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

Percentage Accurate: 99.9% → 99.9%

Time: 10.6s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around 0 99.9%

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

   1. associate-+r+ 99.9%

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

   2. associate-*r* 99.9%

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

   3. neg-mul-1 99.9%

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

   4. *-commutative 99.9%

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

   5. +-commutative 99.9%

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

   6. fma-define 99.9%

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

   7. +-commutative 99.9%

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

5. Simplified 99.9%

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

6. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) - (sin(y) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 3: 90.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ t_1 := x - t\_0\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+40}:\\ \;\;\;\;1 - t\_0\\ \mathbf{elif}\;z \leq -1800000 \lor \neg \left(z \leq 8.8 \cdot 10^{+104}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z)) (t_1 (- x t_0)))
   (if (<= z -2.5e+109)
     t_1
     (if (<= z -8.5e+40)
       (- 1.0 t_0)
       (if (or (<= z -1800000.0) (not (<= z 8.8e+104))) t_1 (+ (cos y) x))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double t_1 = x - t_0;
	double tmp;
	if (z <= -2.5e+109) {
		tmp = t_1;
	} else if (z <= -8.5e+40) {
		tmp = 1.0 - t_0;
	} else if ((z <= -1800000.0) || !(z <= 8.8e+104)) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sin(y) * z
    t_1 = x - t_0
    if (z <= (-2.5d+109)) then
        tmp = t_1
    else if (z <= (-8.5d+40)) then
        tmp = 1.0d0 - t_0
    else if ((z <= (-1800000.0d0)) .or. (.not. (z <= 8.8d+104))) then
        tmp = t_1
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * z;
	double t_1 = x - t_0;
	double tmp;
	if (z <= -2.5e+109) {
		tmp = t_1;
	} else if (z <= -8.5e+40) {
		tmp = 1.0 - t_0;
	} else if ((z <= -1800000.0) || !(z <= 8.8e+104)) {
		tmp = t_1;
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * z
	t_1 = x - t_0
	tmp = 0
	if z <= -2.5e+109:
		tmp = t_1
	elif z <= -8.5e+40:
		tmp = 1.0 - t_0
	elif (z <= -1800000.0) or not (z <= 8.8e+104):
		tmp = t_1
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	t_1 = Float64(x - t_0)
	tmp = 0.0
	if (z <= -2.5e+109)
		tmp = t_1;
	elseif (z <= -8.5e+40)
		tmp = Float64(1.0 - t_0);
	elseif ((z <= -1800000.0) || !(z <= 8.8e+104))
		tmp = t_1;
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * z;
	t_1 = x - t_0;
	tmp = 0.0;
	if (z <= -2.5e+109)
		tmp = t_1;
	elseif (z <= -8.5e+40)
		tmp = 1.0 - t_0;
	elseif ((z <= -1800000.0) || ~((z <= 8.8e+104)))
		tmp = t_1;
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(x - t$95$0), $MachinePrecision]}, If[LessEqual[z, -2.5e+109], t$95$1, If[LessEqual[z, -8.5e+40], N[(1.0 - t$95$0), $MachinePrecision], If[Or[LessEqual[z, -1800000.0], N[Not[LessEqual[z, 8.8e+104]], $MachinePrecision]], t$95$1, N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5000000000000001e109 or -8.49999999999999996e40 < z < -1.8e6 or 8.80000000000000002e104 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. distribute-lft-out-- 99.8%

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

      4. mul-1-neg 99.8%

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

      5. remove-double-neg 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 90.5%

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

   7. Taylor expanded in z around 0 90.6%

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

      1. neg-mul-1 90.6%

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

      2. distribute-lft-neg-in 90.6%

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

      3. *-commutative 90.6%

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

   9. Simplified 90.6%

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

   if -2.5000000000000001e109 < z < -8.49999999999999996e40

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. distribute-lft-out-- 99.8%

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

      4. mul-1-neg 99.8%

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

      5. remove-double-neg 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 99.8%

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

   7. Taylor expanded in x around 0 94.1%

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

      1. sub-neg 94.1%

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

      2. distribute-lft-in 94.1%

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

      3. rgt-mult-inverse 94.2%

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

   9. Simplified 94.2%

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

   if -1.8e6 < z < 8.80000000000000002e104

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.4%

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

      1. +-commutative 97.4%

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

   5. Simplified 97.4%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+109}:\\ \;\;\;\;x - \sin y \cdot z\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+40}:\\ \;\;\;\;1 - \sin y \cdot z\\ \mathbf{elif}\;z \leq -1800000 \lor \neg \left(z \leq 8.8 \cdot 10^{+104}\right):\\ \;\;\;\;x - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+201}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+68}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+105}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= z -9.2e+201)
     t_0
     (if (<= z -6e+68)
       (+ x (- 1.0 (* y z)))
       (if (<= z 3e+105) (+ (cos y) x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (z <= -9.2e+201) {
		tmp = t_0;
	} else if (z <= -6e+68) {
		tmp = x + (1.0 - (y * z));
	} else if (z <= 3e+105) {
		tmp = cos(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin(y) * -z
    if (z <= (-9.2d+201)) then
        tmp = t_0
    else if (z <= (-6d+68)) then
        tmp = x + (1.0d0 - (y * z))
    else if (z <= 3d+105) then
        tmp = cos(y) + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double tmp;
	if (z <= -9.2e+201) {
		tmp = t_0;
	} else if (z <= -6e+68) {
		tmp = x + (1.0 - (y * z));
	} else if (z <= 3e+105) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	tmp = 0
	if z <= -9.2e+201:
		tmp = t_0
	elif z <= -6e+68:
		tmp = x + (1.0 - (y * z))
	elif z <= 3e+105:
		tmp = math.cos(y) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (z <= -9.2e+201)
		tmp = t_0;
	elseif (z <= -6e+68)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	elseif (z <= 3e+105)
		tmp = Float64(cos(y) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	tmp = 0.0;
	if (z <= -9.2e+201)
		tmp = t_0;
	elseif (z <= -6e+68)
		tmp = x + (1.0 - (y * z));
	elseif (z <= 3e+105)
		tmp = cos(y) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -9.2e+201], t$95$0, If[LessEqual[z, -6e+68], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+105], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.2000000000000004e201 or 3.0000000000000001e105 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 75.4%

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

      1. associate-*r* 75.4%

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

      2. neg-mul-1 75.4%

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

      3. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -9.2000000000000004e201 < z < -6.0000000000000004e68

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.0%

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

      1. associate-+r+ 67.0%

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

      2. +-commutative 67.0%

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

      3. associate-+l+ 67.0%

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

      4. mul-1-neg 67.0%

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

      5. unsub-neg 67.0%

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

   5. Simplified 67.0%

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

   if -6.0000000000000004e68 < z < 3.0000000000000001e105

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 94.0%

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

      1. +-commutative 94.0%

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

   5. Simplified 94.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+201}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+68}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+105}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1350000 \lor \neg \left(z \leq 6600000000000\right):\\ \;\;\;\;z \cdot \left(\frac{x + 1}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1350000.0) (not (<= z 6600000000000.0)))
   (* z (- (/ (+ x 1.0) z) (sin y)))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1350000.0) || !(z <= 6600000000000.0)) {
		tmp = z * (((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 <= (-1350000.0d0)) .or. (.not. (z <= 6600000000000.0d0))) then
        tmp = z * (((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 <= -1350000.0) || !(z <= 6600000000000.0)) {
		tmp = z * (((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 <= -1350000.0) or not (z <= 6600000000000.0):
		tmp = z * (((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 <= -1350000.0) || !(z <= 6600000000000.0))
		tmp = Float64(z * Float64(Float64(Float64(x + 1.0) / 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 <= -1350000.0) || ~((z <= 6600000000000.0)))
		tmp = z * (((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, -1350000.0], N[Not[LessEqual[z, 6600000000000.0]], $MachinePrecision]], N[(z * N[(N[(N[(x + 1.0), $MachinePrecision] / z), $MachinePrecision] - N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e6 or 6.6e12 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. distribute-lft-out-- 99.8%

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

      4. mul-1-neg 99.8%

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

      5. remove-double-neg 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 99.6%

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

   if -1.35e6 < z < 6.6e12

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.2%

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

      1. +-commutative 99.2%

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

   5. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1350000 \lor \neg \left(z \leq 6600000000000\right):\\ \;\;\;\;z \cdot \left(\frac{x + 1}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -450000000000 \lor \neg \left(z \leq 7 \cdot 10^{+69}\right):\\ \;\;\;\;1 - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -450000000000.0) (not (<= z 7e+69)))
   (- 1.0 (* (sin y) z))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -450000000000.0) || !(z <= 7e+69)) {
		tmp = 1.0 - (sin(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 <= (-450000000000.0d0)) .or. (.not. (z <= 7d+69))) then
        tmp = 1.0d0 - (sin(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 <= -450000000000.0) || !(z <= 7e+69)) {
		tmp = 1.0 - (Math.sin(y) * z);
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -450000000000.0) or not (z <= 7e+69):
		tmp = 1.0 - (math.sin(y) * z)
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -450000000000.0) || !(z <= 7e+69))
		tmp = Float64(1.0 - Float64(sin(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 <= -450000000000.0) || ~((z <= 7e+69)))
		tmp = 1.0 - (sin(y) * z);
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -450000000000.0], N[Not[LessEqual[z, 7e+69]], $MachinePrecision]], N[(1.0 - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e11 or 6.99999999999999974e69 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. distribute-lft-out-- 99.8%

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

      4. mul-1-neg 99.8%

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

      5. remove-double-neg 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 99.5%

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

   7. Taylor expanded in x around 0 79.1%

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

      1. sub-neg 79.1%

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

      2. distribute-lft-in 79.1%

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

      3. rgt-mult-inverse 79.2%

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

   9. Simplified 79.2%

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

   if -4.5e11 < z < 6.99999999999999974e69

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.5%

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

      1. +-commutative 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -450000000000 \lor \neg \left(z \leq 7 \cdot 10^{+69}\right):\\ \;\;\;\;1 - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.42 \lor \neg \left(y \leq 4600000000\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.42) (not (<= y 4600000000.0)))
   (+ (cos y) x)
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.42) || !(y <= 4600000000.0)) {
		tmp = cos(y) + x;
	} else {
		tmp = x + (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 ((y <= (-0.42d0)) .or. (.not. (y <= 4600000000.0d0))) then
        tmp = cos(y) + x
    else
        tmp = x + (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.42) || !(y <= 4600000000.0)) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.42) or not (y <= 4600000000.0):
		tmp = math.cos(y) + x
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.42) || !(y <= 4600000000.0))
		tmp = Float64(cos(y) + x);
	else
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.42) || ~((y <= 4600000000.0)))
		tmp = cos(y) + x;
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.42], N[Not[LessEqual[y, 4600000000.0]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.419999999999999984 or 4.6e9 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 57.2%

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

      1. +-commutative 57.2%

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

   5. Simplified 57.2%

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

   if -0.419999999999999984 < y < 4.6e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.4%

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

      1. associate-+r+ 99.4%

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

      2. +-commutative 99.4%

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

      3. associate-+l+ 99.4%

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

      4. mul-1-neg 99.4%

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

      5. unsub-neg 99.4%

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

   5. Simplified 99.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.42 \lor \neg \left(y \leq 4600000000\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.0% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.48 \cdot 10^{-12}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 155:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.48e-12)
   (+ x 1.0)
   (if (<= x 155.0) (- 1.0 (* y z)) (* x (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.48e-12) {
		tmp = x + 1.0;
	} else if (x <= 155.0) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x * (1.0 + (1.0 / 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 <= (-1.48d-12)) then
        tmp = x + 1.0d0
    else if (x <= 155.0d0) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x * (1.0d0 + (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.48e-12) {
		tmp = x + 1.0;
	} else if (x <= 155.0) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x * (1.0 + (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.48e-12:
		tmp = x + 1.0
	elif x <= 155.0:
		tmp = 1.0 - (y * z)
	else:
		tmp = x * (1.0 + (1.0 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.48e-12)
		tmp = Float64(x + 1.0);
	elseif (x <= 155.0)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.48e-12)
		tmp = x + 1.0;
	elseif (x <= 155.0)
		tmp = 1.0 - (y * z);
	else
		tmp = x * (1.0 + (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.48e-12], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 155.0], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.47999999999999995e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.4%

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

      1. +-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -1.47999999999999995e-12 < x < 155

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-in 99.7%

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

      3. distribute-lft-out-- 99.7%

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

      4. mul-1-neg 99.7%

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

      5. remove-double-neg 99.7%

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

      6. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 83.7%

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

   7. Taylor expanded in y around 0 59.7%

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

      1. +-commutative 59.7%

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

      2. mul-1-neg 59.7%

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

      3. unsub-neg 59.7%

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

      4. +-commutative 59.7%

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

   9. Simplified 59.7%

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

   10. Taylor expanded in x around 0 59.7%

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

       1. sub-neg 59.7%

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

       2. distribute-rgt-in 59.7%

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

       3. lft-mult-inverse 59.8%

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

       4. distribute-lft-neg-out 59.8%

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

       5. distribute-rgt-neg-in 59.8%

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

   12. Simplified 59.8%

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

   if 155 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-+r+ 100.0%

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

      2. associate-*r* 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-define 100.0%

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

      7. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 99.9%

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

      1. associate-+r+ 99.9%

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

      2. +-commutative 99.9%

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

      3. mul-1-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around 0 79.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.48 \cdot 10^{-12}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 155:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.2% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+147}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+33)
   (* x (+ 1.0 (/ 1.0 x)))
   (if (<= y 5.6e+147) (+ x (- 1.0 (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+33) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 5.6e+147) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.8d+33)) then
        tmp = x * (1.0d0 + (1.0d0 / x))
    else if (y <= 5.6d+147) then
        tmp = x + (1.0d0 - (y * z))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+33) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 5.6e+147) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+33:
		tmp = x * (1.0 + (1.0 / x))
	elif y <= 5.6e+147:
		tmp = x + (1.0 - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+33)
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	elseif (y <= 5.6e+147)
		tmp = Float64(x + 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 (y <= -3.8e+33)
		tmp = x * (1.0 + (1.0 / x));
	elseif (y <= 5.6e+147)
		tmp = x + (1.0 - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+33], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+147], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.80000000000000002e33

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 99.8%

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

      1. associate-+r+ 99.8%

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

      2. associate-*r* 99.8%

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

      3. neg-mul-1 99.8%

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

      4. *-commutative 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-define 99.9%

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

      7. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around inf 82.4%

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

      1. associate-+r+ 82.4%

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

      2. +-commutative 82.4%

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

      3. mul-1-neg 82.4%

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

      4. unsub-neg 82.4%

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

      5. *-commutative 82.4%

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

      6. associate-/l* 82.3%

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

   8. Simplified 82.3%

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

   9. Taylor expanded in y around 0 33.4%

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

   if -3.80000000000000002e33 < y < 5.6000000000000002e147

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.8%

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

      1. associate-+r+ 87.8%

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

      2. +-commutative 87.8%

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

      3. associate-+l+ 87.8%

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

      4. mul-1-neg 87.8%

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

      5. unsub-neg 87.8%

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

   5. Simplified 87.8%

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

   if 5.6000000000000002e147 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 45.2%

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

      1. +-commutative 45.2%

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

   5. Simplified 45.2%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+147}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.1% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-13} \lor \neg \left(x \leq 6.9\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e-13) (not (<= x 6.9))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-13) || !(x <= 6.9)) {
		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 <= (-6d-13)) .or. (.not. (x <= 6.9d0))) 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 <= -6e-13) || !(x <= 6.9)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e-13) or not (x <= 6.9):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e-13) || !(x <= 6.9))
		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 <= -6e-13) || ~((x <= 6.9)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e-13], N[Not[LessEqual[x, 6.9]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.99999999999999968e-13 or 6.9000000000000004 < 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 77.7%

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

      1. +-commutative 77.7%

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

   5. Simplified 77.7%

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

   if -5.99999999999999968e-13 < x < 6.9000000000000004

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-in 99.7%

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

      3. distribute-lft-out-- 99.7%

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

      4. mul-1-neg 99.7%

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

      5. remove-double-neg 99.7%

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

      6. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 83.7%

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

   7. Taylor expanded in y around 0 59.7%

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

      1. +-commutative 59.7%

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

      2. mul-1-neg 59.7%

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

      3. unsub-neg 59.7%

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

      4. +-commutative 59.7%

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

   9. Simplified 59.7%

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

   10. Taylor expanded in x around 0 59.7%

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

       1. sub-neg 59.7%

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

       2. distribute-rgt-in 59.7%

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

       3. lft-mult-inverse 59.8%

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

       4. distribute-lft-neg-out 59.8%

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

       5. distribute-rgt-neg-in 59.8%

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

   12. Simplified 59.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-13} \lor \neg \left(x \leq 6.9\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.0% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+90}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.65e+90) (- x (* y z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.65e+90) {
		tmp = 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 (z <= (-1.65d+90)) then
        tmp = 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 (z <= -1.65e+90) {
		tmp = x - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.65e+90:
		tmp = x - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.65e+90)
		tmp = 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 (z <= -1.65e+90)
		tmp = x - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.65e+90], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65000000000000004e90

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. distribute-lft-out-- 99.8%

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

      4. mul-1-neg 99.8%

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

      5. remove-double-neg 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 90.0%

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

   7. Taylor expanded in y around 0 50.9%

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

      1. mul-1-neg 50.9%

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

      2. unsub-neg 50.9%

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

   9. Simplified 50.9%

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

   if -1.65000000000000004e90 < 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 70.2%

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

      1. +-commutative 70.2%

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

   5. Simplified 70.2%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+90}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.6% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z -4e+209) (* z (- y)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e+209) {
		tmp = z * -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 (z <= (-4d+209)) then
        tmp = z * -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 (z <= -4e+209) {
		tmp = z * -y;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4e+209:
		tmp = z * -y
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4e+209)
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4e+209)
		tmp = z * -y;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4e+209], N[(z * (-y)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0000000000000003e209

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. distribute-rgt-neg-in 99.6%

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

      3. distribute-lft-out-- 99.6%

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

      4. mul-1-neg 99.6%

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

      5. remove-double-neg 99.6%

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

      6. +-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in y around 0 99.6%

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

   7. Taylor expanded in y around 0 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

      4. +-commutative 55.0%

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

   9. Simplified 55.0%

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

   10. Taylor expanded in z around inf 42.6%

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

       1. mul-1-neg 42.6%

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

       2. distribute-lft-neg-out 42.6%

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

       3. *-commutative 42.6%

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

   12. Simplified 42.6%

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

   if -4.0000000000000003e209 < 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 67.3%

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

      1. +-commutative 67.3%

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

   5. Simplified 67.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.5% 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. Add Preprocessing

3. Taylor expanded in y around 0 63.3%

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

   1. +-commutative 63.3%

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

5. Simplified 63.3%

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

6. Final simplification 63.3%

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

Alternative 14: 42.9% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf 41.4%

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

4. Final simplification 41.4%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(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))))