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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 88.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+33}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-26}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e+33)
   (+ z x)
   (if (<= x 1.85e-26) (+ (sin y) (* z (cos y))) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+33) {
		tmp = z + x;
	} else if (x <= 1.85e-26) {
		tmp = sin(y) + (z * cos(y));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.1d+33)) then
        tmp = z + x
    else if (x <= 1.85d-26) then
        tmp = sin(y) + (z * cos(y))
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+33) {
		tmp = z + x;
	} else if (x <= 1.85e-26) {
		tmp = Math.sin(y) + (z * Math.cos(y));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e+33:
		tmp = z + x
	elif x <= 1.85e-26:
		tmp = math.sin(y) + (z * math.cos(y))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e+33)
		tmp = Float64(z + x);
	elseif (x <= 1.85e-26)
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e+33)
		tmp = z + x;
	elseif (x <= 1.85e-26)
		tmp = sin(y) + (z * cos(y));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e+33], N[(z + x), $MachinePrecision], If[LessEqual[x, 1.85e-26], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e33 or 1.8499999999999999e-26 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.7%

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

   if -2.1000000000000001e33 < x < 1.8499999999999999e-26

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 93.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+33}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-26}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 68.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 44000:\\ \;\;\;\;y + \left(\left(z + x\right) + \left(y \cdot \left(z \cdot y\right)\right) \cdot -0.5\right)\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+32} \lor \neg \left(y \leq 1.05 \cdot 10^{+70}\right) \land y \leq 4 \cdot 10^{+129}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2e+15)
   (+ z x)
   (if (<= y 44000.0)
     (+ y (+ (+ z x) (* (* y (* z y)) -0.5)))
     (if (or (<= y 5.7e+32) (and (not (<= y 1.05e+70)) (<= y 4e+129)))
       (sin y)
       (+ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+15) {
		tmp = z + x;
	} else if (y <= 44000.0) {
		tmp = y + ((z + x) + ((y * (z * y)) * -0.5));
	} else if ((y <= 5.7e+32) || (!(y <= 1.05e+70) && (y <= 4e+129))) {
		tmp = sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.2d+15)) then
        tmp = z + x
    else if (y <= 44000.0d0) then
        tmp = y + ((z + x) + ((y * (z * y)) * (-0.5d0)))
    else if ((y <= 5.7d+32) .or. (.not. (y <= 1.05d+70)) .and. (y <= 4d+129)) then
        tmp = sin(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+15) {
		tmp = z + x;
	} else if (y <= 44000.0) {
		tmp = y + ((z + x) + ((y * (z * y)) * -0.5));
	} else if ((y <= 5.7e+32) || (!(y <= 1.05e+70) && (y <= 4e+129))) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.2e+15:
		tmp = z + x
	elif y <= 44000.0:
		tmp = y + ((z + x) + ((y * (z * y)) * -0.5))
	elif (y <= 5.7e+32) or (not (y <= 1.05e+70) and (y <= 4e+129)):
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+15)
		tmp = Float64(z + x);
	elseif (y <= 44000.0)
		tmp = Float64(y + Float64(Float64(z + x) + Float64(Float64(y * Float64(z * y)) * -0.5)));
	elseif ((y <= 5.7e+32) || (!(y <= 1.05e+70) && (y <= 4e+129)))
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.2e+15)
		tmp = z + x;
	elseif (y <= 44000.0)
		tmp = y + ((z + x) + ((y * (z * y)) * -0.5));
	elseif ((y <= 5.7e+32) || (~((y <= 1.05e+70)) && (y <= 4e+129)))
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2e+15], N[(z + x), $MachinePrecision], If[LessEqual[y, 44000.0], N[(y + N[(N[(z + x), $MachinePrecision] + N[(N[(y * N[(z * y), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5.7e+32], And[N[Not[LessEqual[y, 1.05e+70]], $MachinePrecision], LessEqual[y, 4e+129]]], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e15 or 5.7e32 < y < 1.05000000000000004e70 or 4e129 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 42.6%

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

   if -1.2e15 < y < 44000

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.4%

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

      1. fma-def 97.4%

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

      2. *-commutative 97.4%

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

      3. unpow2 97.4%

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

   4. Simplified 97.4%

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

      1. fma-udef 97.4%

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

      2. +-commutative 97.4%

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

      3. associate-+r+ 97.4%

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

      4. *-commutative 97.4%

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

      5. *-commutative 97.4%

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

      6. associate-*l* 97.4%

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

   6. Applied egg-rr 97.4%

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

   if 44000 < y < 5.7e32 or 1.05000000000000004e70 < y < 4e129

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 69.1%

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

   3. Taylor expanded in x around 0 64.6%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 44000:\\ \;\;\;\;y + \left(\left(z + x\right) + \left(y \cdot \left(z \cdot y\right)\right) \cdot -0.5\right)\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+32} \lor \neg \left(y \leq 1.05 \cdot 10^{+70}\right) \land y \leq 4 \cdot 10^{+129}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 5: 83.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -4 \cdot 10^{+90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+74}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq -390 \lor \neg \left(z \leq 0.0095\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -4e+90)
     t_0
     (if (<= z -1.1e+74)
       (+ z x)
       (if (or (<= z -390.0) (not (<= z 0.0095))) t_0 (+ x (sin y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -4e+90) {
		tmp = t_0;
	} else if (z <= -1.1e+74) {
		tmp = z + x;
	} else if ((z <= -390.0) || !(z <= 0.0095)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-4d+90)) then
        tmp = t_0
    else if (z <= (-1.1d+74)) then
        tmp = z + x
    else if ((z <= (-390.0d0)) .or. (.not. (z <= 0.0095d0))) then
        tmp = t_0
    else
        tmp = x + sin(y)
    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 <= -4e+90) {
		tmp = t_0;
	} else if (z <= -1.1e+74) {
		tmp = z + x;
	} else if ((z <= -390.0) || !(z <= 0.0095)) {
		tmp = t_0;
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -4e+90:
		tmp = t_0
	elif z <= -1.1e+74:
		tmp = z + x
	elif (z <= -390.0) or not (z <= 0.0095):
		tmp = t_0
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -4e+90)
		tmp = t_0;
	elseif (z <= -1.1e+74)
		tmp = Float64(z + x);
	elseif ((z <= -390.0) || !(z <= 0.0095))
		tmp = t_0;
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -4e+90)
		tmp = t_0;
	elseif (z <= -1.1e+74)
		tmp = z + x;
	elseif ((z <= -390.0) || ~((z <= 0.0095)))
		tmp = t_0;
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+90], t$95$0, If[LessEqual[z, -1.1e+74], N[(z + x), $MachinePrecision], If[Or[LessEqual[z, -390.0], N[Not[LessEqual[z, 0.0095]], $MachinePrecision]], t$95$0, N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999987e90 or -1.1000000000000001e74 < z < -390 or 0.00949999999999999976 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. add-cube-cbrt 99.2%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} \cdot z + \left(x + \sin y\right) \]

      4. associate-*l* 99.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \left(\sqrt[3]{\cos y} \cdot z\right)} + \left(x + \sin y\right) \]

      5. fma-def 99.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

      6. pow2 99.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right) \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 78.1%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. *-commutative 78.1%

         \[\leadsto {1}^{0.3333333333333333} \cdot \color{blue}{\left(\cos y \cdot z\right)} \]

      2. pow-base-1 78.1%

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

      3. *-lft-identity 78.1%

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

   6. Simplified 78.1%

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

   if -3.99999999999999987e90 < z < -1.1000000000000001e74

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.5%

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

   if -390 < z < 0.00949999999999999976

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 90.1%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+74}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq -390 \lor \neg \left(z \leq 0.0095\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 6: 84.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+73}:\\ \;\;\;\;t_0 + \left(y + x\right)\\ \mathbf{elif}\;z \leq -35 \lor \neg \left(z \leq 0.0095\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -9.2e+73)
     (+ t_0 (+ y x))
     (if (or (<= z -35.0) (not (<= z 0.0095))) t_0 (+ x (sin y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -9.2e+73) {
		tmp = t_0 + (y + x);
	} else if ((z <= -35.0) || !(z <= 0.0095)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-9.2d+73)) then
        tmp = t_0 + (y + x)
    else if ((z <= (-35.0d0)) .or. (.not. (z <= 0.0095d0))) then
        tmp = t_0
    else
        tmp = x + sin(y)
    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 <= -9.2e+73) {
		tmp = t_0 + (y + x);
	} else if ((z <= -35.0) || !(z <= 0.0095)) {
		tmp = t_0;
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -9.2e+73:
		tmp = t_0 + (y + x)
	elif (z <= -35.0) or not (z <= 0.0095):
		tmp = t_0
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -9.2e+73)
		tmp = Float64(t_0 + Float64(y + x));
	elseif ((z <= -35.0) || !(z <= 0.0095))
		tmp = t_0;
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -9.2e+73)
		tmp = t_0 + (y + x);
	elseif ((z <= -35.0) || ~((z <= 0.0095)))
		tmp = t_0;
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+73], N[(t$95$0 + N[(y + x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -35.0], N[Not[LessEqual[z, 0.0095]], $MachinePrecision]], t$95$0, N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.199999999999999e73

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 84.2%

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

   if -9.199999999999999e73 < z < -35 or 0.00949999999999999976 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. add-cube-cbrt 99.2%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} \cdot z + \left(x + \sin y\right) \]

      4. associate-*l* 99.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \left(\sqrt[3]{\cos y} \cdot z\right)} + \left(x + \sin y\right) \]

      5. fma-def 99.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

      6. pow2 99.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right) \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 80.7%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. *-commutative 80.7%

         \[\leadsto {1}^{0.3333333333333333} \cdot \color{blue}{\left(\cos y \cdot z\right)} \]

      2. pow-base-1 80.7%

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

      3. *-lft-identity 80.7%

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

   6. Simplified 80.7%

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

   if -35 < z < 0.00949999999999999976

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 90.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \cos y + \left(y + x\right)\\ \mathbf{elif}\;z \leq -35 \lor \neg \left(z \leq 0.0095\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 7: 72.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.3e+33) (+ z x) (if (<= x 3.2e-27) (* z (cos y)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e+33) {
		tmp = z + x;
	} else if (x <= 3.2e-27) {
		tmp = z * cos(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.3d+33)) then
        tmp = z + x
    else if (x <= 3.2d-27) then
        tmp = z * cos(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e+33) {
		tmp = z + x;
	} else if (x <= 3.2e-27) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.3e+33:
		tmp = z + x
	elif x <= 3.2e-27:
		tmp = z * math.cos(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.3e+33)
		tmp = Float64(z + x);
	elseif (x <= 3.2e-27)
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.3e+33)
		tmp = z + x;
	elseif (x <= 3.2e-27)
		tmp = z * cos(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.3e+33], N[(z + x), $MachinePrecision], If[LessEqual[x, 3.2e-27], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.30000000000000011e33 or 3.19999999999999991e-27 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.0%

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

   if -2.30000000000000011e33 < x < 3.19999999999999991e-27

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. add-cube-cbrt 99.5%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} \cdot z + \left(x + \sin y\right) \]

      4. associate-*l* 99.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \left(\sqrt[3]{\cos y} \cdot z\right)} + \left(x + \sin y\right) \]

      5. fma-def 99.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

      6. pow2 99.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right) \]

   3. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 57.6%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. *-commutative 57.6%

         \[\leadsto {1}^{0.3333333333333333} \cdot \color{blue}{\left(\cos y \cdot z\right)} \]

      2. pow-base-1 57.6%

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

      3. *-lft-identity 57.6%

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

   6. Simplified 57.6%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 8: 69.9% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+15}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 25500000000000:\\ \;\;\;\;y + \left(\left(z + x\right) + \left(y \cdot \left(z \cdot y\right)\right) \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+15)
   (+ z x)
   (if (<= y 25500000000000.0)
     (+ y (+ (+ z x) (* (* y (* z y)) -0.5)))
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+15) {
		tmp = z + x;
	} else if (y <= 25500000000000.0) {
		tmp = y + ((z + x) + ((y * (z * y)) * -0.5));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.9d+15)) then
        tmp = z + x
    else if (y <= 25500000000000.0d0) then
        tmp = y + ((z + x) + ((y * (z * y)) * (-0.5d0)))
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+15) {
		tmp = z + x;
	} else if (y <= 25500000000000.0) {
		tmp = y + ((z + x) + ((y * (z * y)) * -0.5));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e+15:
		tmp = z + x
	elif y <= 25500000000000.0:
		tmp = y + ((z + x) + ((y * (z * y)) * -0.5))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+15)
		tmp = Float64(z + x);
	elseif (y <= 25500000000000.0)
		tmp = Float64(y + Float64(Float64(z + x) + Float64(Float64(y * Float64(z * y)) * -0.5)));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e+15)
		tmp = z + x;
	elseif (y <= 25500000000000.0)
		tmp = y + ((z + x) + ((y * (z * y)) * -0.5));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e+15], N[(z + x), $MachinePrecision], If[LessEqual[y, 25500000000000.0], N[(y + N[(N[(z + x), $MachinePrecision] + N[(N[(y * N[(z * y), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e15 or 2.55e13 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 38.3%

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

   if -1.9e15 < y < 2.55e13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.9%

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

      1. fma-def 95.9%

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

      2. *-commutative 95.9%

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

      3. unpow2 95.9%

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

   4. Simplified 95.9%

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

      1. fma-udef 95.9%

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

      2. +-commutative 95.9%

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

      3. associate-+r+ 95.9%

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

      4. *-commutative 95.9%

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

      5. *-commutative 95.9%

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

      6. associate-*l* 95.9%

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

   6. Applied egg-rr 95.9%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+15}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 25500000000000:\\ \;\;\;\;y + \left(\left(z + x\right) + \left(y \cdot \left(z \cdot y\right)\right) \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 9: 69.8% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+36}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+17}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.4e+36) (+ z x) (if (<= y 9.4e+17) (+ y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.4e+36) {
		tmp = z + x;
	} else if (y <= 9.4e+17) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9.4d+36)) then
        tmp = z + x
    else if (y <= 9.4d+17) then
        tmp = y + (z + x)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.4e+36) {
		tmp = z + x;
	} else if (y <= 9.4e+17) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.4e+36:
		tmp = z + x
	elif y <= 9.4e+17:
		tmp = y + (z + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.4e+36)
		tmp = Float64(z + x);
	elseif (y <= 9.4e+17)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.4e+36)
		tmp = z + x;
	elseif (y <= 9.4e+17)
		tmp = y + (z + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.4e+36], N[(z + x), $MachinePrecision], If[LessEqual[y, 9.4e+17], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.39999999999999978e36 or 9.4e17 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 38.6%

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

   if -9.39999999999999978e36 < y < 9.4e17

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+36}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+17}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 10: 57.3% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+50}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e-8) x (if (<= x 1.3e+50) (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e-8) {
		tmp = x;
	} else if (x <= 1.3e+50) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.3d-8)) then
        tmp = x
    else if (x <= 1.3d+50) then
        tmp = z + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e-8) {
		tmp = x;
	} else if (x <= 1.3e+50) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e-8:
		tmp = x
	elif x <= 1.3e+50:
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e-8)
		tmp = x;
	elseif (x <= 1.3e+50)
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.3e-8)
		tmp = x;
	elseif (x <= 1.3e+50)
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e-8], x, If[LessEqual[x, 1.3e+50], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3000000000000001e-8 or 1.3000000000000001e50 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.8%

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

   if -1.3000000000000001e-8 < x < 1.3000000000000001e50

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 91.1%

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

      1. *-commutative 91.1%

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

      2. fma-def 91.1%

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

   4. Simplified 91.1%

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

   5. Taylor expanded in y around 0 36.9%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+50}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 52.9% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+50}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.3e-93) x (if (<= x 1.3e+50) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.3e-93) {
		tmp = x;
	} else if (x <= 1.3e+50) {
		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 <= (-3.3d-93)) then
        tmp = x
    else if (x <= 1.3d+50) 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 <= -3.3e-93) {
		tmp = x;
	} else if (x <= 1.3e+50) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.3e-93:
		tmp = x
	elif x <= 1.3e+50:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.3e-93)
		tmp = x;
	elseif (x <= 1.3e+50)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.3e-93)
		tmp = x;
	elseif (x <= 1.3e+50)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.3e-93], x, If[LessEqual[x, 1.3e+50], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3000000000000001e-93 or 1.3000000000000001e50 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 68.2%

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

   if -3.3000000000000001e-93 < x < 1.3000000000000001e50

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. add-cube-cbrt 99.5%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} \cdot z + \left(x + \sin y\right) \]

      4. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \left(\sqrt[3]{\cos y} \cdot z\right)} + \left(x + \sin y\right) \]

      5. fma-def 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

      6. pow2 99.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right) \]

   3. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 59.2%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. *-commutative 59.2%

         \[\leadsto {1}^{0.3333333333333333} \cdot \color{blue}{\left(\cos y \cdot z\right)} \]

      2. pow-base-1 59.2%

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

      3. *-lft-identity 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in y around 0 32.1%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+50}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 65.5% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 60.6%

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

3. Final simplification 60.6%

   \[\leadsto z + x \]

Alternative 13: 42.0% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around inf 38.6%

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

3. Final simplification 38.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023192 
(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))))