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

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 14

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 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 97.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+62} \lor \neg \left(z \leq 2 \cdot 10^{-17}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e+62) (not (<= z 2e-17)))
   (- (+ x 1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e+62) || !(z <= 2e-17)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.4d+62)) .or. (.not. (z <= 2d-17))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e+62) || !(z <= 2e-17)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e+62) or not (z <= 2e-17):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e+62) || !(z <= 2e-17))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.4e+62) || ~((z <= 2e-17)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e+62], N[Not[LessEqual[z, 2e-17]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e62 or 2.00000000000000014e-17 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 98.8%

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

      1. +-commutative 98.8%

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

   4. Simplified 98.8%

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

   if -2.4e62 < z < 2.00000000000000014e-17

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.2%

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

   3. Taylor expanded in z around 0 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+62} \lor \neg \left(z \leq 2 \cdot 10^{-17}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 3: 81.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+148}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+235}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (sin y)))))
   (if (<= z -4.6e+191)
     t_0
     (if (<= z 1.1e+148)
       (+ x (cos y))
       (if (<= z 2.6e+235) (- (+ x 1.0) (* y z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * -sin(y);
	double tmp;
	if (z <= -4.6e+191) {
		tmp = t_0;
	} else if (z <= 1.1e+148) {
		tmp = x + cos(y);
	} else if (z <= 2.6e+235) {
		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 = z * -sin(y)
    if (z <= (-4.6d+191)) then
        tmp = t_0
    else if (z <= 1.1d+148) then
        tmp = x + cos(y)
    else if (z <= 2.6d+235) 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 = z * -Math.sin(y);
	double tmp;
	if (z <= -4.6e+191) {
		tmp = t_0;
	} else if (z <= 1.1e+148) {
		tmp = x + Math.cos(y);
	} else if (z <= 2.6e+235) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -math.sin(y)
	tmp = 0
	if z <= -4.6e+191:
		tmp = t_0
	elif z <= 1.1e+148:
		tmp = x + math.cos(y)
	elif z <= 2.6e+235:
		tmp = (x + 1.0) - (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (z <= -4.6e+191)
		tmp = t_0;
	elseif (z <= 1.1e+148)
		tmp = Float64(x + cos(y));
	elseif (z <= 2.6e+235)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -sin(y);
	tmp = 0.0;
	if (z <= -4.6e+191)
		tmp = t_0;
	elseif (z <= 1.1e+148)
		tmp = x + cos(y);
	elseif (z <= 2.6e+235)
		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[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -4.6e+191], t$95$0, If[LessEqual[z, 1.1e+148], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+235], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5999999999999999e191 or 2.5999999999999998e235 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 80.7%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. *-commutative 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

   5. Simplified 72.0%

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

   if -4.5999999999999999e191 < z < 1.0999999999999999e148

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.4%

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

   3. Taylor expanded in z around 0 91.9%

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

   if 1.0999999999999999e148 < z < 2.5999999999999998e235

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 82.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+191}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+148}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+235}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \]

Alternative 4: 84.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+190} \lor \neg \left(z \leq 8.8 \cdot 10^{+58}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e+190) (not (<= z 8.8e+58)))
   (- 1.0 (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e+190) || !(z <= 8.8e+58)) {
		tmp = 1.0 - (z * sin(y));
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.7d+190)) .or. (.not. (z <= 8.8d+58))) then
        tmp = 1.0d0 - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e+190) || !(z <= 8.8e+58)) {
		tmp = 1.0 - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e+190) or not (z <= 8.8e+58):
		tmp = 1.0 - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e+190) || !(z <= 8.8e+58))
		tmp = Float64(1.0 - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7e+190) || ~((z <= 8.8e+58)))
		tmp = 1.0 - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e+190], N[Not[LessEqual[z, 8.8e+58]], $MachinePrecision]], N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e190 or 8.8000000000000003e58 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 70.8%

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

   3. Taylor expanded in y around 0 70.8%

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

   if -1.7e190 < z < 8.8000000000000003e58

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.4%

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

   3. Taylor expanded in z around 0 95.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+190} \lor \neg \left(z \leq 8.8 \cdot 10^{+58}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 90.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+161} \lor \neg \left(z \leq 1.25 \cdot 10^{+35}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.2e+161) (not (<= z 1.25e+35)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.2e+161) || !(z <= 1.25e+35)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-6.2d+161)) .or. (.not. (z <= 1.25d+35))) then
        tmp = x - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.2e+161) || !(z <= 1.25e+35)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.2e+161) or not (z <= 1.25e+35):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.2e+161) || !(z <= 1.25e+35))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.2e+161) || ~((z <= 1.25e+35)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.2e+161], N[Not[LessEqual[z, 1.25e+35]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000013e161 or 1.25000000000000005e35 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 88.3%

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

   if -6.20000000000000013e161 < z < 1.25000000000000005e35

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.5%

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

   3. Taylor expanded in z around 0 96.1%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+161} \lor \neg \left(z \leq 1.25 \cdot 10^{+35}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 6: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -450 \lor \neg \left(y \leq 3.25 \cdot 10^{-34}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot -0.5 - z\right) + \left(x + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -450.0) (not (<= y 3.25e-34)))
   (+ x (cos y))
   (+ (* y (- (* y -0.5) z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -450.0) || !(y <= 3.25e-34)) {
		tmp = x + cos(y);
	} else {
		tmp = (y * ((y * -0.5) - z)) + (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 <= (-450.0d0)) .or. (.not. (y <= 3.25d-34))) then
        tmp = x + cos(y)
    else
        tmp = (y * ((y * (-0.5d0)) - z)) + (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -450.0) || !(y <= 3.25e-34)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = (y * ((y * -0.5) - z)) + (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -450.0) or not (y <= 3.25e-34):
		tmp = x + math.cos(y)
	else:
		tmp = (y * ((y * -0.5) - z)) + (x + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -450.0) || !(y <= 3.25e-34))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(Float64(y * Float64(Float64(y * -0.5) - z)) + Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -450.0) || ~((y <= 3.25e-34)))
		tmp = x + cos(y);
	else
		tmp = (y * ((y * -0.5) - z)) + (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -450.0], N[Not[LessEqual[y, 3.25e-34]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -450 or 3.24999999999999993e-34 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 52.0%

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

   3. Taylor expanded in z around 0 73.8%

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

   if -450 < y < 3.24999999999999993e-34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

      \[\leadsto \left(x + \color{blue}{\left(1 + -0.5 \cdot {y}^{2}\right)}\right) - z \cdot \sin y \]
   3. Step-by-step derivation

      1. unpow2 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.9%

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

   6. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{\left(1 + \left(-0.5 \cdot {y}^{2} + x\right)\right) - y \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(1 + \color{blue}{\left(x + -0.5 \cdot {y}^{2}\right)}\right) - y \cdot z \]

      2. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(1 + x\right) + -0.5 \cdot {y}^{2}\right)} - y \cdot z \]

      3. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(x + 1\right)} + -0.5 \cdot {y}^{2}\right) - y \cdot z \]

      4. *-commutative 99.9%

         \[\leadsto \left(\left(x + 1\right) + \color{blue}{{y}^{2} \cdot -0.5}\right) - y \cdot z \]

      5. unpow2 99.9%

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

      6. associate-*r* 99.9%

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

      7. *-commutative 99.9%

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

      8. associate-+r- 99.9%

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

      9. +-commutative 99.9%

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

      10. *-commutative 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

      12. +-commutative 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -450 \lor \neg \left(y \leq 3.25 \cdot 10^{-34}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot -0.5 - z\right) + \left(x + 1\right)\\ \end{array} \]

Alternative 7: 73.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-8}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-21}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.6e-8) (+ x 1.0) (if (<= x 6e-21) (cos y) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e-8) {
		tmp = x + 1.0;
	} else if (x <= 6e-21) {
		tmp = cos(y);
	} 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 (x <= (-1.6d-8)) then
        tmp = x + 1.0d0
    else if (x <= 6d-21) then
        tmp = cos(y)
    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 (x <= -1.6e-8) {
		tmp = x + 1.0;
	} else if (x <= 6e-21) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e-8:
		tmp = x + 1.0
	elif x <= 6e-21:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e-8)
		tmp = Float64(x + 1.0);
	elseif (x <= 6e-21)
		tmp = cos(y);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e-8)
		tmp = x + 1.0;
	elseif (x <= 6e-21)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e-8], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 6e-21], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6000000000000001e-8 or 5.99999999999999982e-21 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.7%

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

   3. Taylor expanded in y around 0 85.3%

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

   if -1.6000000000000001e-8 < x < 5.99999999999999982e-21

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.4%

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

   3. Taylor expanded in z around 0 72.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-8}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-21}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8: 69.9% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+28}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(y \cdot -0.5 - z\right) + \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4e+28)
   (+ x 1.0)
   (if (<= y 1.45e+34) (+ (* y (- (* y -0.5) z)) (+ x 1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e+28) {
		tmp = x + 1.0;
	} else if (y <= 1.45e+34) {
		tmp = (y * ((y * -0.5) - z)) + (x + 1.0);
	} 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 <= (-2.4d+28)) then
        tmp = x + 1.0d0
    else if (y <= 1.45d+34) then
        tmp = (y * ((y * (-0.5d0)) - z)) + (x + 1.0d0)
    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 <= -2.4e+28) {
		tmp = x + 1.0;
	} else if (y <= 1.45e+34) {
		tmp = (y * ((y * -0.5) - z)) + (x + 1.0);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4e+28:
		tmp = x + 1.0
	elif y <= 1.45e+34:
		tmp = (y * ((y * -0.5) - z)) + (x + 1.0)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4e+28)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.45e+34)
		tmp = Float64(Float64(y * Float64(Float64(y * -0.5) - z)) + Float64(x + 1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.4e+28)
		tmp = x + 1.0;
	elseif (y <= 1.45e+34)
		tmp = (y * ((y * -0.5) - z)) + (x + 1.0);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4e+28], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.45e+34], N[(N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999981e28 or 1.4500000000000001e34 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 46.5%

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

   3. Taylor expanded in y around 0 50.8%

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

   if -2.39999999999999981e28 < y < 1.4500000000000001e34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.5%

      \[\leadsto \left(x + \color{blue}{\left(1 + -0.5 \cdot {y}^{2}\right)}\right) - z \cdot \sin y \]
   3. Step-by-step derivation

      1. unpow2 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in y around 0 95.9%

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

   6. Taylor expanded in x around 0 95.9%

      \[\leadsto \color{blue}{\left(1 + \left(-0.5 \cdot {y}^{2} + x\right)\right) - y \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 95.9%

         \[\leadsto \left(1 + \color{blue}{\left(x + -0.5 \cdot {y}^{2}\right)}\right) - y \cdot z \]

      2. associate-+r+ 95.9%

         \[\leadsto \color{blue}{\left(\left(1 + x\right) + -0.5 \cdot {y}^{2}\right)} - y \cdot z \]

      3. +-commutative 95.9%

         \[\leadsto \left(\color{blue}{\left(x + 1\right)} + -0.5 \cdot {y}^{2}\right) - y \cdot z \]

      4. *-commutative 95.9%

         \[\leadsto \left(\left(x + 1\right) + \color{blue}{{y}^{2} \cdot -0.5}\right) - y \cdot z \]

      5. unpow2 95.9%

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

      6. associate-*r* 95.9%

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

      7. *-commutative 95.9%

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

      8. associate-+r- 95.9%

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

      9. +-commutative 95.9%

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

      10. *-commutative 95.9%

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

      11. distribute-rgt-out-- 95.9%

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

      12. +-commutative 95.9%

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

   8. Simplified 95.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+28}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(y \cdot -0.5 - z\right) + \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9: 70.0% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+28}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4e+28)
   (+ x 1.0)
   (if (<= y 5.2e+56) (- (+ x 1.0) (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e+28) {
		tmp = x + 1.0;
	} else if (y <= 5.2e+56) {
		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 <= (-2.4d+28)) then
        tmp = x + 1.0d0
    else if (y <= 5.2d+56) 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 <= -2.4e+28) {
		tmp = x + 1.0;
	} else if (y <= 5.2e+56) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4e+28:
		tmp = x + 1.0
	elif y <= 5.2e+56:
		tmp = (x + 1.0) - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4e+28)
		tmp = Float64(x + 1.0);
	elseif (y <= 5.2e+56)
		tmp = Float64(Float64(x + 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 <= -2.4e+28)
		tmp = x + 1.0;
	elseif (y <= 5.2e+56)
		tmp = (x + 1.0) - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4e+28], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 5.2e+56], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999981e28 or 5.20000000000000022e56 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 45.3%

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

   3. Taylor expanded in y around 0 49.8%

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

   if -2.39999999999999981e28 < y < 5.20000000000000022e56

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.8%

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

      1. +-commutative 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in y around 0 95.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+28}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 10: 67.2% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-31}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-11}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.9e-31) (+ x 1.0) (if (<= x 1.75e-11) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.9e-31) {
		tmp = x + 1.0;
	} else if (x <= 1.75e-11) {
		tmp = 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 (x <= (-3.9d-31)) then
        tmp = x + 1.0d0
    else if (x <= 1.75d-11) then
        tmp = 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 (x <= -3.9e-31) {
		tmp = x + 1.0;
	} else if (x <= 1.75e-11) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.9e-31:
		tmp = x + 1.0
	elif x <= 1.75e-11:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.9e-31)
		tmp = Float64(x + 1.0);
	elseif (x <= 1.75e-11)
		tmp = 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 (x <= -3.9e-31)
		tmp = x + 1.0;
	elseif (x <= 1.75e-11)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.9e-31], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 1.75e-11], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9000000000000001e-31 or 1.7500000000000001e-11 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.3%

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

   3. Taylor expanded in y around 0 85.0%

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

   if -3.9000000000000001e-31 < x < 1.7500000000000001e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in y around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. *-commutative 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

   5. Simplified 64.1%

      \[\leadsto \color{blue}{1 - y \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-31}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-11}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 11: 63.0% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+210}:\\ \;\;\;\;-y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.8e+210) (- (* y z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.8e+210) {
		tmp = -(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 (z <= (-8.8d+210)) then
        tmp = -(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 (z <= -8.8e+210) {
		tmp = -(y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.8e+210:
		tmp = -(y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.8e+210)
		tmp = Float64(-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 (z <= -8.8e+210)
		tmp = -(y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.8e+210], (-N[(y * z), $MachinePrecision]), N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999948e210

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 65.1%

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

   3. Taylor expanded in y around inf 46.3%

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

      1. associate-*r* 46.3%

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

      2. neg-mul-1 46.3%

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

      3. *-commutative 46.3%

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

   5. Simplified 46.3%

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

   if -8.79999999999999948e210 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.8%

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

   3. Taylor expanded in y around 0 73.3%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+210}:\\ \;\;\;\;-y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 12: 61.6% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.95:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.68:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -0.95) x (if (<= x 0.68) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.95) {
		tmp = x;
	} else if (x <= 0.68) {
		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 <= (-0.95d0)) then
        tmp = x
    else if (x <= 0.68d0) 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 <= -0.95) {
		tmp = x;
	} else if (x <= 0.68) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.95:
		tmp = x
	elif x <= 0.68:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.95)
		tmp = x;
	elseif (x <= 0.68)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.95)
		tmp = x;
	elseif (x <= 0.68)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.95], x, If[LessEqual[x, 0.68], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.94999999999999996 or 0.680000000000000049 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.1%

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

   3. Taylor expanded in x around inf 86.1%

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

   if -0.94999999999999996 < x < 0.680000000000000049

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 98.2%

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

   3. Taylor expanded in y around 0 51.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.95:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.68:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 62.2% 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 100.0%

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

2. Taylor expanded in y around 0 76.1%

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

3. Taylor expanded in y around 0 70.2%

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

4. Final simplification 70.2%

   \[\leadsto x + 1 \]

Alternative 14: 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 100.0%

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

2. Taylor expanded in x around 0 55.6%

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

3. Taylor expanded in y around 0 27.3%

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

4. Final simplification 27.3%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023238 
(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))))