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

Percentage Accurate: 99.9% → 99.9%

Time: 8.6s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -6 \cdot 10^{+120}:\\ \;\;\;\;t_0 + \left(y + x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+176}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -6e+120)
     (+ t_0 (+ y x))
     (if (<= z 2.35e+176) (+ z (+ x (sin y))) (+ (sin y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -6e+120) {
		tmp = t_0 + (y + x);
	} else if (z <= 2.35e+176) {
		tmp = z + (x + sin(y));
	} else {
		tmp = sin(y) + 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 <= (-6d+120)) then
        tmp = t_0 + (y + x)
    else if (z <= 2.35d+176) then
        tmp = z + (x + sin(y))
    else
        tmp = sin(y) + 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 <= -6e+120) {
		tmp = t_0 + (y + x);
	} else if (z <= 2.35e+176) {
		tmp = z + (x + Math.sin(y));
	} else {
		tmp = Math.sin(y) + t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -6e+120:
		tmp = t_0 + (y + x)
	elif z <= 2.35e+176:
		tmp = z + (x + math.sin(y))
	else:
		tmp = math.sin(y) + t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -6e+120)
		tmp = Float64(t_0 + Float64(y + x));
	elseif (z <= 2.35e+176)
		tmp = Float64(z + Float64(x + sin(y)));
	else
		tmp = Float64(sin(y) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -6e+120)
		tmp = t_0 + (y + x);
	elseif (z <= 2.35e+176)
		tmp = z + (x + sin(y));
	else
		tmp = sin(y) + 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, -6e+120], N[(t$95$0 + N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+176], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e120

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.7%

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

   if -6e120 < z < 2.34999999999999991e176

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.3%

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

   if 2.34999999999999991e176 < 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. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.0%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \cos y + \left(y + x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+176}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 71.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -0.045:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-308}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-262}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-36}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= x -0.045)
     (+ z x)
     (if (<= x -4.4e-308)
       t_0
       (if (<= x 2.4e-262)
         (sin y)
         (if (<= x 1.35e-65) t_0 (if (<= x 2.45e-36) (sin y) (+ z x))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (x <= -0.045) {
		tmp = z + x;
	} else if (x <= -4.4e-308) {
		tmp = t_0;
	} else if (x <= 2.4e-262) {
		tmp = sin(y);
	} else if (x <= 1.35e-65) {
		tmp = t_0;
	} else if (x <= 2.45e-36) {
		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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (x <= (-0.045d0)) then
        tmp = z + x
    else if (x <= (-4.4d-308)) then
        tmp = t_0
    else if (x <= 2.4d-262) then
        tmp = sin(y)
    else if (x <= 1.35d-65) then
        tmp = t_0
    else if (x <= 2.45d-36) 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 t_0 = z * Math.cos(y);
	double tmp;
	if (x <= -0.045) {
		tmp = z + x;
	} else if (x <= -4.4e-308) {
		tmp = t_0;
	} else if (x <= 2.4e-262) {
		tmp = Math.sin(y);
	} else if (x <= 1.35e-65) {
		tmp = t_0;
	} else if (x <= 2.45e-36) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if x <= -0.045:
		tmp = z + x
	elif x <= -4.4e-308:
		tmp = t_0
	elif x <= 2.4e-262:
		tmp = math.sin(y)
	elif x <= 1.35e-65:
		tmp = t_0
	elif x <= 2.45e-36:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (x <= -0.045)
		tmp = Float64(z + x);
	elseif (x <= -4.4e-308)
		tmp = t_0;
	elseif (x <= 2.4e-262)
		tmp = sin(y);
	elseif (x <= 1.35e-65)
		tmp = t_0;
	elseif (x <= 2.45e-36)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (x <= -0.045)
		tmp = z + x;
	elseif (x <= -4.4e-308)
		tmp = t_0;
	elseif (x <= 2.4e-262)
		tmp = sin(y);
	elseif (x <= 1.35e-65)
		tmp = t_0;
	elseif (x <= 2.45e-36)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.045], N[(z + x), $MachinePrecision], If[LessEqual[x, -4.4e-308], t$95$0, If[LessEqual[x, 2.4e-262], N[Sin[y], $MachinePrecision], If[LessEqual[x, 1.35e-65], t$95$0, If[LessEqual[x, 2.45e-36], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.044999999999999998 or 2.4499999999999998e-36 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.6%

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

   if -0.044999999999999998 < x < -4.3999999999999999e-308 or 2.4e-262 < x < 1.3499999999999999e-65

   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%

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

      7. +-commutative 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in z around inf 64.4%

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

      1. pow-base-1 64.4%

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

      2. *-commutative 64.4%

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

      3. *-lft-identity 64.4%

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

   6. Simplified 64.4%

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

   if -4.3999999999999999e-308 < x < 2.4e-262 or 1.3499999999999999e-65 < x < 2.4499999999999998e-36

   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 96.9%

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

   5. Taylor expanded in z around 0 80.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.045:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-308}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-262}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-65}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-36}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 5: 82.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+136}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-35}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+53}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.5e+136)
     t_0
     (if (<= z -2.35e-35) (+ z x) (if (<= z 6.2e+53) (+ 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+136) {
		tmp = t_0;
	} else if (z <= -2.35e-35) {
		tmp = z + x;
	} else if (z <= 6.2e+53) {
		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+136)) then
        tmp = t_0
    else if (z <= (-2.35d-35)) then
        tmp = z + x
    else if (z <= 6.2d+53) 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+136) {
		tmp = t_0;
	} else if (z <= -2.35e-35) {
		tmp = z + x;
	} else if (z <= 6.2e+53) {
		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+136:
		tmp = t_0
	elif z <= -2.35e-35:
		tmp = z + x
	elif z <= 6.2e+53:
		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+136)
		tmp = t_0;
	elseif (z <= -2.35e-35)
		tmp = Float64(z + x);
	elseif (z <= 6.2e+53)
		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+136)
		tmp = t_0;
	elseif (z <= -2.35e-35)
		tmp = z + x;
	elseif (z <= 6.2e+53)
		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+136], t$95$0, If[LessEqual[z, -2.35e-35], N[(z + x), $MachinePrecision], If[LessEqual[z, 6.2e+53], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5000000000000001e136 or 6.20000000000000038e53 < 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%

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

      7. +-commutative 99.2%

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

   3. Applied egg-rr 99.2%

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

   4. Taylor expanded in z around inf 82.7%

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

      1. pow-base-1 82.7%

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

      2. *-commutative 82.7%

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

      3. *-lft-identity 82.7%

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

   6. Simplified 82.7%

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

   if -2.5000000000000001e136 < z < -2.35e-35

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.6%

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

   if -2.35e-35 < z < 6.20000000000000038e53

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 93.7%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+136}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-35}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+53}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 6: 88.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+135} \lor \neg \left(z \leq 1.5 \cdot 10^{+182}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.8e+135) (not (<= z 1.5e+182)))
   (* z (cos y))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.8e+135) || !(z <= 1.5e+182)) {
		tmp = z * cos(y);
	} else {
		tmp = z + (x + sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8.8d+135)) .or. (.not. (z <= 1.5d+182))) then
        tmp = z * cos(y)
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.8e+135) || !(z <= 1.5e+182)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.8e+135) or not (z <= 1.5e+182):
		tmp = z * math.cos(y)
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.8e+135) || !(z <= 1.5e+182))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.8e+135) || ~((z <= 1.5e+182)))
		tmp = z * cos(y);
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.8e+135], N[Not[LessEqual[z, 1.5e+182]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.7999999999999998e135 or 1.5000000000000001e182 < 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%

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

      7. +-commutative 99.2%

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

   3. Applied egg-rr 99.2%

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

   4. Taylor expanded in z around inf 88.2%

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

      1. pow-base-1 88.2%

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

      2. *-commutative 88.2%

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

      3. *-lft-identity 88.2%

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

   6. Simplified 88.2%

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

   if -8.7999999999999998e135 < z < 1.5000000000000001e182

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.0%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+135} \lor \neg \left(z \leq 1.5 \cdot 10^{+182}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 7: 89.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+121}:\\ \;\;\;\;t_0 + \left(y + x\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+176}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.2e+121)
     (+ t_0 (+ y x))
     (if (<= z 3.7e+176) (+ z (+ x (sin y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.2e+121) {
		tmp = t_0 + (y + x);
	} else if (z <= 3.7e+176) {
		tmp = z + (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 <= (-2.2d+121)) then
        tmp = t_0 + (y + x)
    else if (z <= 3.7d+176) then
        tmp = z + (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 <= -2.2e+121) {
		tmp = t_0 + (y + x);
	} else if (z <= 3.7e+176) {
		tmp = z + (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 <= -2.2e+121:
		tmp = t_0 + (y + x)
	elif z <= 3.7e+176:
		tmp = z + (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 <= -2.2e+121)
		tmp = Float64(t_0 + Float64(y + x));
	elseif (z <= 3.7e+176)
		tmp = Float64(z + 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 <= -2.2e+121)
		tmp = t_0 + (y + x);
	elseif (z <= 3.7e+176)
		tmp = z + (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, -2.2e+121], N[(t$95$0 + N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+176], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000001e121

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.7%

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

   if -2.20000000000000001e121 < z < 3.6999999999999998e176

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.3%

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

   if 3.6999999999999998e176 < 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 99.1%

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

      4. associate-*l* 99.1%

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

      5. fma-def 99.1%

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

      6. pow2 99.1%

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

      7. +-commutative 99.1%

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

   3. Applied egg-rr 99.1%

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

   4. Taylor expanded in z around inf 97.0%

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

      1. pow-base-1 97.0%

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

      2. *-commutative 97.0%

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

      3. *-lft-identity 97.0%

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

   6. Simplified 97.0%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \cos y + \left(y + x\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+176}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 8: 78.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-38} \lor \neg \left(x \leq 2.9 \cdot 10^{-35}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.5e-38) (not (<= x 2.9e-35))) (+ z x) (+ z (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.5e-38) || !(x <= 2.9e-35)) {
		tmp = z + x;
	} else {
		tmp = z + 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 ((x <= (-4.5d-38)) .or. (.not. (x <= 2.9d-35))) then
        tmp = z + x
    else
        tmp = z + sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.5e-38) || !(x <= 2.9e-35)) {
		tmp = z + x;
	} else {
		tmp = z + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.5e-38) or not (x <= 2.9e-35):
		tmp = z + x
	else:
		tmp = z + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.5e-38) || !(x <= 2.9e-35))
		tmp = Float64(z + x);
	else
		tmp = Float64(z + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.5e-38) || ~((x <= 2.9e-35)))
		tmp = z + x;
	else
		tmp = z + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.5e-38], N[Not[LessEqual[x, 2.9e-35]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.50000000000000009e-38 or 2.9000000000000002e-35 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 84.7%

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

   if -4.50000000000000009e-38 < x < 2.9000000000000002e-35

   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 95.8%

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

      1. *-commutative 95.8%

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

      2. add-cube-cbrt 94.7%

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

      3. unpow3 94.7%

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

      4. add-sqr-sqrt 46.9%

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

      5. pow2 46.9%

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

      6. unpow3 46.8%

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

      7. add-cube-cbrt 47.1%

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

      8. *-commutative 47.1%

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

   6. Applied egg-rr 47.1%

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

   7. Taylor expanded in y around 0 73.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-38} \lor \neg \left(x \leq 2.9 \cdot 10^{-35}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \sin y\\ \end{array} \]

Alternative 9: 70.4% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+79}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+42}:\\ \;\;\;\;x + \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e+79) (+ z x) (if (<= y 1.4e+42) (+ x (+ z y)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+79) {
		tmp = z + x;
	} else if (y <= 1.4e+42) {
		tmp = x + (z + 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 <= (-8.5d+79)) then
        tmp = z + x
    else if (y <= 1.4d+42) then
        tmp = x + (z + 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 <= -8.5e+79) {
		tmp = z + x;
	} else if (y <= 1.4e+42) {
		tmp = x + (z + y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e+79:
		tmp = z + x
	elif y <= 1.4e+42:
		tmp = x + (z + y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e+79)
		tmp = Float64(z + x);
	elseif (y <= 1.4e+42)
		tmp = Float64(x + Float64(z + y));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.5e+79)
		tmp = z + x;
	elseif (y <= 1.4e+42)
		tmp = x + (z + y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e+79], N[(z + x), $MachinePrecision], If[LessEqual[y, 1.4e+42], N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999998e79 or 1.4e42 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 41.3%

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

   if -8.4999999999999998e79 < y < 1.4e42

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.0%

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

      1. associate-+r+ 87.0%

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

   4. Simplified 87.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+79}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+42}:\\ \;\;\;\;x + \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 10: 45.7% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+43}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.8e+79) x (if (<= y 1.3e+43) (+ y x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e+79) {
		tmp = x;
	} else if (y <= 1.3e+43) {
		tmp = y + x;
	} 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 (y <= (-9.8d+79)) then
        tmp = x
    else if (y <= 1.3d+43) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e+79) {
		tmp = x;
	} else if (y <= 1.3e+43) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.8e+79:
		tmp = x
	elif y <= 1.3e+43:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.8e+79)
		tmp = x;
	elseif (y <= 1.3e+43)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.8e+79)
		tmp = x;
	elseif (y <= 1.3e+43)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.8e+79], x, If[LessEqual[y, 1.3e+43], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -9.7999999999999997e79 or 1.3000000000000001e43 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 37.9%

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

   if -9.7999999999999997e79 < y < 1.3000000000000001e43

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 55.8%

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

   3. Taylor expanded in y around 0 50.6%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+43}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 57.4% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e-74) x (if (<= x 9.5e-33) (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e-74) {
		tmp = x;
	} else if (x <= 9.5e-33) {
		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 <= (-1.9d-74)) then
        tmp = x
    else if (x <= 9.5d-33) 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 <= -1.9e-74) {
		tmp = x;
	} else if (x <= 9.5e-33) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.9e-74:
		tmp = x
	elif x <= 9.5e-33:
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e-74)
		tmp = x;
	elseif (x <= 9.5e-33)
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.9e-74)
		tmp = x;
	elseif (x <= 9.5e-33)
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e-74], x, If[LessEqual[x, 9.5e-33], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8999999999999998e-74 or 9.50000000000000019e-33 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 66.5%

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

   if -1.8999999999999998e-74 < x < 9.50000000000000019e-33

   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 96.5%

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

   5. Taylor expanded in y around 0 47.3%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 68.1% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-71}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-197}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.6e-71) (+ z x) (if (<= x 2.7e-197) (+ z y) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.6e-71) {
		tmp = z + x;
	} else if (x <= 2.7e-197) {
		tmp = z + 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 <= (-6.6d-71)) then
        tmp = z + x
    else if (x <= 2.7d-197) then
        tmp = z + 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 <= -6.6e-71) {
		tmp = z + x;
	} else if (x <= 2.7e-197) {
		tmp = z + y;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.6e-71:
		tmp = z + x
	elif x <= 2.7e-197:
		tmp = z + y
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.6e-71)
		tmp = Float64(z + x);
	elseif (x <= 2.7e-197)
		tmp = Float64(z + y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.6e-71)
		tmp = z + x;
	elseif (x <= 2.7e-197)
		tmp = z + y;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.6e-71], N[(z + x), $MachinePrecision], If[LessEqual[x, 2.7e-197], N[(z + y), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6000000000000003e-71 or 2.70000000000000017e-197 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.5%

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

   if -6.6000000000000003e-71 < x < 2.70000000000000017e-197

   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 98.6%

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

   5. Taylor expanded in y around 0 49.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-71}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-197}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 13: 42.3% 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 40.6%

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

3. Final simplification 40.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023199 
(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))))