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

Percentage Accurate: 99.9% → 99.9%

Time: 10.8s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

   1. fma-undefine 99.9%

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

6. Applied egg-rr 99.9%

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

Alternative 2: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+39}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \cos y + \sin y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.75e+39)
   (+ x z)
   (if (<= x 1.15e-73) (+ (* z (cos y)) (sin y)) (+ z (+ x (sin y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e+39) {
		tmp = x + z;
	} else if (x <= 1.15e-73) {
		tmp = (z * cos(y)) + sin(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 (x <= (-1.75d+39)) then
        tmp = x + z
    else if (x <= 1.15d-73) then
        tmp = (z * cos(y)) + sin(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 (x <= -1.75e+39) {
		tmp = x + z;
	} else if (x <= 1.15e-73) {
		tmp = (z * Math.cos(y)) + Math.sin(y);
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.75e+39:
		tmp = x + z
	elif x <= 1.15e-73:
		tmp = (z * math.cos(y)) + math.sin(y)
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.75e+39)
		tmp = Float64(x + z);
	elseif (x <= 1.15e-73)
		tmp = Float64(Float64(z * cos(y)) + sin(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 (x <= -1.75e+39)
		tmp = x + z;
	elseif (x <= 1.15e-73)
		tmp = (z * cos(y)) + sin(y);
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.75e+39], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.15e-73], N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7500000000000001e39

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 90.8%

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

      1. +-commutative 90.8%

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

   7. Simplified 90.8%

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

   if -1.7500000000000001e39 < x < 1.14999999999999994e-73

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 93.8%

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

   if 1.14999999999999994e-73 < x

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. cube-mult 99.8%

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

      2. add-cube-cbrt 99.8%

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

      3. associate-*l* 99.8%

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

      4. cbrt-unprod 99.8%

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

      5. pow2 99.8%

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

      6. pow2 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r* 99.8%

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

      3. rem-cube-cbrt 99.7%

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

      4. pow-plus 99.7%

         \[\leadsto \left(x + \sin y\right) + z \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \color{blue}{{\left(\sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right)}^{\left(3 + 1\right)}}\right) \]

      5. metadata-eval 99.7%

         \[\leadsto \left(x + \sin y\right) + z \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot {\left(\sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right)}^{\color{blue}{4}}\right) \]

   8. Simplified 99.7%

      \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot {\left(\sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right)}^{4}\right)} \]

   9. Taylor expanded in y around 0 90.5%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+39}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \cos y + \sin y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+184}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-56}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-60}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+191}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -5.4e+184)
     t_0
     (if (<= z -1.85e-56)
       (+ x z)
       (if (<= z 8e-60) (+ x (sin y)) (if (<= z 3.7e+191) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -5.4e+184) {
		tmp = t_0;
	} else if (z <= -1.85e-56) {
		tmp = x + z;
	} else if (z <= 8e-60) {
		tmp = x + sin(y);
	} else if (z <= 3.7e+191) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-5.4d+184)) then
        tmp = t_0
    else if (z <= (-1.85d-56)) then
        tmp = x + z
    else if (z <= 8d-60) then
        tmp = x + sin(y)
    else if (z <= 3.7d+191) then
        tmp = x + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -5.4e+184) {
		tmp = t_0;
	} else if (z <= -1.85e-56) {
		tmp = x + z;
	} else if (z <= 8e-60) {
		tmp = x + Math.sin(y);
	} else if (z <= 3.7e+191) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -5.4e+184:
		tmp = t_0
	elif z <= -1.85e-56:
		tmp = x + z
	elif z <= 8e-60:
		tmp = x + math.sin(y)
	elif z <= 3.7e+191:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -5.4e+184)
		tmp = t_0;
	elseif (z <= -1.85e-56)
		tmp = Float64(x + z);
	elseif (z <= 8e-60)
		tmp = Float64(x + sin(y));
	elseif (z <= 3.7e+191)
		tmp = Float64(x + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -5.4e+184)
		tmp = t_0;
	elseif (z <= -1.85e-56)
		tmp = x + z;
	elseif (z <= 8e-60)
		tmp = x + sin(y);
	elseif (z <= 3.7e+191)
		tmp = x + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+184], t$95$0, If[LessEqual[z, -1.85e-56], N[(x + z), $MachinePrecision], If[LessEqual[z, 8e-60], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+191], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.3999999999999998e184 or 3.70000000000000019e191 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 91.3%

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

   if -5.3999999999999998e184 < z < -1.8500000000000001e-56 or 7.9999999999999998e-60 < z < 3.70000000000000019e191

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 83.7%

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

      1. +-commutative 83.7%

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

   7. Simplified 83.7%

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

   if -1.8500000000000001e-56 < z < 7.9999999999999998e-60

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 96.8%

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

      1. +-commutative 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+184}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-56}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-60}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+191}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+184}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-251}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-64}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+191}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.35e+184)
     t_0
     (if (<= z -3e-251)
       (+ x z)
       (if (<= z 3.1e-64) (sin y) (if (<= z 3.7e+191) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.35e+184) {
		tmp = t_0;
	} else if (z <= -3e-251) {
		tmp = x + z;
	} else if (z <= 3.1e-64) {
		tmp = sin(y);
	} else if (z <= 3.7e+191) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-1.35d+184)) then
        tmp = t_0
    else if (z <= (-3d-251)) then
        tmp = x + z
    else if (z <= 3.1d-64) then
        tmp = sin(y)
    else if (z <= 3.7d+191) then
        tmp = x + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -1.35e+184) {
		tmp = t_0;
	} else if (z <= -3e-251) {
		tmp = x + z;
	} else if (z <= 3.1e-64) {
		tmp = Math.sin(y);
	} else if (z <= 3.7e+191) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1.35e+184:
		tmp = t_0
	elif z <= -3e-251:
		tmp = x + z
	elif z <= 3.1e-64:
		tmp = math.sin(y)
	elif z <= 3.7e+191:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1.35e+184)
		tmp = t_0;
	elseif (z <= -3e-251)
		tmp = Float64(x + z);
	elseif (z <= 3.1e-64)
		tmp = sin(y);
	elseif (z <= 3.7e+191)
		tmp = Float64(x + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1.35e+184)
		tmp = t_0;
	elseif (z <= -3e-251)
		tmp = x + z;
	elseif (z <= 3.1e-64)
		tmp = sin(y);
	elseif (z <= 3.7e+191)
		tmp = x + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+184], t$95$0, If[LessEqual[z, -3e-251], N[(x + z), $MachinePrecision], If[LessEqual[z, 3.1e-64], N[Sin[y], $MachinePrecision], If[LessEqual[z, 3.7e+191], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e184 or 3.70000000000000019e191 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 91.3%

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

   if -1.35e184 < z < -2.9999999999999999e-251 or 3.10000000000000025e-64 < z < 3.70000000000000019e191

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 77.5%

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

      1. +-commutative 77.5%

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

   7. Simplified 77.5%

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

   if -2.9999999999999999e-251 < z < 3.10000000000000025e-64

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 65.2%

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

   6. Taylor expanded in z around 0 65.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+184}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-251}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-64}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+191}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+184} \lor \neg \left(z \leq 2.3 \cdot 10^{+195}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.25e+184) (not (<= z 2.3e+195)))
   (* z (cos y))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.25e+184) || !(z <= 2.3e+195)) {
		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 <= (-1.25d+184)) .or. (.not. (z <= 2.3d+195))) 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 <= -1.25e+184) || !(z <= 2.3e+195)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.25e+184) or not (z <= 2.3e+195):
		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 <= -1.25e+184) || !(z <= 2.3e+195))
		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 <= -1.25e+184) || ~((z <= 2.3e+195)))
		tmp = z * cos(y);
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.25e+184], N[Not[LessEqual[z, 2.3e+195]], $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 < -1.25e184 or 2.3000000000000001e195 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 91.3%

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

   if -1.25e184 < z < 2.3000000000000001e195

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. cube-mult 99.8%

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

      2. add-cube-cbrt 99.8%

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

      3. associate-*l* 99.8%

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

      4. cbrt-unprod 99.8%

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

      5. pow2 99.8%

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

      6. pow2 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r* 99.8%

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

      3. rem-cube-cbrt 99.8%

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

      4. pow-plus 99.8%

         \[\leadsto \left(x + \sin y\right) + z \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \color{blue}{{\left(\sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right)}^{\left(3 + 1\right)}}\right) \]

      5. metadata-eval 99.8%

         \[\leadsto \left(x + \sin y\right) + z \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot {\left(\sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right)}^{\color{blue}{4}}\right) \]

   8. Simplified 99.8%

      \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot {\left(\sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right)}^{4}\right)} \]

   9. Taylor expanded in y around 0 92.3%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+184} \lor \neg \left(z \leq 2.3 \cdot 10^{+195}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-251} \lor \neg \left(z \leq 3.5 \cdot 10^{-64}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.6e-251) (not (<= z 3.5e-64))) (+ x z) (sin y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.6e-251) || !(z <= 3.5e-64)) {
		tmp = x + z;
	} else {
		tmp = 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 <= (-5.6d-251)) .or. (.not. (z <= 3.5d-64))) then
        tmp = x + z
    else
        tmp = sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.6e-251) || !(z <= 3.5e-64)) {
		tmp = x + z;
	} else {
		tmp = Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.6e-251) or not (z <= 3.5e-64):
		tmp = x + z
	else:
		tmp = math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.6e-251) || !(z <= 3.5e-64))
		tmp = Float64(x + z);
	else
		tmp = sin(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.6e-251) || ~((z <= 3.5e-64)))
		tmp = x + z;
	else
		tmp = sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.6e-251], N[Not[LessEqual[z, 3.5e-64]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[Sin[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999978e-251 or 3.5000000000000003e-64 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 72.8%

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

      1. +-commutative 72.8%

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

   7. Simplified 72.8%

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

   if -5.59999999999999978e-251 < z < 3.5000000000000003e-64

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 65.2%

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

   6. Taylor expanded in z around 0 65.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-251} \lor \neg \left(z \leq 3.5 \cdot 10^{-64}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.4% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+33} \lor \neg \left(y \leq 0.0058\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2e+33) (not (<= y 0.0058)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e+33) || !(y <= 0.0058)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2d+33)) .or. (.not. (y <= 0.0058d0))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e+33) || !(y <= 0.0058)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2e+33) or not (y <= 0.0058):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2e+33) || !(y <= 0.0058))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2e+33) || ~((y <= 0.0058)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2e+33], N[Not[LessEqual[y, 0.0058]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9999999999999999e33 or 0.0058 < y

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 36.6%

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

      1. +-commutative 36.6%

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

   7. Simplified 36.6%

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

   if -1.9999999999999999e33 < y < 0.0058

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+33} \lor \neg \left(y \leq 0.0058\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+38} \lor \neg \left(y \leq 0.0058\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.9e+38) (not (<= y 0.0058)))
   (+ x z)
   (+ (+ x z) (* y (+ 1.0 (* -0.5 (* z y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e+38) || !(y <= 0.0058)) {
		tmp = x + z;
	} else {
		tmp = (x + z) + (y * (1.0 + (-0.5 * (z * y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.9d+38)) .or. (.not. (y <= 0.0058d0))) then
        tmp = x + z
    else
        tmp = (x + z) + (y * (1.0d0 + ((-0.5d0) * (z * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e+38) || !(y <= 0.0058)) {
		tmp = x + z;
	} else {
		tmp = (x + z) + (y * (1.0 + (-0.5 * (z * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.9e+38) or not (y <= 0.0058):
		tmp = x + z
	else:
		tmp = (x + z) + (y * (1.0 + (-0.5 * (z * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.9e+38) || !(y <= 0.0058))
		tmp = Float64(x + z);
	else
		tmp = Float64(Float64(x + z) + Float64(y * Float64(1.0 + Float64(-0.5 * Float64(z * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.9e+38) || ~((y <= 0.0058)))
		tmp = x + z;
	else
		tmp = (x + z) + (y * (1.0 + (-0.5 * (z * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.9e+38], N[Not[LessEqual[y, 0.0058]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[(y * N[(1.0 + N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.90000000000000007e38 or 0.0058 < y

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 36.9%

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

      1. +-commutative 36.9%

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

   7. Simplified 36.9%

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

   if -2.90000000000000007e38 < y < 0.0058

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.7%

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

      1. associate-+r+ 97.7%

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

      2. +-commutative 97.7%

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

   7. Simplified 97.7%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+38} \lor \neg \left(y \leq 0.0058\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-80} \lor \neg \left(x \leq 0.075\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.65e-80) (not (<= x 0.075))) (+ x z) (+ y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e-80) || !(x <= 0.075)) {
		tmp = x + z;
	} else {
		tmp = y + (x + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.65d-80)) .or. (.not. (x <= 0.075d0))) then
        tmp = x + z
    else
        tmp = y + (x + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e-80) || !(x <= 0.075)) {
		tmp = x + z;
	} else {
		tmp = y + (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.65e-80) or not (x <= 0.075):
		tmp = x + z
	else:
		tmp = y + (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.65e-80) || !(x <= 0.075))
		tmp = Float64(x + z);
	else
		tmp = Float64(y + Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.65e-80) || ~((x <= 0.075)))
		tmp = x + z;
	else
		tmp = y + (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.65e-80], N[Not[LessEqual[x, 0.075]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e-80 or 0.0749999999999999972 < x

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 86.0%

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

      1. +-commutative 86.0%

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

   7. Simplified 86.0%

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

   if -1.65e-80 < x < 0.0749999999999999972

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 48.9%

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

      1. +-commutative 48.9%

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

      2. associate-+l+ 48.9%

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

   7. Simplified 48.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-80} \lor \neg \left(x \leq 0.075\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.9% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-203} \lor \neg \left(x \leq 1.02 \cdot 10^{-88}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.2e-203) (not (<= x 1.02e-88))) (+ x z) (+ z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.2e-203) || !(x <= 1.02e-88)) {
		tmp = x + z;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-9.2d-203)) .or. (.not. (x <= 1.02d-88))) then
        tmp = x + z
    else
        tmp = z + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.2e-203) || !(x <= 1.02e-88)) {
		tmp = x + z;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.2e-203) or not (x <= 1.02e-88):
		tmp = x + z
	else:
		tmp = z + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.2e-203) || !(x <= 1.02e-88))
		tmp = Float64(x + z);
	else
		tmp = Float64(z + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.2e-203) || ~((x <= 1.02e-88)))
		tmp = x + z;
	else
		tmp = z + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.2e-203], N[Not[LessEqual[x, 1.02e-88]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.19999999999999966e-203 or 1.02000000000000001e-88 < x

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 73.2%

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

      1. +-commutative 73.2%

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

   7. Simplified 73.2%

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

   if -9.19999999999999966e-203 < x < 1.02000000000000001e-88

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.9%

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

   6. Taylor expanded in y around 0 53.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-203} \lor \neg \left(x \leq 1.02 \cdot 10^{-88}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.7% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+75}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e+97) x (if (<= x 2.5e+75) (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+97) {
		tmp = x;
	} else if (x <= 2.5e+75) {
		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 <= (-7.5d+97)) then
        tmp = x
    else if (x <= 2.5d+75) 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 <= -7.5e+97) {
		tmp = x;
	} else if (x <= 2.5e+75) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e+97:
		tmp = x
	elif x <= 2.5e+75:
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e+97)
		tmp = x;
	elseif (x <= 2.5e+75)
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.5e+97)
		tmp = x;
	elseif (x <= 2.5e+75)
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e+97], x, If[LessEqual[x, 2.5e+75], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000004e97 or 2.5000000000000001e75 < x

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 80.7%

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

   if -7.5000000000000004e97 < x < 2.5000000000000001e75

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 85.3%

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

   6. Taylor expanded in y around 0 42.2%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+75}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.2% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+75}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e+97) x (if (<= x 2.5e+75) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+97) {
		tmp = x;
	} else if (x <= 2.5e+75) {
		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 <= (-7.5d+97)) then
        tmp = x
    else if (x <= 2.5d+75) 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 <= -7.5e+97) {
		tmp = x;
	} else if (x <= 2.5e+75) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e+97:
		tmp = x
	elif x <= 2.5e+75:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e+97)
		tmp = x;
	elseif (x <= 2.5e+75)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.5e+97)
		tmp = x;
	elseif (x <= 2.5e+75)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e+97], x, If[LessEqual[x, 2.5e+75], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000004e97 or 2.5000000000000001e75 < x

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 80.7%

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

   if -7.5000000000000004e97 < x < 2.5000000000000001e75

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 85.3%

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

   6. Taylor expanded in y around 0 36.9%

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

Alternative 13: 43.8% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-74}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.2e-203) x (if (<= x 6.8e-74) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.2e-203) {
		tmp = x;
	} else if (x <= 6.8e-74) {
		tmp = 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 <= (-9.2d-203)) then
        tmp = x
    else if (x <= 6.8d-74) then
        tmp = 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 <= -9.2e-203) {
		tmp = x;
	} else if (x <= 6.8e-74) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.2e-203:
		tmp = x
	elif x <= 6.8e-74:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.2e-203)
		tmp = x;
	elseif (x <= 6.8e-74)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.2e-203)
		tmp = x;
	elseif (x <= 6.8e-74)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.2e-203], x, If[LessEqual[x, 6.8e-74], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.19999999999999966e-203 or 6.8000000000000001e-74 < x

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 49.0%

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

   if -9.19999999999999966e-203 < x < 6.8000000000000001e-74

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.9%

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

   6. Taylor expanded in z around 0 44.2%

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

   7. Taylor expanded in y around 0 18.1%

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

Alternative 14: 41.9% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 37.2%

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

Reproduce

herbie shell --seed 2024145 
(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))))