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

Percentage Accurate: 99.9% → 99.9%

Time: 10.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 99.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + 1\right) - z \cdot \sin y\\ \mathbf{if}\;z \leq -65000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.0001:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x 1.0) (* z (sin y)))))
   (if (<= z -65000000000000.0) t_0 (if (<= z 0.0001) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + 1.0) - (z * sin(y));
	double tmp;
	if (z <= -65000000000000.0) {
		tmp = t_0;
	} else if (z <= 0.0001) {
		tmp = x + cos(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 + 1.0d0) - (z * sin(y))
    if (z <= (-65000000000000.0d0)) then
        tmp = t_0
    else if (z <= 0.0001d0) then
        tmp = x + cos(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 + 1.0) - (z * Math.sin(y));
	double tmp;
	if (z <= -65000000000000.0) {
		tmp = t_0;
	} else if (z <= 0.0001) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + 1.0) - (z * math.sin(y))
	tmp = 0
	if z <= -65000000000000.0:
		tmp = t_0
	elif z <= 0.0001:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + 1.0) - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -65000000000000.0)
		tmp = t_0;
	elseif (z <= 0.0001)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + 1.0) - (z * sin(y));
	tmp = 0.0;
	if (z <= -65000000000000.0)
		tmp = t_0;
	elseif (z <= 0.0001)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -65000000000000.0], t$95$0, If[LessEqual[z, 0.0001], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e13 or 1.00000000000000005e-4 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(1 + x\right)}, \mathsf{*.f64}\left(z, \mathsf{sin.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 99.8%

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

   5. Simplified 99.8%

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

   if -6.5e13 < z < 1.00000000000000005e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

      3. cos-lowering-cos.f64 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -65000000000000:\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{elif}\;z \leq 0.0001:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - z \cdot \sin y\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+50}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (* z (sin y)))))
   (if (<= z -7.8e+33) t_0 (if (<= z 1.45e+50) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (z * sin(y));
	double tmp;
	if (z <= -7.8e+33) {
		tmp = t_0;
	} else if (z <= 1.45e+50) {
		tmp = x + cos(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 * sin(y))
    if (z <= (-7.8d+33)) then
        tmp = t_0
    else if (z <= 1.45d+50) then
        tmp = x + cos(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.sin(y));
	double tmp;
	if (z <= -7.8e+33) {
		tmp = t_0;
	} else if (z <= 1.45e+50) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (z * math.sin(y))
	tmp = 0
	if z <= -7.8e+33:
		tmp = t_0
	elif z <= 1.45e+50:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -7.8e+33)
		tmp = t_0;
	elseif (z <= 1.45e+50)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (z * sin(y));
	tmp = 0.0;
	if (z <= -7.8e+33)
		tmp = t_0;
	elseif (z <= 1.45e+50)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+33], t$95$0, If[LessEqual[z, 1.45e+50], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000004e33 or 1.45e50 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 94.2%

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

   if -7.8000000000000004e33 < z < 1.45e50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

      3. cos-lowering-cos.f64 98.4%

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

   5. Simplified 98.4%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+50}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - z \cdot \sin y\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+36}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+114}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* z (sin y)))))
   (if (<= z -4.6e+36) t_0 (if (<= z 1.6e+114) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (z * sin(y));
	double tmp;
	if (z <= -4.6e+36) {
		tmp = t_0;
	} else if (z <= 1.6e+114) {
		tmp = x + cos(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 = 1.0d0 - (z * sin(y))
    if (z <= (-4.6d+36)) then
        tmp = t_0
    else if (z <= 1.6d+114) then
        tmp = x + cos(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 = 1.0 - (z * Math.sin(y));
	double tmp;
	if (z <= -4.6e+36) {
		tmp = t_0;
	} else if (z <= 1.6e+114) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (z * math.sin(y))
	tmp = 0
	if z <= -4.6e+36:
		tmp = t_0
	elif z <= 1.6e+114:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -4.6e+36)
		tmp = t_0;
	elseif (z <= 1.6e+114)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (z * sin(y));
	tmp = 0.0;
	if (z <= -4.6e+36)
		tmp = t_0;
	elseif (z <= 1.6e+114)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+36], t$95$0, If[LessEqual[z, 1.6e+114], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.59999999999999993e36 or 1.6e114 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(1 + x\right)}, \mathsf{*.f64}\left(z, \mathsf{sin.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. sin-lowering-sin.f64 68.0%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{sin.f64}\left(y\right)\right)\right) \]

   8. Simplified 68.0%

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

   if -4.59999999999999993e36 < z < 1.6e114

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

      3. cos-lowering-cos.f64 96.4%

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

   5. Simplified 96.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+36}:\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+114}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -3.55 \cdot 10^{+21}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+16}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (<= y -3.55e+21) t_0 (if (<= y 2.6e+16) (+ x (- 1.0 (* y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if (y <= -3.55e+21) {
		tmp = t_0;
	} else if (y <= 2.6e+16) {
		tmp = x + (1.0 - (y * 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 = x + cos(y)
    if (y <= (-3.55d+21)) then
        tmp = t_0
    else if (y <= 2.6d+16) then
        tmp = x + (1.0d0 - (y * 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 = x + Math.cos(y);
	double tmp;
	if (y <= -3.55e+21) {
		tmp = t_0;
	} else if (y <= 2.6e+16) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	tmp = 0
	if y <= -3.55e+21:
		tmp = t_0
	elif y <= 2.6e+16:
		tmp = x + (1.0 - (y * z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if (y <= -3.55e+21)
		tmp = t_0;
	elseif (y <= 2.6e+16)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	tmp = 0.0;
	if (y <= -3.55e+21)
		tmp = t_0;
	elseif (y <= 2.6e+16)
		tmp = x + (1.0 - (y * z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.55e+21], t$95$0, If[LessEqual[y, 2.6e+16], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.55e21 or 2.6e16 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

      3. cos-lowering-cos.f64 59.6%

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

   5. Simplified 59.6%

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

   if -3.55e21 < y < 2.6e16

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

      8. *-lowering-*.f64 94.6%

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

   5. Simplified 94.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+21}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+16}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.6% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{+22}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+62}:\\ \;\;\;\;\left(x + 1\right) + y \cdot \left(y \cdot -0.5 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{z} \cdot \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.72e+22)
   (+ x 1.0)
   (if (<= y 3.9e+62)
     (+ (+ x 1.0) (* y (- (* y -0.5) z)))
     (* x (+ 1.0 (* (/ 1.0 z) (/ z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.72e+22) {
		tmp = x + 1.0;
	} else if (y <= 3.9e+62) {
		tmp = (x + 1.0) + (y * ((y * -0.5) - z));
	} else {
		tmp = x * (1.0 + ((1.0 / z) * (z / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.72d+22)) then
        tmp = x + 1.0d0
    else if (y <= 3.9d+62) then
        tmp = (x + 1.0d0) + (y * ((y * (-0.5d0)) - z))
    else
        tmp = x * (1.0d0 + ((1.0d0 / z) * (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.72e+22) {
		tmp = x + 1.0;
	} else if (y <= 3.9e+62) {
		tmp = (x + 1.0) + (y * ((y * -0.5) - z));
	} else {
		tmp = x * (1.0 + ((1.0 / z) * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.72e+22:
		tmp = x + 1.0
	elif y <= 3.9e+62:
		tmp = (x + 1.0) + (y * ((y * -0.5) - z))
	else:
		tmp = x * (1.0 + ((1.0 / z) * (z / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.72e+22)
		tmp = Float64(x + 1.0);
	elseif (y <= 3.9e+62)
		tmp = Float64(Float64(x + 1.0) + Float64(y * Float64(Float64(y * -0.5) - z)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(1.0 / z) * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.72e+22)
		tmp = x + 1.0;
	elseif (y <= 3.9e+62)
		tmp = (x + 1.0) + (y * ((y * -0.5) - z));
	else
		tmp = x * (1.0 + ((1.0 / z) * (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.72e+22], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 3.9e+62], N[(N[(x + 1.0), $MachinePrecision] + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(1.0 / z), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.72e22

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 43.4%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 43.4%

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

   if -1.72e22 < y < 3.9e62

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

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

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 90.5%

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

   5. Simplified 90.5%

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

   if 3.9e62 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. distribute-lft-out-- N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

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

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

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

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

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

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

      9. +-commutative N/A

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

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

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

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

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

      12. sin-lowering-sin.f64 92.2%

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

   5. Simplified 92.2%

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

   6. Taylor expanded in x around inf

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

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

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

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

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

      10. /-lowering-/.f64 94.2%

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

   8. Simplified 94.2%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\color{blue}{\left(\frac{1}{z}\right)}, \mathsf{/.f64}\left(z, x\right)\right)\right)\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 40.0%

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

   11. Simplified 40.0%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{1}{z}} \cdot \frac{z}{x}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 69.9% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+23}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+56}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{z} \cdot \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+23)
   (+ x 1.0)
   (if (<= y 4.5e+56)
     (+ x (- 1.0 (* y z)))
     (* x (+ 1.0 (* (/ 1.0 z) (/ z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+23) {
		tmp = x + 1.0;
	} else if (y <= 4.5e+56) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x * (1.0 + ((1.0 / z) * (z / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.25d+23)) then
        tmp = x + 1.0d0
    else if (y <= 4.5d+56) then
        tmp = x + (1.0d0 - (y * z))
    else
        tmp = x * (1.0d0 + ((1.0d0 / z) * (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+23) {
		tmp = x + 1.0;
	} else if (y <= 4.5e+56) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x * (1.0 + ((1.0 / z) * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e+23:
		tmp = x + 1.0
	elif y <= 4.5e+56:
		tmp = x + (1.0 - (y * z))
	else:
		tmp = x * (1.0 + ((1.0 / z) * (z / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e+23)
		tmp = Float64(x + 1.0);
	elseif (y <= 4.5e+56)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(1.0 / z) * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.25e+23)
		tmp = x + 1.0;
	elseif (y <= 4.5e+56)
		tmp = x + (1.0 - (y * z));
	else
		tmp = x * (1.0 + ((1.0 / z) * (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e+23], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 4.5e+56], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(1.0 / z), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e23

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 43.4%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 43.4%

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

   if -1.25e23 < y < 4.5000000000000003e56

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

      8. *-lowering-*.f64 91.5%

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

   5. Simplified 91.5%

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

   if 4.5000000000000003e56 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. distribute-lft-out-- N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

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

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

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

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

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

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

      9. +-commutative N/A

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

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

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

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

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

      12. sin-lowering-sin.f64 92.6%

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

   5. Simplified 92.6%

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

   6. Taylor expanded in x around inf

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

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

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

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

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

      10. /-lowering-/.f64 94.5%

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

   8. Simplified 94.5%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\color{blue}{\left(\frac{1}{z}\right)}, \mathsf{/.f64}\left(z, x\right)\right)\right)\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 39.7%

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

   11. Simplified 39.7%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{1}{z}} \cdot \frac{z}{x}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 69.9% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+23}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+57}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.02e+23)
   (+ x 1.0)
   (if (<= y 5.8e+57) (+ x (- 1.0 (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.02e+23) {
		tmp = x + 1.0;
	} else if (y <= 5.8e+57) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.02d+23)) then
        tmp = x + 1.0d0
    else if (y <= 5.8d+57) then
        tmp = x + (1.0d0 - (y * z))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.02e+23) {
		tmp = x + 1.0;
	} else if (y <= 5.8e+57) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.02e+23:
		tmp = x + 1.0
	elif y <= 5.8e+57:
		tmp = x + (1.0 - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.02e+23)
		tmp = Float64(x + 1.0);
	elseif (y <= 5.8e+57)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.02e+23)
		tmp = x + 1.0;
	elseif (y <= 5.8e+57)
		tmp = x + (1.0 - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.02e+23], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 5.8e+57], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e23 or 5.8000000000000003e57 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 41.6%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 41.6%

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

   if -1.02e23 < y < 5.8000000000000003e57

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

      8. *-lowering-*.f64 91.5%

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

   5. Simplified 91.5%

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

Alternative 9: 65.4% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - y \cdot z\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+158}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+156}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (* y z))))
   (if (<= z -3.2e+158) t_0 (if (<= z 6.6e+156) (+ x 1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (y * z);
	double tmp;
	if (z <= -3.2e+158) {
		tmp = t_0;
	} else if (z <= 6.6e+156) {
		tmp = x + 1.0;
	} 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 - (y * z)
    if (z <= (-3.2d+158)) then
        tmp = t_0
    else if (z <= 6.6d+156) then
        tmp = x + 1.0d0
    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 - (y * z);
	double tmp;
	if (z <= -3.2e+158) {
		tmp = t_0;
	} else if (z <= 6.6e+156) {
		tmp = x + 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (y * z)
	tmp = 0
	if z <= -3.2e+158:
		tmp = t_0
	elif z <= 6.6e+156:
		tmp = x + 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (z <= -3.2e+158)
		tmp = t_0;
	elseif (z <= 6.6e+156)
		tmp = Float64(x + 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (y * z);
	tmp = 0.0;
	if (z <= -3.2e+158)
		tmp = t_0;
	elseif (z <= 6.6e+156)
		tmp = x + 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+158], t$95$0, If[LessEqual[z, 6.6e+156], N[(x + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999995e158 or 6.5999999999999997e156 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 96.8%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 57.4%

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

   if -3.19999999999999995e158 < z < 6.5999999999999997e156

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 69.7%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 69.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+158}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+156}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.0% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00055:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.00055) x (if (<= x 1.0) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.00055) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.00055d0)) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.00055) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.00055:
		tmp = x
	elif x <= 1.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.00055)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.00055)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.00055], x, If[LessEqual[x, 1.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000033e-4 or 1 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 78.1%

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

   if -5.50000000000000033e-4 < x < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 40.6%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 40.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Simplified 40.1%

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

Alternative 11: 61.7% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. +-lowering-+.f64 60.3%

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

5. Simplified 60.3%

   \[\leadsto \color{blue}{x + 1} \]
6. Add Preprocessing

Alternative 12: 21.6% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. +-lowering-+.f64 60.3%

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

5. Simplified 60.3%

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

6. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
7. Step-by-step derivation

8. Simplified 20.7%

   \[\leadsto \color{blue}{1} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))