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

Percentage Accurate: 99.9% → 99.9%

Time: 10.1s

Alternatives: 17

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   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. Add Preprocessing

Alternative 2: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-8}:\\ \;\;\;\;\left(x + 1\right) - t\_0\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-22}:\\ \;\;\;\;\cos y - t\_0\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -\sin y, x\right) + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (<= x -1.8e-8)
     (- (+ x 1.0) t_0)
     (if (<= x 1.55e-22) (- (cos y) t_0) (+ (fma z (- (sin y)) x) 1.0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if (x <= -1.8e-8) {
		tmp = (x + 1.0) - t_0;
	} else if (x <= 1.55e-22) {
		tmp = cos(y) - t_0;
	} else {
		tmp = fma(z, -sin(y), x) + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if (x <= -1.8e-8)
		tmp = Float64(Float64(x + 1.0) - t_0);
	elseif (x <= 1.55e-22)
		tmp = Float64(cos(y) - t_0);
	else
		tmp = Float64(fma(z, Float64(-sin(y)), x) + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e-8], N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, 1.55e-22], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(z * (-N[Sin[y], $MachinePrecision]) + x), $MachinePrecision] + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999991e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.6%

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

   if -1.79999999999999991e-8 < x < 1.55000000000000006e-22

   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 99.4%

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

      1. neg-mul-1 99.4%

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

      2. sub-neg 99.4%

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

   7. Simplified 99.4%

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

   if 1.55000000000000006e-22 < 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 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 99.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-8}:\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-22}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -\sin y, x\right) + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{-7} \lor \neg \left(x \leq 1.55 \cdot 10^{-22}\right):\\ \;\;\;\;\left(x + 1\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -3.2e-7) (not (<= x 1.55e-22)))
     (- (+ 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 <= -3.2e-7) || !(x <= 1.55e-22)) {
		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 <= (-3.2d-7)) .or. (.not. (x <= 1.55d-22))) 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 <= -3.2e-7) || !(x <= 1.55e-22)) {
		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 <= -3.2e-7) or not (x <= 1.55e-22):
		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 <= -3.2e-7) || !(x <= 1.55e-22))
		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 <= -3.2e-7) || ~((x <= 1.55e-22)))
		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, -3.2e-7], N[Not[LessEqual[x, 1.55e-22]], $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 < -3.2000000000000001e-7 or 1.55000000000000006e-22 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

   if -3.2000000000000001e-7 < x < 1.55000000000000006e-22

   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 99.4%

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

      1. neg-mul-1 99.4%

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

      2. sub-neg 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-7} \lor \neg \left(x \leq 1.55 \cdot 10^{-22}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (cos(y) + x) - (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 = (cos(y) + x) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[Cos[y], $MachinePrecision] + x), $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. Final simplification 99.9%

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

Alternative 5: 80.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+160}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+60} \lor \neg \left(z \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.95e+160)
   (* (sin y) (- z))
   (if (or (<= z -3.2e+60) (not (<= z 2.8e+34)))
     (+ 1.0 (- x (* y z)))
     (+ (cos y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.95e+160) {
		tmp = sin(y) * -z;
	} else if ((z <= -3.2e+60) || !(z <= 2.8e+34)) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = cos(y) + 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 (z <= (-1.95d+160)) then
        tmp = sin(y) * -z
    else if ((z <= (-3.2d+60)) .or. (.not. (z <= 2.8d+34))) then
        tmp = 1.0d0 + (x - (y * z))
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.95e+160) {
		tmp = Math.sin(y) * -z;
	} else if ((z <= -3.2e+60) || !(z <= 2.8e+34)) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.95e+160:
		tmp = math.sin(y) * -z
	elif (z <= -3.2e+60) or not (z <= 2.8e+34):
		tmp = 1.0 + (x - (y * z))
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.95e+160)
		tmp = Float64(sin(y) * Float64(-z));
	elseif ((z <= -3.2e+60) || !(z <= 2.8e+34))
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.95e+160)
		tmp = sin(y) * -z;
	elseif ((z <= -3.2e+60) || ~((z <= 2.8e+34)))
		tmp = 1.0 + (x - (y * z));
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.95e+160], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], If[Or[LessEqual[z, -3.2e+60], N[Not[LessEqual[z, 2.8e+34]], $MachinePrecision]], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95000000000000004e160

   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 99.9%

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

      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 z around inf 85.1%

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

      1. neg-mul-1 85.1%

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

      2. distribute-rgt-neg-in 85.1%

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

   7. Simplified 85.1%

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

   if -1.95000000000000004e160 < z < -3.19999999999999991e60 or 2.80000000000000008e34 < z

   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 70.6%

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

      1. mul-1-neg 70.6%

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

      2. unsub-neg 70.6%

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

   7. Simplified 70.6%

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

   if -3.19999999999999991e60 < z < 2.80000000000000008e34

   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 94.6%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+160}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+60} \lor \neg \left(z \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -48000000 \lor \neg \left(z \leq 10^{-30}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -48000000.0) (not (<= z 1e-30)))
   (- (+ x 1.0) (* z (sin y)))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -48000000.0) || !(z <= 1e-30)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = cos(y) + 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 ((z <= (-48000000.0d0)) .or. (.not. (z <= 1d-30))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -48000000.0) || !(z <= 1e-30)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -48000000.0) or not (z <= 1e-30):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -48000000.0) || !(z <= 1e-30))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -48000000.0) || ~((z <= 1e-30)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -48000000.0], N[Not[LessEqual[z, 1e-30]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e7 or 1e-30 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.1%

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

   if -4.8e7 < z < 1e-30

   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 99.0%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -48000000 \lor \neg \left(z \leq 10^{-30}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -215000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+88}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -215000000.0) (not (<= z 2.35e+88)))
   (- x (* z (sin y)))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -215000000.0) || !(z <= 2.35e+88)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = cos(y) + 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 ((z <= (-215000000.0d0)) .or. (.not. (z <= 2.35d+88))) then
        tmp = x - (z * sin(y))
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -215000000.0) || !(z <= 2.35e+88)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -215000000.0) or not (z <= 2.35e+88):
		tmp = x - (z * math.sin(y))
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -215000000.0) || !(z <= 2.35e+88))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -215000000.0) || ~((z <= 2.35e+88)))
		tmp = x - (z * sin(y));
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -215000000.0], N[Not[LessEqual[z, 2.35e+88]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e8 or 2.35000000000000004e88 < z

   1. Initial program 99.9%

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

      1. log1p-expm1-u 99.9%

         \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\cos y\right)\right)}\right) - z \cdot \sin y \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(x + \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\cos y\right)\right)}\right) - z \cdot \sin y \]

   5. Taylor expanded in x around inf 91.3%

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

   if -2.15e8 < z < 2.35000000000000004e88

   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 z around 0 95.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -215000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+88}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00076 \lor \neg \left(y \leq 48\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(y \cdot \left(z \cdot 0.16666666666666666\right)\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00076) (not (<= y 48.0)))
   (+ (cos y) x)
   (+ 1.0 (+ x (* y (- (* y (* y (* z 0.16666666666666666))) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00076) || !(y <= 48.0)) {
		tmp = cos(y) + x;
	} else {
		tmp = 1.0 + (x + (y * ((y * (y * (z * 0.16666666666666666))) - 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 <= (-0.00076d0)) .or. (.not. (y <= 48.0d0))) then
        tmp = cos(y) + x
    else
        tmp = 1.0d0 + (x + (y * ((y * (y * (z * 0.16666666666666666d0))) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00076) || !(y <= 48.0)) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = 1.0 + (x + (y * ((y * (y * (z * 0.16666666666666666))) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00076) or not (y <= 48.0):
		tmp = math.cos(y) + x
	else:
		tmp = 1.0 + (x + (y * ((y * (y * (z * 0.16666666666666666))) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00076) || !(y <= 48.0))
		tmp = Float64(cos(y) + x);
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(y * Float64(z * 0.16666666666666666))) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00076) || ~((y <= 48.0)))
		tmp = cos(y) + x;
	else
		tmp = 1.0 + (x + (y * ((y * (y * (z * 0.16666666666666666))) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00076], N[Not[LessEqual[y, 48.0]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(y * N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.6000000000000004e-4 or 48 < 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 63.2%

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

   if -7.6000000000000004e-4 < y < 48

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.8%

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

   4. Taylor expanded in y around inf 98.8%

      \[\leadsto 1 + \left(x + y \cdot \left(y \cdot \color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right)\right)} - z\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 98.8%

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

      2. associate-*r* 98.8%

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

   6. Simplified 98.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00076 \lor \neg \left(y \leq 48\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(y \cdot \left(z \cdot 0.16666666666666666\right)\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+59}:\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+34}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e+59)
   (- 1.0 (* z (sin y)))
   (if (<= z 5.5e+34) (+ (cos y) x) (+ 1.0 (- x (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+59) {
		tmp = 1.0 - (z * sin(y));
	} else if (z <= 5.5e+34) {
		tmp = cos(y) + x;
	} 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 (z <= (-2.5d+59)) then
        tmp = 1.0d0 - (z * sin(y))
    else if (z <= 5.5d+34) then
        tmp = cos(y) + x
    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 (z <= -2.5e+59) {
		tmp = 1.0 - (z * Math.sin(y));
	} else if (z <= 5.5e+34) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e+59:
		tmp = 1.0 - (z * math.sin(y))
	elif z <= 5.5e+34:
		tmp = math.cos(y) + x
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e+59)
		tmp = Float64(1.0 - Float64(z * sin(y)));
	elseif (z <= 5.5e+34)
		tmp = Float64(cos(y) + x);
	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 (z <= -2.5e+59)
		tmp = 1.0 - (z * sin(y));
	elseif (z <= 5.5e+34)
		tmp = cos(y) + x;
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e+59], N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+34], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999999e59

   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 x around 0 78.0%

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

      1. neg-mul-1 78.0%

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

      2. sub-neg 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in y around 0 78.0%

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

   if -2.4999999999999999e59 < z < 5.4999999999999996e34

   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 94.6%

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

   if 5.4999999999999996e34 < z

   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 71.1%

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

      1. mul-1-neg 71.1%

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

      2. unsub-neg 71.1%

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

   7. Simplified 71.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+59}:\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+34}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-9} \lor \neg \left(x \leq 1.55 \cdot 10^{-22}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.7e-9) (not (<= x 1.55e-22))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e-9) || !(x <= 1.55e-22)) {
		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 <= (-2.7d-9)) .or. (.not. (x <= 1.55d-22))) 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 <= -2.7e-9) || !(x <= 1.55e-22)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.7e-9) or not (x <= 1.55e-22):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.7e-9) || !(x <= 1.55e-22))
		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 <= -2.7e-9) || ~((x <= 1.55e-22)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.7e-9], N[Not[LessEqual[x, 1.55e-22]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000002e-9 or 1.55000000000000006e-22 < 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 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 85.4%

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

   if -2.7000000000000002e-9 < x < 1.55000000000000006e-22

   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 z around 0 60.9%

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

   6. Taylor expanded in x around 0 60.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-9} \lor \neg \left(x \leq 1.55 \cdot 10^{-22}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.2% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -500000000000 \lor \neg \left(y \leq 54\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -500000000000.0) (not (<= y 54.0)))
   (+ x 1.0)
   (+ 1.0 (+ x (* y (- (* y (- (* (* y z) 0.16666666666666666) 0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -500000000000.0) || !(y <= 54.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 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 <= (-500000000000.0d0)) .or. (.not. (y <= 54.0d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x + (y * ((y * (((y * z) * 0.16666666666666666d0) - 0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -500000000000.0) || !(y <= 54.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -500000000000.0) or not (y <= 54.0):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -500000000000.0) || !(y <= 54.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(Float64(y * z) * 0.16666666666666666) - 0.5)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -500000000000.0) || ~((y <= 54.0)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -500000000000.0], N[Not[LessEqual[y, 54.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(N[(y * z), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e11 or 54 < 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 37.3%

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

   if -5e11 < y < 54

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.1%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -500000000000 \lor \neg \left(y \leq 54\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.1% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1600 \lor \neg \left(y \leq 53000000000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1600.0) (not (<= y 53000000000000.0)))
   (+ x 1.0)
   (+ 1.0 (+ x (* y (- (* y -0.5) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1600.0) || !(y <= 53000000000000.0)) {
		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 <= (-1600.0d0)) .or. (.not. (y <= 53000000000000.0d0))) 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 <= -1600.0) || !(y <= 53000000000000.0)) {
		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 <= -1600.0) or not (y <= 53000000000000.0):
		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 <= -1600.0) || !(y <= 53000000000000.0))
		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 <= -1600.0) || ~((y <= 53000000000000.0)))
		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, -1600.0], N[Not[LessEqual[y, 53000000000000.0]], $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 < -1600 or 5.3e13 < 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 37.8%

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

   if -1600 < y < 5.3e13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.0%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1600 \lor \neg \left(y \leq 53000000000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.9% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00076:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+63}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.00076)
   (* x (+ 1.0 (/ 1.0 x)))
   (if (<= y 2.5e+63) (+ 1.0 (- x (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.00076) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 2.5e+63) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-0.00076d0)) then
        tmp = x * (1.0d0 + (1.0d0 / x))
    else if (y <= 2.5d+63) then
        tmp = 1.0d0 + (x - (y * z))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.00076) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 2.5e+63) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.00076:
		tmp = x * (1.0 + (1.0 / x))
	elif y <= 2.5e+63:
		tmp = 1.0 + (x - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.00076)
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	elseif (y <= 2.5e+63)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.00076)
		tmp = x * (1.0 + (1.0 / x));
	elseif (y <= 2.5e+63)
		tmp = 1.0 + (x - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.00076], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+63], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.6000000000000004e-4

   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 99.9%

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

      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 33.8%

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

   6. Taylor expanded in x around inf 33.8%

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

   if -7.6000000000000004e-4 < y < 2.50000000000000005e63

   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 96.9%

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

      1. mul-1-neg 96.9%

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

      2. unsub-neg 96.9%

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

   7. Simplified 96.9%

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

   if 2.50000000000000005e63 < 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 44.2%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00076:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+63}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.2% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-10} \lor \neg \left(x \leq 0.00016\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e-10) (not (<= x 0.00016))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e-10) || !(x <= 0.00016)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-4d-10)) .or. (.not. (x <= 0.00016d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e-10) || !(x <= 0.00016)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e-10) or not (x <= 0.00016):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e-10) || !(x <= 0.00016))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4e-10) || ~((x <= 0.00016)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e-10], N[Not[LessEqual[x, 0.00016]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000015e-10 or 1.60000000000000013e-4 < 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 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 86.1%

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

   if -4.00000000000000015e-10 < x < 1.60000000000000013e-4

   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 99.6%

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

      1. neg-mul-1 99.6%

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

      2. sub-neg 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0 49.3%

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

      1. *-commutative 49.3%

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

   10. Simplified 49.3%

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

   11. Taylor expanded in y around 0 50.8%

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

       1. mul-1-neg 50.8%

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

       2. unsub-neg 50.8%

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

   13. Simplified 50.8%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-10} \lor \neg \left(x \leq 0.00016\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.9% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e-67) x (if (<= x 1.0) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e-67) {
		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 <= (-1.8d-67)) 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 <= -1.8e-67) {
		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 <= -1.8e-67:
		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 <= -1.8e-67)
		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 <= -1.8e-67)
		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, -1.8e-67], x, If[LessEqual[x, 1.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e-67 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 80.6%

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

   if -1.8e-67 < x < 1

   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 40.5%

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

   6. Taylor expanded in x around 0 40.5%

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

Alternative 16: 61.4% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

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

6. Final simplification 61.7%

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

Alternative 17: 21.8% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

   1. cancel-sign-sub-inv 99.9%

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

   2. +-commutative 99.9%

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

   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%

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

6. Taylor expanded in x around 0 21.4%

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

Reproduce

herbie shell --seed 2024185 
(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))))