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

Percentage Accurate: 99.9% → 99.9%

Time: 8.3s

Alternatives: 13

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. Final simplification 99.9%

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

Alternative 2: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -0.0148 \lor \neg \left(x \leq 2.9 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + 1\right) - t_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -0.0148) (not (<= x 2.9e-6)))
     (- (+ x 1.0) t_0)
     (- (cos y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if ((x <= -0.0148) || !(x <= 2.9e-6)) {
		tmp = (x + 1.0) - t_0;
	} else {
		tmp = cos(y) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * sin(y)
    if ((x <= (-0.0148d0)) .or. (.not. (x <= 2.9d-6))) then
        tmp = (x + 1.0d0) - t_0
    else
        tmp = cos(y) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if ((x <= -0.0148) || !(x <= 2.9e-6)) {
		tmp = (x + 1.0) - t_0;
	} else {
		tmp = Math.cos(y) - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if (x <= -0.0148) or not (x <= 2.9e-6):
		tmp = (x + 1.0) - t_0
	else:
		tmp = math.cos(y) - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if ((x <= -0.0148) || !(x <= 2.9e-6))
		tmp = Float64(Float64(x + 1.0) - t_0);
	else
		tmp = Float64(cos(y) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if ((x <= -0.0148) || ~((x <= 2.9e-6)))
		tmp = (x + 1.0) - t_0;
	else
		tmp = cos(y) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -0.0148], N[Not[LessEqual[x, 2.9e-6]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.014800000000000001 or 2.9000000000000002e-6 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.5%

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

   if -0.014800000000000001 < x < 2.9000000000000002e-6

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 98.1%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0148 \lor \neg \left(x \leq 2.9 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]

Alternative 3: 83.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - z \cdot \sin y\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+70}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+97}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* z (sin y)))))
   (if (<= z -5.5e+116)
     t_0
     (if (<= z -4.4e+70)
       (+ x 1.0)
       (if (<= z -5.2e+32)
         (* (sin y) (- z))
         (if (<= z 2.7e+97) (+ 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 <= -5.5e+116) {
		tmp = t_0;
	} else if (z <= -4.4e+70) {
		tmp = x + 1.0;
	} else if (z <= -5.2e+32) {
		tmp = sin(y) * -z;
	} else if (z <= 2.7e+97) {
		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 <= (-5.5d+116)) then
        tmp = t_0
    else if (z <= (-4.4d+70)) then
        tmp = x + 1.0d0
    else if (z <= (-5.2d+32)) then
        tmp = sin(y) * -z
    else if (z <= 2.7d+97) 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 <= -5.5e+116) {
		tmp = t_0;
	} else if (z <= -4.4e+70) {
		tmp = x + 1.0;
	} else if (z <= -5.2e+32) {
		tmp = Math.sin(y) * -z;
	} else if (z <= 2.7e+97) {
		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 <= -5.5e+116:
		tmp = t_0
	elif z <= -4.4e+70:
		tmp = x + 1.0
	elif z <= -5.2e+32:
		tmp = math.sin(y) * -z
	elif z <= 2.7e+97:
		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 <= -5.5e+116)
		tmp = t_0;
	elseif (z <= -4.4e+70)
		tmp = Float64(x + 1.0);
	elseif (z <= -5.2e+32)
		tmp = Float64(sin(y) * Float64(-z));
	elseif (z <= 2.7e+97)
		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 <= -5.5e+116)
		tmp = t_0;
	elseif (z <= -4.4e+70)
		tmp = x + 1.0;
	elseif (z <= -5.2e+32)
		tmp = sin(y) * -z;
	elseif (z <= 2.7e+97)
		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, -5.5e+116], t$95$0, If[LessEqual[z, -4.4e+70], N[(x + 1.0), $MachinePrecision], If[LessEqual[z, -5.2e+32], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[z, 2.7e+97], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.50000000000000035e116 or 2.69999999999999993e97 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 73.4%

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

   3. Taylor expanded in y around 0 73.4%

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

   if -5.50000000000000035e116 < z < -4.40000000000000001e70

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 78.6%

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

      1. +-commutative 78.6%

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

   4. Simplified 78.6%

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

   if -4.40000000000000001e70 < z < -5.2000000000000004e32

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 87.4%

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

      1. neg-mul-1 87.4%

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

      2. *-commutative 87.4%

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

      3. distribute-rgt-neg-in 87.4%

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

   4. Simplified 87.4%

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

   if -5.2000000000000004e32 < z < 2.69999999999999993e97

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 94.2%

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

      1. +-commutative 94.2%

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

   4. Simplified 94.2%

      \[\leadsto \color{blue}{\cos y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+116}:\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+70}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+97}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot \sin y\\ \end{array} \]

Alternative 4: 81.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{+178}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+70}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+32} \lor \neg \left(z \leq 2 \cdot 10^{+129}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= z -1.06e+178)
     t_0
     (if (<= z -5.1e+70)
       (+ x 1.0)
       (if (or (<= z -5.2e+32) (not (<= z 2e+129))) t_0 (+ x (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (z <= -1.06e+178) {
		tmp = t_0;
	} else if (z <= -5.1e+70) {
		tmp = x + 1.0;
	} else if ((z <= -5.2e+32) || !(z <= 2e+129)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = sin(y) * -z
    if (z <= (-1.06d+178)) then
        tmp = t_0
    else if (z <= (-5.1d+70)) then
        tmp = x + 1.0d0
    else if ((z <= (-5.2d+32)) .or. (.not. (z <= 2d+129))) then
        tmp = t_0
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double tmp;
	if (z <= -1.06e+178) {
		tmp = t_0;
	} else if (z <= -5.1e+70) {
		tmp = x + 1.0;
	} else if ((z <= -5.2e+32) || !(z <= 2e+129)) {
		tmp = t_0;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	tmp = 0
	if z <= -1.06e+178:
		tmp = t_0
	elif z <= -5.1e+70:
		tmp = x + 1.0
	elif (z <= -5.2e+32) or not (z <= 2e+129):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (z <= -1.06e+178)
		tmp = t_0;
	elseif (z <= -5.1e+70)
		tmp = Float64(x + 1.0);
	elseif ((z <= -5.2e+32) || !(z <= 2e+129))
		tmp = t_0;
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	tmp = 0.0;
	if (z <= -1.06e+178)
		tmp = t_0;
	elseif (z <= -5.1e+70)
		tmp = x + 1.0;
	elseif ((z <= -5.2e+32) || ~((z <= 2e+129)))
		tmp = t_0;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.06e+178], t$95$0, If[LessEqual[z, -5.1e+70], N[(x + 1.0), $MachinePrecision], If[Or[LessEqual[z, -5.2e+32], N[Not[LessEqual[z, 2e+129]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05999999999999994e178 or -5.10000000000000014e70 < z < -5.2000000000000004e32 or 2e129 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 73.6%

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

      1. neg-mul-1 73.6%

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

      2. *-commutative 73.6%

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

      3. distribute-rgt-neg-in 73.6%

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

   4. Simplified 73.6%

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

   if -1.05999999999999994e178 < z < -5.10000000000000014e70

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 66.0%

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

      1. +-commutative 66.0%

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

   4. Simplified 66.0%

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

   if -5.2000000000000004e32 < z < 2e129

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 93.2%

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

      1. +-commutative 93.2%

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

   4. Simplified 93.2%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+178}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+70}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+32} \lor \neg \left(z \leq 2 \cdot 10^{+129}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 99.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.7 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.7) (not (<= z 0.5)))
   (- (+ x 1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.7) || !(z <= 0.5)) {
		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 <= (-0.7d0)) .or. (.not. (z <= 0.5d0))) 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 <= -0.7) || !(z <= 0.5)) {
		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 <= -0.7) or not (z <= 0.5):
		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 <= -0.7) || !(z <= 0.5))
		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 <= -0.7) || ~((z <= 0.5)))
		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, -0.7], N[Not[LessEqual[z, 0.5]], $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 < -0.69999999999999996 or 0.5 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 98.7%

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

   if -0.69999999999999996 < z < 0.5

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.8%

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

      1. +-commutative 98.8%

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

   4. Simplified 98.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.7 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 6: 80.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-5} \lor \neg \left(y \leq 0.45\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.4e-5) (not (<= y 0.45)))
   (+ x (cos y))
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.4e-5) || !(y <= 0.45)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.4d-5)) .or. (.not. (y <= 0.45d0))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.4e-5) || !(y <= 0.45)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.4e-5) or not (y <= 0.45):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.4e-5) || !(y <= 0.45))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.4e-5) || ~((y <= 0.45)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.4e-5], N[Not[LessEqual[y, 0.45]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.39999999999999971e-5 or 0.450000000000000011 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 65.9%

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

      1. +-commutative 65.9%

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

   4. Simplified 65.9%

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

   if -6.39999999999999971e-5 < y < 0.450000000000000011

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

   4. Simplified 98.9%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-5} \lor \neg \left(y \leq 0.45\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]

Alternative 7: 71.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0148 \lor \neg \left(x \leq 0.013\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0148) (not (<= x 0.013))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0148) || !(x <= 0.013)) {
		tmp = x + 1.0;
	} else {
		tmp = 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 ((x <= (-0.0148d0)) .or. (.not. (x <= 0.013d0))) then
        tmp = x + 1.0d0
    else
        tmp = cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0148) || !(x <= 0.013)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0148) or not (x <= 0.013):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0148) || !(x <= 0.013))
		tmp = Float64(x + 1.0);
	else
		tmp = cos(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.0148) || ~((x <= 0.013)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0148], N[Not[LessEqual[x, 0.013]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.014800000000000001 or 0.0129999999999999994 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

   4. Simplified 83.9%

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

   if -0.014800000000000001 < x < 0.0129999999999999994

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 60.8%

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

      1. +-commutative 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in x around 0 59.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0148 \lor \neg \left(x \leq 0.013\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]

Alternative 8: 69.4% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+51} \lor \neg \left(y \leq 2.1 \cdot 10^{+23}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.36e+51) (not (<= y 2.1e+23)))
   (+ x 1.0)
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.36e+51) || !(y <= 2.1e+23)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.36d+51)) .or. (.not. (y <= 2.1d+23))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.36e+51) || !(y <= 2.1e+23)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.36e+51) or not (y <= 2.1e+23):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.36e+51) || !(y <= 2.1e+23))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.36e+51) || ~((y <= 2.1e+23)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.36e+51], N[Not[LessEqual[y, 2.1e+23]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3599999999999999e51 or 2.1000000000000001e23 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 49.0%

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

      1. +-commutative 49.0%

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

   4. Simplified 49.0%

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

   if -1.3599999999999999e51 < y < 2.1000000000000001e23

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

   4. Simplified 89.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+51} \lor \neg \left(y \leq 2.1 \cdot 10^{+23}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]

Alternative 9: 66.5% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-16} \lor \neg \left(x \leq 6 \cdot 10^{-19}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.85e-16) (not (<= x 6e-19))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.85e-16) || !(x <= 6e-19)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.85d-16)) .or. (.not. (x <= 6d-19))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.85e-16) || !(x <= 6e-19)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.85e-16) or not (x <= 6e-19):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.85e-16) || !(x <= 6e-19))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.85e-16) || ~((x <= 6e-19)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.85e-16], N[Not[LessEqual[x, 6e-19]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.85e-16 or 5.99999999999999985e-19 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.8%

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

      1. +-commutative 78.8%

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

   4. Simplified 78.8%

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

   if -1.85e-16 < x < 5.99999999999999985e-19

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. sin-neg 99.8%

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

      6. fma-def 99.9%

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

      7. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.9%

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

   5. Taylor expanded in y around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. unsub-neg 54.0%

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

   7. Simplified 54.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-16} \lor \neg \left(x \leq 6 \cdot 10^{-19}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]

Alternative 10: 61.5% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+188}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.36e+188) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.36e+188) {
		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 <= (-1.36d+188)) 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 <= -1.36e+188) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.36e+188:
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.36e+188)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.36e+188)
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.36e+188], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.36e188

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 72.2%

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

      1. neg-mul-1 72.2%

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

      2. *-commutative 72.2%

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

      3. distribute-rgt-neg-in 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in y around 0 47.7%

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

      1. mul-1-neg 47.7%

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

      2. distribute-rgt-neg-in 47.7%

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

   7. Simplified 47.7%

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

   if -1.36e188 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 67.1%

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

      1. +-commutative 67.1%

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

   4. Simplified 67.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+188}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 11: 60.7% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0) x (if (<= x 2.85e-6) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x;
	} else if (x <= 2.85e-6) {
		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 <= (-1.0d0)) then
        tmp = x
    else if (x <= 2.85d-6) 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 <= -1.0) {
		tmp = x;
	} else if (x <= 2.85e-6) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = x
	elif x <= 2.85e-6:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = x;
	elseif (x <= 2.85e-6)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x;
	elseif (x <= 2.85e-6)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], x, If[LessEqual[x, 2.85e-6], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 2.8499999999999998e-6 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 81.7%

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

   if -1 < x < 2.8499999999999998e-6

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. sin-neg 99.8%

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

      6. fma-def 99.8%

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

      7. sin-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.9%

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

   5. Taylor expanded in y around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. unsub-neg 50.7%

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

   7. Simplified 50.7%

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

   8. Taylor expanded in y around 0 40.9%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 61.4% 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. Taylor expanded in y around 0 63.4%

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

   1. +-commutative 63.4%

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

4. Simplified 63.4%

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

5. Final simplification 63.4%

   \[\leadsto x + 1 \]

Alternative 13: 22.1% 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. Step-by-step derivation

   1. cancel-sign-sub-inv 99.9%

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

   2. +-commutative 99.9%

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

   3. distribute-lft-neg-out 99.9%

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

   4. distribute-rgt-neg-in 99.9%

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

   5. sin-neg 99.9%

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

   6. fma-def 99.9%

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

   7. sin-neg 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 55.5%

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

5. Taylor expanded in y around 0 28.7%

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

   1. mul-1-neg 28.7%

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

   2. unsub-neg 28.7%

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

7. Simplified 28.7%

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

8. Taylor expanded in y around 0 20.6%

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

9. Final simplification 20.6%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023333 
(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))))