else if (z <= -7.8e+154) {
		tmp = t_0;
	} else if (z <= -4.2e+95) {
		tmp = 1.0 + (x - (y * z));
	} else if ((z <= -4.65e+61) || !(z <= 6.5e+178)) {
		tmp = t_0;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -math.sin(y)
	tmp = 0
	if z <= -2.9e+233:
		tmp = t_0
	elif z <= -4.6e+215:
		tmp = x
	elif z <= -7.8e+154:
		tmp = t_0
	elif z <= -4.2e+95:
		tmp = 1.0 + (x - (y * z))
	elif (z <= -4.65e+61) or not (z <= 6.5e+178):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (z <= -2.9e+233)
		tmp = t_0;
	elseif (z <= -4.6e+215)
		tmp = x;
	elseif (z <= -7.8e+154)
		tmp = t_0;
	elseif (z <= -4.2e+95)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	elseif ((z <= -4.65e+61) || !(z <= 6.5e+178))
		tmp = t_0;
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -sin(y);
	tmp = 0.0;
	if (z <= -2.9e+233)
		tmp = t_0;
	elseif (z <= -4.6e+215)
		tmp = x;
	elseif (z <= -7.8e+154)
		tmp = t_0;
	elseif (z <= -4.2e+95)
		tmp = 1.0 + (x - (y * z));
	elseif ((z <= -4.65e+61) || ~((z <= 6.5e+178)))
		tmp = t_0;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -2.9e+233], t$95$0, If[LessEqual[z, -4.6e+215], x, If[LessEqual[z, -7.8e+154], t$95$0, If[LessEqual[z, -4.2e+95], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.65e+61], N[Not[LessEqual[z, 6.5e+178]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.90000000000000012e233 or -4.6000000000000002e215 < z < -7.8000000000000006e154 or -4.2e95 < z < -4.64999999999999987e61 or 6.5000000000000005e178 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 81.1%

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

      2. neg-mul-1 81.1%

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

      3. *-commutative 81.1%

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

   4. Simplified 81.1%

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

   if -2.90000000000000012e233 < z < -4.6000000000000002e215

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

   if -7.8000000000000006e154 < z < -4.2e95

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

   4. Simplified 89.6%

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

   if -4.64999999999999987e61 < z < 6.5000000000000005e178

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 90.4%

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

      1. +-commutative 90.4%

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

   4. Simplified 90.4%

      \[\leadsto \color{blue}{\cos y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+233}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+215}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+95}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.65 \cdot 10^{+61} \lor \neg \left(z \leq 6.5 \cdot 10^{+178}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 3: 83.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - z \cdot \sin y\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+233}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+215}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.65 \cdot 10^{+61} \lor \neg \left(z \leq 4.7 \cdot 10^{+178}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* z (sin y)))))
   (if (<= z -4.2e+233)
     t_0
     (if (<= z -4.6e+215)
       x
       (if (or (<= z -4.65e+61) (not (<= z 4.7e+178))) t_0 (+ x (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (z * sin(y));
	double tmp;
	if (z <= -4.2e+233) {
		tmp = t_0;
	} else if (z <= -4.6e+215) {
		tmp = x;
	} else if ((z <= -4.65e+61) || !(z <= 4.7e+178)) {
		tmp = t_0;
	} else {
		tmp = x + 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (z * sin(y))
    if (z <= (-4.2d+233)) then
        tmp = t_0
    else if (z <= (-4.6d+215)) then
        tmp = x
    else if ((z <= (-4.65d+61)) .or. (.not. (z <= 4.7d+178))) then
        tmp = t_0
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (z * Math.sin(y));
	double tmp;
	if (z <= -4.2e+233) {
		tmp = t_0;
	} else if (z <= -4.6e+215) {
		tmp = x;
	} else if ((z <= -4.65e+61) || !(z <= 4.7e+178)) {
		tmp = t_0;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (z * math.sin(y))
	tmp = 0
	if z <= -4.2e+233:
		tmp = t_0
	elif z <= -4.6e+215:
		tmp = x
	elif (z <= -4.65e+61) or not (z <= 4.7e+178):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -4.2e+233)
		tmp = t_0;
	elseif (z <= -4.6e+215)
		tmp = x;
	elseif ((z <= -4.65e+61) || !(z <= 4.7e+178))
		tmp = t_0;
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (z * sin(y));
	tmp = 0.0;
	if (z <= -4.2e+233)
		tmp = t_0;
	elseif (z <= -4.6e+215)
		tmp = x;
	elseif ((z <= -4.65e+61) || ~((z <= 4.7e+178)))
		tmp = t_0;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+233], t$95$0, If[LessEqual[z, -4.6e+215], x, If[Or[LessEqual[z, -4.65e+61], N[Not[LessEqual[z, 4.7e+178]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999993e233 or -4.6000000000000002e215 < z < -4.64999999999999987e61 or 4.69999999999999992e178 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 81.4%

      \[\leadsto \color{blue}{1 - z \cdot \sin y} \]
   6. Step-by-step derivation

      1. *-commutative 81.4%

         \[\leadsto 1 - \color{blue}{\sin y \cdot z} \]

   7. Simplified 81.4%

      \[\leadsto \color{blue}{1 - \sin y \cdot z} \]

   if -4.19999999999999993e233 < z < -4.6000000000000002e215

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

   if -4.64999999999999987e61 < z < 4.69999999999999992e178

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 90.4%

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

      1. +-commutative 90.4%

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

   4. Simplified 90.4%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+233}:\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+215}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.65 \cdot 10^{+61} \lor \neg \left(z \leq 4.7 \cdot 10^{+178}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 4: 98.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \lor \neg \left(z \leq 7.2 \cdot 10^{-47}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.55) (not (<= z 7.2e-47)))
   (- (+ x 1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.55) || !(z <= 7.2e-47)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = x + 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 ((z <= (-1.55d0)) .or. (.not. (z <= 7.2d-47))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.55) || !(z <= 7.2e-47)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.55) or not (z <= 7.2e-47):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.55) || !(z <= 7.2e-47))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.55) || ~((z <= 7.2e-47)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.55], N[Not[LessEqual[z, 7.2e-47]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55000000000000004 or 7.19999999999999982e-47 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 98.9%

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

      1. +-commutative 98.9%

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

   4. Simplified 98.9%

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

   if -1.55000000000000004 < z < 7.19999999999999982e-47

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.6%

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

      1. +-commutative 99.6%

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

   4. Simplified 99.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \lor \neg \left(z \leq 7.2 \cdot 10^{-47}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 92.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.65 \cdot 10^{+61} \lor \neg \left(z \leq 8 \cdot 10^{-10}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.65e+61) (not (<= z 8e-10)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.65e+61) || !(z <= 8e-10)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = x + 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 ((z <= (-4.65d+61)) .or. (.not. (z <= 8d-10))) then
        tmp = x - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.65e+61) || !(z <= 8e-10)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.65e+61) or not (z <= 8e-10):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.65e+61) || !(z <= 8e-10))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.65e+61) || ~((z <= 8e-10)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.65e+61], N[Not[LessEqual[z, 8e-10]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.64999999999999987e61 or 8.00000000000000029e-10 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 91.2%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   if -4.64999999999999987e61 < z < 8.00000000000000029e-10

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 97.2%

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

      1. +-commutative 97.2%

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

   4. Simplified 97.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.65 \cdot 10^{+61} \lor \neg \left(z \leq 8 \cdot 10^{-10}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 6: 80.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.042 \lor \neg \left(y \leq 6 \cdot 10^{-6}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.042) (not (<= y 6e-6))) (+ x (cos y)) (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.042) || !(y <= 6e-6)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x - (y * 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 <= (-0.042d0)) .or. (.not. (y <= 6d-6))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.042) || !(y <= 6e-6)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.042) or not (y <= 6e-6):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.042) || !(y <= 6e-6))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.042) || ~((y <= 6e-6)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.042], N[Not[LessEqual[y, 6e-6]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0420000000000000026 or 6.0000000000000002e-6 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 65.0%

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

      1. +-commutative 65.0%

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

   4. Simplified 65.0%

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

   if -0.0420000000000000026 < y < 6.0000000000000002e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.1%

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

      1. mul-1-neg 99.1%

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

      2. unsub-neg 99.1%

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

   4. Simplified 99.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.042 \lor \neg \left(y \leq 6 \cdot 10^{-6}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]

Alternative 7: 71.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-14}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e+15) x (if (<= x 9.2e-14) (cos y) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+15) {
		tmp = x;
	} else if (x <= 9.2e-14) {
		tmp = cos(y);
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (x <= (-4.6d+15)) then
        tmp = x
    else if (x <= 9.2d-14) then
        tmp = cos(y)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+15) {
		tmp = x;
	} else if (x <= 9.2e-14) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e+15:
		tmp = x
	elif x <= 9.2e-14:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e+15)
		tmp = x;
	elseif (x <= 9.2e-14)
		tmp = cos(y);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.6e+15)
		tmp = x;
	elseif (x <= 9.2e-14)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e+15], x, If[LessEqual[x, 9.2e-14], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6e15

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 84.3%

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

   if -4.6e15 < x < 9.19999999999999993e-14

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 98.3%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   3. Step-by-step derivation

      1. cancel-sign-sub-inv 98.3%

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

      2. *-commutative 98.3%

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

      3. +-commutative 98.3%

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

      4. fma-def 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in z around 0 59.1%

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

   if 9.19999999999999993e-14 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.7%

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

      1. mul-1-neg 74.7%

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

      2. unsub-neg 74.7%

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

   4. Simplified 74.7%

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

   5. Taylor expanded in x around inf 83.5%

      \[\leadsto 1 + \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-14}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8: 69.7% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -500000000000 \lor \neg \left(y \leq 1.5 \cdot 10^{+31}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -500000000000.0) (not (<= y 1.5e+31)))
   (+ x 1.0)
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -500000000000.0) || !(y <= 1.5e+31)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * 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 <= (-500000000000.0d0)) .or. (.not. (y <= 1.5d+31))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -500000000000.0) || !(y <= 1.5e+31)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -500000000000.0) or not (y <= 1.5e+31):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -500000000000.0) || !(y <= 1.5e+31))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -500000000000.0) || ~((y <= 1.5e+31)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -500000000000.0], N[Not[LessEqual[y, 1.5e+31]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e11 or 1.49999999999999995e31 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 31.1%

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

      1. mul-1-neg 31.1%

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

      2. unsub-neg 31.1%

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

   4. Simplified 31.1%

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

   5. Taylor expanded in x around inf 43.3%

      \[\leadsto 1 + \color{blue}{x} \]

   if -5e11 < y < 1.49999999999999995e31

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 92.6%

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

      1. mul-1-neg 92.6%

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

      2. unsub-neg 92.6%

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

   4. Simplified 92.6%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -500000000000 \lor \neg \left(y \leq 1.5 \cdot 10^{+31}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]

Alternative 9: 65.5% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-128}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e+15) x (if (<= x 2.4e-128) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+15) {
		tmp = x;
	} else if (x <= 2.4e-128) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (x <= (-4.6d+15)) then
        tmp = x
    else if (x <= 2.4d-128) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+15) {
		tmp = x;
	} else if (x <= 2.4e-128) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e+15:
		tmp = x
	elif x <= 2.4e-128:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e+15)
		tmp = x;
	elseif (x <= 2.4e-128)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.6e+15)
		tmp = x;
	elseif (x <= 2.4e-128)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e+15], x, If[LessEqual[x, 2.4e-128], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6e15

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 84.3%

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

   if -4.6e15 < x < 2.3999999999999998e-128

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

   4. Simplified 47.2%

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

   5. Taylor expanded in x around 0 47.2%

      \[\leadsto \color{blue}{1 - y \cdot z} \]

   if 2.3999999999999998e-128 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. unsub-neg 66.0%

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

   4. Simplified 66.0%

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

   5. Taylor expanded in x around inf 73.5%

      \[\leadsto 1 + \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-128}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 10: 62.0% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.35e+233) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.35e+233) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (z <= (-3.35d+233)) then
        tmp = y * -z
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.35e+233) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.35e+233:
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.35e+233)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.35e+233)
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.35e+233], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.35000000000000021e233

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 48.0%

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

      1. mul-1-neg 48.0%

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

      2. unsub-neg 48.0%

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

   4. Simplified 48.0%

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

   5. Taylor expanded in x around 0 48.0%

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

      1. associate--l+ 48.0%

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

      2. +-commutative 48.0%

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

      3. associate--r- 48.0%

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

      4. fma-neg 48.0%

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(y, z, -1\right)} \]

      5. metadata-eval 48.0%

         \[\leadsto x - \mathsf{fma}\left(y, z, \color{blue}{-1}\right) \]

   7. Simplified 48.0%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(y, z, -1\right)} \]

   8. Taylor expanded in y around inf 38.6%

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

      1. mul-1-neg 38.6%

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

      2. distribute-rgt-neg-in 38.6%

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

   10. Simplified 38.6%

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

   if -3.35000000000000021e233 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 62.8%

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

      1. mul-1-neg 62.8%

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

      2. unsub-neg 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in x around inf 64.8%

      \[\leadsto 1 + \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 11: 60.6% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e+15) x (if (<= x 1.0) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+15) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = 1.0;
	} 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 <= (-4.6d+15)) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+15) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e+15:
		tmp = x
	elif x <= 1.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e+15)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.6e+15)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e+15], x, If[LessEqual[x, 1.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6e15 or 1 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 82.9%

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

   if -4.6e15 < x < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 97.6%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   3. Step-by-step derivation

      1. cancel-sign-sub-inv 97.6%

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

      2. *-commutative 97.6%

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

      3. +-commutative 97.6%

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

      4. fma-def 97.7%

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

   4. Simplified 97.7%

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

   5. Taylor expanded in y around 0 36.1%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 61.9% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

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 + 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 61.6%

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

   1. mul-1-neg 61.6%

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

   2. unsub-neg 61.6%

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

4. Simplified 61.6%

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

5. Taylor expanded in x around inf 60.5%

   \[\leadsto 1 + \color{blue}{x} \]

6. Final simplification 60.5%

   \[\leadsto x + 1 \]

Alternative 13: 21.0% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 57.0%

   \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
3. Step-by-step derivation

   1. cancel-sign-sub-inv 57.0%

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

   2. *-commutative 57.0%

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

   3. +-commutative 57.0%

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

   4. fma-def 57.0%

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

4. Simplified 57.0%

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

5. Taylor expanded in y around 0 19.3%

   \[\leadsto \color{blue}{1} \]

6. Final simplification 19.3%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))