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

Percentage Accurate: 99.9% → 99.9%

Time: 10.8s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ t_1 := x + t\_0\\ \mathbf{if}\;x \leq -3.65 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-15}:\\ \;\;\;\;\sin y + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))) (t_1 (+ x t_0)))
   (if (<= x -3.65e-59) t_1 (if (<= x 1.75e-15) (+ (sin y) t_0) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double t_1 = x + t_0;
	double tmp;
	if (x <= -3.65e-59) {
		tmp = t_1;
	} else if (x <= 1.75e-15) {
		tmp = sin(y) + t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = z * cos(y)
    t_1 = x + t_0
    if (x <= (-3.65d-59)) then
        tmp = t_1
    else if (x <= 1.75d-15) then
        tmp = sin(y) + t_0
    else
        tmp = t_1
    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 t_1 = x + t_0;
	double tmp;
	if (x <= -3.65e-59) {
		tmp = t_1;
	} else if (x <= 1.75e-15) {
		tmp = Math.sin(y) + t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	t_1 = x + t_0
	tmp = 0
	if x <= -3.65e-59:
		tmp = t_1
	elif x <= 1.75e-15:
		tmp = math.sin(y) + t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	t_1 = Float64(x + t_0)
	tmp = 0.0
	if (x <= -3.65e-59)
		tmp = t_1;
	elseif (x <= 1.75e-15)
		tmp = Float64(sin(y) + t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	t_1 = x + t_0;
	tmp = 0.0;
	if (x <= -3.65e-59)
		tmp = t_1;
	elseif (x <= 1.75e-15)
		tmp = sin(y) + t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + t$95$0), $MachinePrecision]}, If[LessEqual[x, -3.65e-59], t$95$1, If[LessEqual[x, 1.75e-15], N[(N[Sin[y], $MachinePrecision] + t$95$0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6500000000000002e-59 or 1.75e-15 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 98.1%

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

   if -3.6500000000000002e-59 < x < 1.75e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{\left(z \cdot \cos y\right)}\right) \]

      2. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \left(\color{blue}{z} \cdot \cos y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right)\right) \]

      4. cos-lowering-cos.f64 97.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   5. Simplified 97.5%

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

Alternative 3: 84.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -36000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-23}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+102}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -36000000000000.0)
     t_0
     (if (<= z 9.8e-23) (+ x (sin y)) (if (<= z 3.95e+102) (+ x z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -36000000000000.0) {
		tmp = t_0;
	} else if (z <= 9.8e-23) {
		tmp = x + sin(y);
	} else if (z <= 3.95e+102) {
		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 <= (-36000000000000.0d0)) then
        tmp = t_0
    else if (z <= 9.8d-23) then
        tmp = x + sin(y)
    else if (z <= 3.95d+102) 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 <= -36000000000000.0) {
		tmp = t_0;
	} else if (z <= 9.8e-23) {
		tmp = x + Math.sin(y);
	} else if (z <= 3.95e+102) {
		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 <= -36000000000000.0:
		tmp = t_0
	elif z <= 9.8e-23:
		tmp = x + math.sin(y)
	elif z <= 3.95e+102:
		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 <= -36000000000000.0)
		tmp = t_0;
	elseif (z <= 9.8e-23)
		tmp = Float64(x + sin(y));
	elseif (z <= 3.95e+102)
		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 <= -36000000000000.0)
		tmp = t_0;
	elseif (z <= 9.8e-23)
		tmp = x + sin(y);
	elseif (z <= 3.95e+102)
		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, -36000000000000.0], t$95$0, If[LessEqual[z, 9.8e-23], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.95e+102], N[(x + z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e13 or 3.9500000000000001e102 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right) \]

      2. cos-lowering-cos.f64 82.5%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right) \]

   5. Simplified 82.5%

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

   if -3.6e13 < z < 9.7999999999999996e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 92.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 92.4%

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

   if 9.7999999999999996e-23 < z < 3.9500000000000001e102

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 80.5%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 80.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -36000000000000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-23}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+102}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-49}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-19}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (cos y)))))
   (if (<= z -4.8e-49) t_0 (if (<= z 8e-19) (+ x (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z * cos(y));
	double tmp;
	if (z <= -4.8e-49) {
		tmp = t_0;
	} else if (z <= 8e-19) {
		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 = x + (z * cos(y))
    if (z <= (-4.8d-49)) then
        tmp = t_0
    else if (z <= 8d-19) 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 = x + (z * Math.cos(y));
	double tmp;
	if (z <= -4.8e-49) {
		tmp = t_0;
	} else if (z <= 8e-19) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z * math.cos(y))
	tmp = 0
	if z <= -4.8e-49:
		tmp = t_0
	elif z <= 8e-19:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(z * cos(y)))
	tmp = 0.0
	if (z <= -4.8e-49)
		tmp = t_0;
	elseif (z <= 8e-19)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (z * cos(y));
	tmp = 0.0;
	if (z <= -4.8e-49)
		tmp = t_0;
	elseif (z <= 8e-19)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-49], t$95$0, If[LessEqual[z, 8e-19], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999985e-49 or 7.9999999999999998e-19 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 99.3%

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

   if -4.79999999999999985e-49 < z < 7.9999999999999998e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 95.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 95.1%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-19}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7600000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7600000.0) (+ x z) (if (<= x 5e-16) (* z (cos y)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7600000.0) {
		tmp = x + z;
	} else if (x <= 5e-16) {
		tmp = z * cos(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-7600000.0d0)) then
        tmp = x + z
    else if (x <= 5d-16) then
        tmp = z * cos(y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7600000.0) {
		tmp = x + z;
	} else if (x <= 5e-16) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7600000.0:
		tmp = x + z
	elif x <= 5e-16:
		tmp = z * math.cos(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7600000.0)
		tmp = Float64(x + z);
	elseif (x <= 5e-16)
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7600000.0)
		tmp = x + z;
	elseif (x <= 5e-16)
		tmp = z * cos(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7600000.0], N[(x + z), $MachinePrecision], If[LessEqual[x, 5e-16], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6e6 or 5.0000000000000004e-16 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 87.2%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 87.2%

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

   if -7.6e6 < x < 5.0000000000000004e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right) \]

      2. cos-lowering-cos.f64 64.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right) \]

   5. Simplified 64.8%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7600000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -3.1:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;y + \left(x + z \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4e+73)
   (+ x z)
   (if (<= y -3.1)
     (sin y)
     (if (<= y 2.8e-7) (+ y (+ x (* z (+ 1.0 (* -0.5 (* y y)))))) (+ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e+73) {
		tmp = x + z;
	} else if (y <= -3.1) {
		tmp = sin(y);
	} else if (y <= 2.8e-7) {
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.4d+73)) then
        tmp = x + z
    else if (y <= (-3.1d0)) then
        tmp = sin(y)
    else if (y <= 2.8d-7) then
        tmp = y + (x + (z * (1.0d0 + ((-0.5d0) * (y * y)))))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e+73) {
		tmp = x + z;
	} else if (y <= -3.1) {
		tmp = Math.sin(y);
	} else if (y <= 2.8e-7) {
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4e+73:
		tmp = x + z
	elif y <= -3.1:
		tmp = math.sin(y)
	elif y <= 2.8e-7:
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4e+73)
		tmp = Float64(x + z);
	elseif (y <= -3.1)
		tmp = sin(y);
	elseif (y <= 2.8e-7)
		tmp = Float64(y + Float64(x + Float64(z * Float64(1.0 + Float64(-0.5 * Float64(y * y))))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.4e+73)
		tmp = x + z;
	elseif (y <= -3.1)
		tmp = sin(y);
	elseif (y <= 2.8e-7)
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4e+73], N[(x + z), $MachinePrecision], If[LessEqual[y, -3.1], N[Sin[y], $MachinePrecision], If[LessEqual[y, 2.8e-7], N[(y + N[(x + N[(z * N[(1.0 + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000002e73 or 2.80000000000000019e-7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 45.8%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 45.8%

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

   if -2.40000000000000002e73 < y < -3.10000000000000009

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 62.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 62.3%

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

   6. Taylor expanded in x around 0

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

      1. sin-lowering-sin.f64 52.2%

         \[\leadsto \mathsf{sin.f64}\left(y\right) \]

   8. Simplified 52.2%

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

   if -3.10000000000000009 < y < 2.80000000000000019e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto x + \left(z + \left(1 \cdot y + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) \cdot y}\right)\right) \]

      2. *-lft-identity N/A

         \[\leadsto x + \left(z + \left(y + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right)} \cdot y\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto x + \left(\left(z + y\right) + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) \cdot y}\right) \]

      4. *-commutative N/A

         \[\leadsto x + \left(\left(z + y\right) + \left(\frac{-1}{2} \cdot \left(z \cdot y\right)\right) \cdot y\right) \]

      5. associate-*r* N/A

         \[\leadsto x + \left(\left(z + y\right) + \left(\left(\frac{-1}{2} \cdot z\right) \cdot y\right) \cdot y\right) \]

      6. associate-*r* N/A

         \[\leadsto x + \left(\left(z + y\right) + \left(\frac{-1}{2} \cdot z\right) \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      7. unpow2 N/A

         \[\leadsto x + \left(\left(z + y\right) + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{\color{blue}{2}}\right) \]

      8. +-commutative N/A

         \[\leadsto x + \left(\left(y + z\right) + \color{blue}{\left(\frac{-1}{2} \cdot z\right)} \cdot {y}^{2}\right) \]

      9. associate-+r+ N/A

         \[\leadsto x + \left(y + \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(x + y\right) + \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)} \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)}\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y + x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \left({y}^{2} \cdot \color{blue}{z}\right)\right)\right) \]

      16. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \left(\frac{-1}{2} \cdot {y}^{2}\right) \cdot \color{blue}{z}\right)\right) \]

      17. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\left(\frac{-1}{2} \cdot {y}^{2} + 1\right) \cdot \color{blue}{z}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z \cdot \color{blue}{\left(\frac{-1}{2} \cdot {y}^{2} + 1\right)}\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{-1}{2} \cdot {y}^{2} + 1\right)}\right)\right) \]

      20. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{\frac{-1}{2} \cdot {y}^{2}}\right)\right)\right) \]

      21. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{2} \cdot {y}^{2}\right)}\right)\right)\right) \]

   5. Simplified 100.0%

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

      1. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(x + z \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x + z \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right) + \color{blue}{y} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + z \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right), \color{blue}{y}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right)\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(1 + \frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \left(\frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{2}, \left(y \cdot y\right)\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), y\right) \]

   7. Applied egg-rr 100.0%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -3.1:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;y + \left(x + z \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.8% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -105000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -105000000.0)
   (+ x z)
   (if (<= y 2.8e-7)
     (+ (+ x z) (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666))))))
     (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -105000000.0) {
		tmp = x + z;
	} else if (y <= 2.8e-7) {
		tmp = (x + z) + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-105000000.0d0)) then
        tmp = x + z
    else if (y <= 2.8d-7) then
        tmp = (x + z) + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0))))))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -105000000.0) {
		tmp = x + z;
	} else if (y <= 2.8e-7) {
		tmp = (x + z) + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -105000000.0:
		tmp = x + z
	elif y <= 2.8e-7:
		tmp = (x + z) + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666)))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -105000000.0)
		tmp = Float64(x + z);
	elseif (y <= 2.8e-7)
		tmp = Float64(Float64(x + z) + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666))))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -105000000.0)
		tmp = x + z;
	elseif (y <= 2.8e-7)
		tmp = (x + z) + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666)))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -105000000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.8e-7], N[(N[(x + z), $MachinePrecision] + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e8 or 2.80000000000000019e-7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 41.5%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 41.5%

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

   if -1.05e8 < y < 2.80000000000000019e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + z\right) + \color{blue}{y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + z\right), \color{blue}{\left(y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z + x\right), \left(\color{blue}{y} \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\color{blue}{y} \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \color{blue}{\left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)}\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-1}{2} \cdot z\right), \color{blue}{\left(\frac{-1}{6} \cdot y\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \frac{-1}{2}\right), \left(\color{blue}{\frac{-1}{6}} \cdot y\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \left(\color{blue}{\frac{-1}{6}} \cdot y\right)\right)\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \left(y \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 98.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \mathsf{*.f64}\left(y, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   5. Simplified 98.7%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -105000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -110000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;y + \left(x + z \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -110000000.0)
   (+ x z)
   (if (<= y 2.8e-7) (+ y (+ x (* z (+ 1.0 (* -0.5 (* y y)))))) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -110000000.0) {
		tmp = x + z;
	} else if (y <= 2.8e-7) {
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-110000000.0d0)) then
        tmp = x + z
    else if (y <= 2.8d-7) then
        tmp = y + (x + (z * (1.0d0 + ((-0.5d0) * (y * y)))))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -110000000.0) {
		tmp = x + z;
	} else if (y <= 2.8e-7) {
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -110000000.0:
		tmp = x + z
	elif y <= 2.8e-7:
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -110000000.0)
		tmp = Float64(x + z);
	elseif (y <= 2.8e-7)
		tmp = Float64(y + Float64(x + Float64(z * Float64(1.0 + Float64(-0.5 * Float64(y * y))))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -110000000.0)
		tmp = x + z;
	elseif (y <= 2.8e-7)
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -110000000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.8e-7], N[(y + N[(x + N[(z * N[(1.0 + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e8 or 2.80000000000000019e-7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 41.5%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 41.5%

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

   if -1.1e8 < y < 2.80000000000000019e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto x + \left(z + \left(1 \cdot y + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) \cdot y}\right)\right) \]

      2. *-lft-identity N/A

         \[\leadsto x + \left(z + \left(y + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right)} \cdot y\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto x + \left(\left(z + y\right) + \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) \cdot y}\right) \]

      4. *-commutative N/A

         \[\leadsto x + \left(\left(z + y\right) + \left(\frac{-1}{2} \cdot \left(z \cdot y\right)\right) \cdot y\right) \]

      5. associate-*r* N/A

         \[\leadsto x + \left(\left(z + y\right) + \left(\left(\frac{-1}{2} \cdot z\right) \cdot y\right) \cdot y\right) \]

      6. associate-*r* N/A

         \[\leadsto x + \left(\left(z + y\right) + \left(\frac{-1}{2} \cdot z\right) \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      7. unpow2 N/A

         \[\leadsto x + \left(\left(z + y\right) + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{\color{blue}{2}}\right) \]

      8. +-commutative N/A

         \[\leadsto x + \left(\left(y + z\right) + \color{blue}{\left(\frac{-1}{2} \cdot z\right)} \cdot {y}^{2}\right) \]

      9. associate-+r+ N/A

         \[\leadsto x + \left(y + \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(x + y\right) + \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)} \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)}\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y + x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \left({y}^{2} \cdot \color{blue}{z}\right)\right)\right) \]

      16. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \left(\frac{-1}{2} \cdot {y}^{2}\right) \cdot \color{blue}{z}\right)\right) \]

      17. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\left(\frac{-1}{2} \cdot {y}^{2} + 1\right) \cdot \color{blue}{z}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z \cdot \color{blue}{\left(\frac{-1}{2} \cdot {y}^{2} + 1\right)}\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{-1}{2} \cdot {y}^{2} + 1\right)}\right)\right) \]

      20. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \left(1 + \color{blue}{\frac{-1}{2} \cdot {y}^{2}}\right)\right)\right) \]

      21. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{2} \cdot {y}^{2}\right)}\right)\right)\right) \]

   5. Simplified 98.5%

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

      1. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(x + z \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x + z \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right) + \color{blue}{y} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + z \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right), \color{blue}{y}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(z \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right)\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(1 + \frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \left(\frac{-1}{2} \cdot \left(y \cdot y\right)\right)\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{2}, \left(y \cdot y\right)\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 98.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), y\right) \]

   7. Applied egg-rr 98.6%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -110000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;y + \left(x + z \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.6% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-11}:\\ \;\;\;\;x + \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8e+51) (+ x z) (if (<= y 2.65e-11) (+ x (+ y z)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e+51) {
		tmp = x + z;
	} else if (y <= 2.65e-11) {
		tmp = x + (y + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.8d+51)) then
        tmp = x + z
    else if (y <= 2.65d-11) then
        tmp = x + (y + z)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e+51) {
		tmp = x + z;
	} else if (y <= 2.65e-11) {
		tmp = x + (y + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8e+51:
		tmp = x + z
	elif y <= 2.65e-11:
		tmp = x + (y + z)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8e+51)
		tmp = Float64(x + z);
	elseif (y <= 2.65e-11)
		tmp = Float64(x + Float64(y + z));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.8e+51)
		tmp = x + z;
	elseif (y <= 2.65e-11)
		tmp = x + (y + z);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8e+51], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.65e-11], N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7999999999999997e51 or 2.6499999999999999e-11 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 45.8%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 45.8%

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

   if -4.7999999999999997e51 < y < 2.6499999999999999e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      2. +-lowering-+.f64 91.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 91.0%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-11}:\\ \;\;\;\;x + \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.2% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -54000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 350000000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -54000.0) x (if (<= x 350000000000.0) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -54000.0) {
		tmp = x;
	} else if (x <= 350000000000.0) {
		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 <= (-54000.0d0)) then
        tmp = x
    else if (x <= 350000000000.0d0) 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 <= -54000.0) {
		tmp = x;
	} else if (x <= 350000000000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -54000.0:
		tmp = x
	elif x <= 350000000000.0:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -54000.0)
		tmp = x;
	elseif (x <= 350000000000.0)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -54000.0)
		tmp = x;
	elseif (x <= 350000000000.0)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -54000.0], x, If[LessEqual[x, 350000000000.0], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -54000 or 3.5e11 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 74.3%

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

   if -54000 < x < 3.5e11

   1. Initial program 99.9%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(x + \sin y\right) - z \cdot \cos y}{\left(x + \sin y\right) \cdot \left(x + \sin y\right) - \left(z \cdot \cos y\right) \cdot \left(z \cdot \cos y\right)}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{\left(x + \sin y\right) \cdot \left(x + \sin y\right) - \left(z \cdot \cos y\right) \cdot \left(z \cdot \cos y\right)}{\left(x + \sin y\right) - z \cdot \cos y}}}\right)\right) \]

      5. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\left(x + \sin y\right) + \color{blue}{z \cdot \cos y}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \color{blue}{\left(\left(x + \sin y\right) + z \cdot \cos y\right)}\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \left(\left(\sin y + x\right) + \color{blue}{z} \cdot \cos y\right)\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \left(\sin y + \color{blue}{\left(x + z \cdot \cos y\right)}\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\sin y, \color{blue}{\left(x + z \cdot \cos y\right)}\right)\right)\right) \]

      10. sin-lowering-sin.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \left(\color{blue}{x} + z \cdot \cos y\right)\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \cos y\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right)\right)\right)\right)\right) \]

      13. cos-lowering-cos.f64 99.6%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right)\right)\right)\right) \]

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{y}{{\left(x + z\right)}^{2}} + \frac{1}{x + z}\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x + z} + \color{blue}{-1 \cdot \frac{y}{{\left(x + z\right)}^{2}}}\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x + z} + \left(\mathsf{neg}\left(\frac{y}{{\left(x + z\right)}^{2}}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x + z} - \color{blue}{\frac{y}{{\left(x + z\right)}^{2}}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{1}{x + z}\right), \color{blue}{\left(\frac{y}{{\left(x + z\right)}^{2}}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(x + z\right)\right), \left(\frac{\color{blue}{y}}{{\left(x + z\right)}^{2}}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, z\right)\right), \left(\frac{y}{{\left(x + z\right)}^{2}}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{/.f64}\left(y, \color{blue}{\left({\left(x + z\right)}^{2}\right)}\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{/.f64}\left(y, \left(\left(x + z\right) \cdot \color{blue}{\left(x + z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\left(x + z\right), \color{blue}{\left(x + z\right)}\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, z\right), \left(\color{blue}{x} + z\right)\right)\right)\right)\right) \]

      11. +-lowering-+.f64 42.1%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, z\right)\right), \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, z\right), \mathsf{+.f64}\left(x, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 42.1%

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

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} \]
   9. Step-by-step derivation

   10. Simplified 38.7%

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

Alternative 11: 44.3% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e-101) x (if (<= x 3.3e-52) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e-101) {
		tmp = x;
	} else if (x <= 3.3e-52) {
		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 <= (-3.4d-101)) then
        tmp = x
    else if (x <= 3.3d-52) 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 <= -3.4e-101) {
		tmp = x;
	} else if (x <= 3.3e-52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.4e-101:
		tmp = x
	elif x <= 3.3e-52:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e-101)
		tmp = x;
	elseif (x <= 3.3e-52)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.4e-101)
		tmp = x;
	elseif (x <= 3.3e-52)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.4e-101], x, If[LessEqual[x, 3.3e-52], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.39999999999999989e-101 or 3.29999999999999995e-52 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 60.5%

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

   if -3.39999999999999989e-101 < x < 3.29999999999999995e-52

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 38.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 38.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{y}, x\right) \]
   7. Step-by-step derivation

   8. Simplified 16.2%

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

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   10. Step-by-step derivation

   11. Simplified 15.2%

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

Alternative 12: 65.8% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 64.6%

      \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

5. Simplified 64.6%

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

6. Final simplification 64.6%

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

Alternative 13: 42.4% 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. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 38.4%

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

Reproduce

herbie shell --seed 2024161 
(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))))