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

Percentage Accurate: 99.9% → 99.9%

Time: 8.6s

Alternatives: 11

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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 100.0%

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

   7. sin-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 90.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.006:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 0.105:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.006)
   (+ x 1.0)
   (if (<= x 0.105) (- (cos y) (* z (sin y))) (+ x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.006) {
		tmp = x + 1.0;
	} else if (x <= 0.105) {
		tmp = cos(y) - (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 (x <= (-0.006d0)) then
        tmp = x + 1.0d0
    else if (x <= 0.105d0) then
        tmp = cos(y) - (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 (x <= -0.006) {
		tmp = x + 1.0;
	} else if (x <= 0.105) {
		tmp = Math.cos(y) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.006:
		tmp = x + 1.0
	elif x <= 0.105:
		tmp = math.cos(y) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.006)
		tmp = Float64(x + 1.0);
	elseif (x <= 0.105)
		tmp = Float64(cos(y) - 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 (x <= -0.006)
		tmp = x + 1.0;
	elseif (x <= 0.105)
		tmp = cos(y) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.006], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 0.105], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0060000000000000001

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.1%

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

      1. +-commutative 83.1%

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

   4. Simplified 83.1%

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

   if -0.0060000000000000001 < x < 0.104999999999999996

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.5%

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

   if 0.104999999999999996 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 88.0%

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

      1. +-commutative 88.0%

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

   4. Simplified 88.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.006:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 0.105:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 3: 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 4: 81.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+183} \lor \neg \left(z \leq 5.8 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.2e+183) (not (<= z 5.8e+105)))
   (* z (- (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e+183) || !(z <= 5.8e+105)) {
		tmp = 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 <= (-4.2d+183)) .or. (.not. (z <= 5.8d+105))) then
        tmp = 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 <= -4.2e+183) || !(z <= 5.8e+105)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.2e+183) or not (z <= 5.8e+105):
		tmp = z * -math.sin(y)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.2e+183) || !(z <= 5.8e+105))
		tmp = Float64(z * Float64(-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 <= -4.2e+183) || ~((z <= 5.8e+105)))
		tmp = z * -sin(y);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.2e+183], N[Not[LessEqual[z, 5.8e+105]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e183 or 5.8000000000000002e105 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 74.7%

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

      1. neg-mul-1 74.7%

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

      2. *-commutative 74.7%

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

      3. distribute-rgt-neg-in 74.7%

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

   4. Simplified 74.7%

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

   if -4.2e183 < z < 5.8000000000000002e105

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 89.0%

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

      1. +-commutative 89.0%

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

   4. Simplified 89.0%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+183} \lor \neg \left(z \leq 5.8 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 80.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.027 \lor \neg \left(y \leq 1.2 \cdot 10^{-8}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.027) (not (<= y 1.2e-8)))
   (+ x (cos y))
   (+ 1.0 (- x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.027) || !(y <= 1.2e-8)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x - (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-0.027d0)) .or. (.not. (y <= 1.2d-8))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x - (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.027) || !(y <= 1.2e-8)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x - (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.027) or not (y <= 1.2e-8):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x - (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.027) || !(y <= 1.2e-8))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x - Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.027) || ~((y <= 1.2e-8)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x - (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.027], N[Not[LessEqual[y, 1.2e-8]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0269999999999999997 or 1.19999999999999999e-8 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 65.5%

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

      1. +-commutative 65.5%

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

   4. Simplified 65.5%

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

   if -0.0269999999999999997 < y < 1.19999999999999999e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.027 \lor \neg \left(y \leq 1.2 \cdot 10^{-8}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - z \cdot y\right)\\ \end{array} \]

Alternative 6: 71.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0002 \lor \neg \left(x \leq 2.35 \cdot 10^{-30}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0002) (not (<= x 2.35e-30))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0002) || !(x <= 2.35e-30)) {
		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 <= (-0.0002d0)) .or. (.not. (x <= 2.35d-30))) 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 <= -0.0002) || !(x <= 2.35e-30)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0002) or not (x <= 2.35e-30):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0002) || !(x <= 2.35e-30))
		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 <= -0.0002) || ~((x <= 2.35e-30)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0002], N[Not[LessEqual[x, 2.35e-30]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0000000000000001e-4 or 2.34999999999999985e-30 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.4%

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

      1. +-commutative 82.4%

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

   4. Simplified 82.4%

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

   if -2.0000000000000001e-4 < x < 2.34999999999999985e-30

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 65.5%

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

      1. +-commutative 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in x around 0 65.0%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0002 \lor \neg \left(x \leq 2.35 \cdot 10^{-30}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]

Alternative 7: 68.9% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \lor \neg \left(y \leq 1.2 \cdot 10^{-8}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1) (not (<= y 1.2e-8))) (+ x 1.0) (+ 1.0 (- x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1) || !(y <= 1.2e-8)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.1d0)) .or. (.not. (y <= 1.2d-8))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x - (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1) || !(y <= 1.2e-8)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1) or not (y <= 1.2e-8):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x - (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1) || !(y <= 1.2e-8))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x - Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.1) || ~((y <= 1.2e-8)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x - (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1], N[Not[LessEqual[y, 1.2e-8]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000009 or 1.19999999999999999e-8 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 43.7%

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

      1. +-commutative 43.7%

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

   4. Simplified 43.7%

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

   if -3.10000000000000009 < y < 1.19999999999999999e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \lor \neg \left(y \leq 1.2 \cdot 10^{-8}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - z \cdot y\right)\\ \end{array} \]

Alternative 8: 66.2% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-28} \lor \neg \left(x \leq 0.017\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e-28) (not (<= x 0.017))) (+ x 1.0) (- 1.0 (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-28) || !(x <= 0.017)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-6d-28)) .or. (.not. (x <= 0.017d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-28) || !(x <= 0.017)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e-28) or not (x <= 0.017):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e-28) || !(x <= 0.017))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6e-28) || ~((x <= 0.017)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e-28], N[Not[LessEqual[x, 0.017]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.00000000000000005e-28 or 0.017000000000000001 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.3%

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

      1. +-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -6.00000000000000005e-28 < x < 0.017000000000000001

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

   4. Simplified 52.3%

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

   5. Taylor expanded in x around 0 52.3%

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

      1. associate-*r* 52.3%

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

      2. neg-mul-1 52.3%

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

   7. Simplified 52.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-28} \lor \neg \left(x \leq 0.017\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot y\\ \end{array} \]

Alternative 9: 60.0% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.88:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.88) x (if (<= x 1.32e-21) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.88) {
		tmp = x;
	} else if (x <= 1.32e-21) {
		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 <= (-0.88d0)) then
        tmp = x
    else if (x <= 1.32d-21) 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 <= -0.88) {
		tmp = x;
	} else if (x <= 1.32e-21) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.88:
		tmp = x
	elif x <= 1.32e-21:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.88)
		tmp = x;
	elseif (x <= 1.32e-21)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.88)
		tmp = x;
	elseif (x <= 1.32e-21)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.88], x, If[LessEqual[x, 1.32e-21], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.880000000000000004 or 1.32e-21 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 83.5%

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

   if -0.880000000000000004 < x < 1.32e-21

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.5%

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

   3. Taylor expanded in y around 0 41.5%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.88:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 61.0% 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 62.8%

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

   1. +-commutative 62.8%

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

4. Simplified 62.8%

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

5. Final simplification 62.8%

   \[\leadsto x + 1 \]

Alternative 11: 21.2% 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. Taylor expanded in x around 0 57.9%

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

3. Taylor expanded in y around 0 22.3%

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

4. Final simplification 22.3%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023321 
(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))))