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

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-7} \lor \neg \left(x \leq 3.4 \cdot 10^{-17}\right):\\ \;\;\;\;1 + \mathsf{fma}\left(z, -\sin y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.4e-7) (not (<= x 3.4e-17)))
   (+ 1.0 (fma z (- (sin y)) x))
   (- (cos y) (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.4e-7) || !(x <= 3.4e-17)) {
		tmp = 1.0 + fma(z, -sin(y), x);
	} else {
		tmp = cos(y) - (z * sin(y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.4e-7) || !(x <= 3.4e-17))
		tmp = Float64(1.0 + fma(z, Float64(-sin(y)), x));
	else
		tmp = Float64(cos(y) - Float64(z * sin(y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.4e-7], N[Not[LessEqual[x, 3.4e-17]], $MachinePrecision]], N[(1.0 + N[(z * (-N[Sin[y], $MachinePrecision]) + x), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4e-7 or 3.3999999999999998e-17 < x

   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%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.6%

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

   if -9.4e-7 < x < 3.3999999999999998e-17

   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%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.2%

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

      1. neg-mul-1 99.2%

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

      2. sub-neg 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-7} \lor \neg \left(x \leq 3.4 \cdot 10^{-17}\right):\\ \;\;\;\;1 + \mathsf{fma}\left(z, -\sin y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{-6} \lor \neg \left(x \leq 3.4 \cdot 10^{-17}\right):\\ \;\;\;\;\left(x + 1\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -1.05e-6) (not (<= x 3.4e-17)))
     (- (+ 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 <= -1.05e-6) || !(x <= 3.4e-17)) {
		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 <= (-1.05d-6)) .or. (.not. (x <= 3.4d-17))) 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 <= -1.05e-6) || !(x <= 3.4e-17)) {
		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 <= -1.05e-6) or not (x <= 3.4e-17):
		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 <= -1.05e-6) || !(x <= 3.4e-17))
		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 <= -1.05e-6) || ~((x <= 3.4e-17)))
		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, -1.05e-6], N[Not[LessEqual[x, 3.4e-17]], $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 < -1.0499999999999999e-6 or 3.3999999999999998e-17 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.6%

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

   if -1.0499999999999999e-6 < x < 3.3999999999999998e-17

   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%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.2%

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

      1. neg-mul-1 99.2%

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

      2. sub-neg 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-6} \lor \neg \left(x \leq 3.4 \cdot 10^{-17}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.75 \lor \neg \left(z \leq 0.26\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.75) (not (<= z 0.26)))
   (- (+ x 1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.75) || !(z <= 0.26)) {
		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 <= (-0.75d0)) .or. (.not. (z <= 0.26d0))) 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 <= -0.75) || !(z <= 0.26)) {
		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 <= -0.75) or not (z <= 0.26):
		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 <= -0.75) || !(z <= 0.26))
		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 <= -0.75) || ~((z <= 0.26)))
		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, -0.75], N[Not[LessEqual[z, 0.26]], $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 < -0.75 or 0.26000000000000001 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.1%

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

   if -0.75 < z < 0.26000000000000001

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 99.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.75 \lor \neg \left(z \leq 0.26\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-123}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-9}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6e+92)
   x
   (if (<= x -1.05e-123)
     (+ 1.0 (+ x (* y (- (* y (- (* 0.16666666666666666 (* y z)) 0.5)) z))))
     (if (<= x 1.05e-9) (cos y) (+ x 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6e+92) {
		tmp = x;
	} else if (x <= -1.05e-123) {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	} else if (x <= 1.05e-9) {
		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 <= (-6d+92)) then
        tmp = x
    else if (x <= (-1.05d-123)) then
        tmp = 1.0d0 + (x + (y * ((y * ((0.16666666666666666d0 * (y * z)) - 0.5d0)) - z)))
    else if (x <= 1.05d-9) 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 <= -6e+92) {
		tmp = x;
	} else if (x <= -1.05e-123) {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	} else if (x <= 1.05e-9) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6e+92:
		tmp = x
	elif x <= -1.05e-123:
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)))
	elif x <= 1.05e-9:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6e+92)
		tmp = x;
	elseif (x <= -1.05e-123)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(0.16666666666666666 * Float64(y * z)) - 0.5)) - z))));
	elseif (x <= 1.05e-9)
		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 <= -6e+92)
		tmp = x;
	elseif (x <= -1.05e-123)
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	elseif (x <= 1.05e-9)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6e+92], x, If[LessEqual[x, -1.05e-123], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-9], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.00000000000000026e92

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 90.7%

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

   if -6.00000000000000026e92 < x < -1.05e-123

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 73.5%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)} \]

   if -1.05e-123 < x < 1.0500000000000001e-9

   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%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. sub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 67.1%

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

   if 1.0500000000000001e-9 < x

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 79.2%

      \[\leadsto \color{blue}{1 + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-123}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-9}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+86} \lor \neg \left(z \leq 1.42 \cdot 10^{+50}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.15e+86) (not (<= z 1.42e+50)))
   (- 1.0 (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.15e+86) || !(z <= 1.42e+50)) {
		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 <= (-1.15d+86)) .or. (.not. (z <= 1.42d+50))) 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 <= -1.15e+86) || !(z <= 1.42e+50)) {
		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 <= -1.15e+86) or not (z <= 1.42e+50):
		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 <= -1.15e+86) || !(z <= 1.42e+50))
		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 <= -1.15e+86) || ~((z <= 1.42e+50)))
		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, -1.15e+86], N[Not[LessEqual[z, 1.42e+50]], $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 < -1.14999999999999995e86 or 1.41999999999999994e50 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

   4. Taylor expanded in x around 0 77.1%

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

   if -1.14999999999999995e86 < z < 1.41999999999999994e50

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 93.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+86} \lor \neg \left(z \leq 1.42 \cdot 10^{+50}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+100} \lor \neg \left(z \leq 1.6 \cdot 10^{+155}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e+100) (not (<= z 1.6e+155)))
   (* (sin y) (- z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e+100) || !(z <= 1.6e+155)) {
		tmp = sin(y) * -z;
	} 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+100)) .or. (.not. (z <= 1.6d+155))) then
        tmp = sin(y) * -z
    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+100) || !(z <= 1.6e+155)) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e+100) or not (z <= 1.6e+155):
		tmp = math.sin(y) * -z
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e+100) || !(z <= 1.6e+155))
		tmp = Float64(sin(y) * Float64(-z));
	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+100) || ~((z <= 1.6e+155)))
		tmp = sin(y) * -z;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e+100], N[Not[LessEqual[z, 1.6e+155]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000012e100 or 1.60000000000000006e155 < z

   1. Initial program 99.7%

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

      1. cancel-sign-sub-inv 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sin-neg 99.7%

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

      8. fma-define 99.7%

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

      9. sin-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 71.8%

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

      1. neg-mul-1 71.8%

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

      2. distribute-rgt-neg-in 71.8%

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

   7. Simplified 71.8%

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

   if -2.40000000000000012e100 < z < 1.60000000000000006e155

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 88.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+100} \lor \neg \left(z \leq 1.6 \cdot 10^{+155}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6300000 \lor \neg \left(y \leq 3.3\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6300000.0) (not (<= y 3.3)))
   (+ x (cos y))
   (+ 1.0 (+ x (* y (- (* y (- (* 0.16666666666666666 (* y z)) 0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6300000.0) || !(y <= 3.3)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - 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 <= (-6300000.0d0)) .or. (.not. (y <= 3.3d0))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x + (y * ((y * ((0.16666666666666666d0 * (y * z)) - 0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6300000.0) || !(y <= 3.3)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6300000.0) or not (y <= 3.3):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6300000.0) || !(y <= 3.3))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(0.16666666666666666 * Float64(y * z)) - 0.5)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6300000.0) || ~((y <= 3.3)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6300000.0], N[Not[LessEqual[y, 3.3]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.3e6 or 3.2999999999999998 < y

   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%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sin-neg 99.8%

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

      8. fma-define 99.8%

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

      9. sin-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 58.1%

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

   if -6.3e6 < y < 3.2999999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6300000 \lor \neg \left(y \leq 3.3\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.7% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7000000000000 \lor \neg \left(y \leq 3.7 \cdot 10^{+28}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7000000000000.0) (not (<= y 3.7e+28)))
   (+ x 1.0)
   (+ 1.0 (+ x (* y (- (* y -0.5) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7000000000000.0) || !(y <= 3.7e+28)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * -0.5) - 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 <= (-7000000000000.0d0)) .or. (.not. (y <= 3.7d+28))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x + (y * ((y * (-0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7000000000000.0) || !(y <= 3.7e+28)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7000000000000.0) or not (y <= 3.7e+28):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7000000000000.0) || !(y <= 3.7e+28))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * -0.5) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7000000000000.0) || ~((y <= 3.7e+28)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7000000000000.0], N[Not[LessEqual[y, 3.7e+28]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7e12 or 3.6999999999999999e28 < y

   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%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sin-neg 99.8%

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

      8. fma-define 99.8%

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

      9. sin-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 31.8%

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

   if -7e12 < y < 3.6999999999999999e28

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.1%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7000000000000 \lor \neg \left(y \leq 3.7 \cdot 10^{+28}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.7% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000000000000 \lor \neg \left(y \leq 1.56 \cdot 10^{+28}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4000000000000.0) (not (<= y 1.56e+28)))
   (+ x 1.0)
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4000000000000.0) || !(y <= 1.56e+28)) {
		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 <= (-4000000000000.0d0)) .or. (.not. (y <= 1.56d+28))) 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 <= -4000000000000.0) || !(y <= 1.56e+28)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4000000000000.0) or not (y <= 1.56e+28):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4000000000000.0) || !(y <= 1.56e+28))
		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 <= -4000000000000.0) || ~((y <= 1.56e+28)))
		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, -4000000000000.0], N[Not[LessEqual[y, 1.56e+28]], $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 < -4e12 or 1.5599999999999999e28 < y

   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%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sin-neg 99.8%

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

      8. fma-define 99.8%

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

      9. sin-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 31.5%

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

   if -4e12 < y < 1.5599999999999999e28

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 96.7%

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

      1. mul-1-neg 96.7%

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

      2. unsub-neg 96.7%

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

   7. Simplified 96.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4000000000000 \lor \neg \left(y \leq 1.56 \cdot 10^{+28}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-63}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.8e+36) x (if (<= x 3.8e-63) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e+36) {
		tmp = x;
	} else if (x <= 3.8e-63) {
		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 <= (-5.8d+36)) then
        tmp = x
    else if (x <= 3.8d-63) 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 <= -5.8e+36) {
		tmp = x;
	} else if (x <= 3.8e-63) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.8e+36:
		tmp = x
	elif x <= 3.8e-63:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.8e+36)
		tmp = x;
	elseif (x <= 3.8e-63)
		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 <= -5.8e+36)
		tmp = x;
	elseif (x <= 3.8e-63)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.8e+36], x, If[LessEqual[x, 3.8e-63], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.8e36

   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%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 83.2%

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

   if -5.8e36 < x < 3.80000000000000017e-63

   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%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 98.4%

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

      1. neg-mul-1 98.4%

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

      2. sub-neg 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in y around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. unsub-neg 54.0%

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

      3. *-commutative 54.0%

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

   10. Simplified 54.0%

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

   if 3.80000000000000017e-63 < x

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 74.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-63}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.6% accurate, 18.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   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%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 78.3%

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

   if -1 < x < 1

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.3%

         \[\leadsto \left(x + \cos y\right) - \color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}} \]

      2. pow3 99.4%

         \[\leadsto \left(x + \cos y\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

   4. Applied egg-rr 99.4%

      \[\leadsto \left(x + \cos y\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

   5. Taylor expanded in y around 0 44.1%

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

      1. +-commutative 44.1%

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

   7. Simplified 44.1%

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

   8. Taylor expanded in x around 0 43.3%

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

Alternative 13: 63.0% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.22 \cdot 10^{+238}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.22e+238) (+ x 1.0) (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.22e+238) {
		tmp = x + 1.0;
	} else {
		tmp = 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 (z <= 1.22d+238) then
        tmp = x + 1.0d0
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.22e+238) {
		tmp = x + 1.0;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.22e+238:
		tmp = x + 1.0
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.22e+238)
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.22e+238)
		tmp = x + 1.0;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.22e+238], N[(x + 1.0), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.2200000000000001e238

   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%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 61.7%

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

   if 1.2200000000000001e238 < z

   1. Initial program 99.6%

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

      1. cancel-sign-sub-inv 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. distribute-lft-neg-out 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. sin-neg 99.6%

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

      8. fma-define 99.6%

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

      9. sin-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 87.6%

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

      1. neg-mul-1 87.6%

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

      2. distribute-rgt-neg-in 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in y around 0 46.9%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.22 \cdot 10^{+238}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.4% 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. 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%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. distribute-lft-neg-out 99.9%

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

   6. distribute-rgt-neg-in 99.9%

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

   7. sin-neg 99.9%

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

   8. fma-define 99.9%

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

   9. sin-neg 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around 0 58.9%

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

6. Final simplification 58.9%

   \[\leadsto x + 1 \]
7. Add Preprocessing

Alternative 15: 21.5% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 99.4%

      \[\leadsto \left(x + \cos y\right) - \color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}} \]

   2. pow3 99.4%

      \[\leadsto \left(x + \cos y\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

4. Applied egg-rr 99.4%

   \[\leadsto \left(x + \cos y\right) - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

5. Taylor expanded in y around 0 58.9%

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

   1. +-commutative 58.9%

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

7. Simplified 58.9%

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

8. Taylor expanded in x around 0 26.1%

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

Reproduce

herbie shell --seed 2024163 
(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))))