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

Percentage Accurate: 99.9% → 99.9%

Time: 10.1s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. cancel-sign-sub-inv 99.9%

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

   2. +-commutative 99.9%

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

   3. *-commutative 99.9%

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

   4. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+16}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.4e+46)
   x
   (if (<= x 2.4e+16) (- (cos y) (* (sin y) z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.4e+46) {
		tmp = x;
	} else if (x <= 2.4e+16) {
		tmp = cos(y) - (sin(y) * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-8.4d+46)) then
        tmp = x
    else if (x <= 2.4d+16) then
        tmp = cos(y) - (sin(y) * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.4e+46) {
		tmp = x;
	} else if (x <= 2.4e+16) {
		tmp = Math.cos(y) - (Math.sin(y) * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.4e+46:
		tmp = x
	elif x <= 2.4e+16:
		tmp = math.cos(y) - (math.sin(y) * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.4e+46)
		tmp = x;
	elseif (x <= 2.4e+16)
		tmp = Float64(cos(y) - Float64(sin(y) * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.4e+46)
		tmp = x;
	elseif (x <= 2.4e+16)
		tmp = cos(y) - (sin(y) * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.4e+46], x, If[LessEqual[x, 2.4e+16], N[(N[Cos[y], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.4e46

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.5%

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

   if -8.4e46 < x < 2.4e16

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 97.2%

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

   if 2.4e16 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

   4. Simplified 83.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+16}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 4: 80.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+196}:\\ \;\;\;\;\left(1 + \left(x + -0.5 \cdot \left(y \cdot y\right)\right)\right) - \sin y \cdot z\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+64} \lor \neg \left(z \leq 5.2 \cdot 10^{+56}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e+196)
   (- (+ 1.0 (+ x (* -0.5 (* y y)))) (* (sin y) z))
   (if (or (<= z -4.9e+64) (not (<= z 5.2e+56)))
     (* (sin y) (- z))
     (+ x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+196) {
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (sin(y) * z);
	} else if ((z <= -4.9e+64) || !(z <= 5.2e+56)) {
		tmp = sin(y) * -z;
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.5d+196)) then
        tmp = (1.0d0 + (x + ((-0.5d0) * (y * y)))) - (sin(y) * z)
    else if ((z <= (-4.9d+64)) .or. (.not. (z <= 5.2d+56))) then
        tmp = sin(y) * -z
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+196) {
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (Math.sin(y) * z);
	} else if ((z <= -4.9e+64) || !(z <= 5.2e+56)) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e+196:
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (math.sin(y) * z)
	elif (z <= -4.9e+64) or not (z <= 5.2e+56):
		tmp = math.sin(y) * -z
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e+196)
		tmp = Float64(Float64(1.0 + Float64(x + Float64(-0.5 * Float64(y * y)))) - Float64(sin(y) * z));
	elseif ((z <= -4.9e+64) || !(z <= 5.2e+56))
		tmp = Float64(sin(y) * Float64(-z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.5e+196)
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (sin(y) * z);
	elseif ((z <= -4.9e+64) || ~((z <= 5.2e+56)))
		tmp = sin(y) * -z;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e+196], N[(N[(1.0 + N[(x + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.9e+64], N[Not[LessEqual[z, 5.2e+56]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999999e196

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 79.3%

      \[\leadsto \color{blue}{\left(1 + \left(x + -0.5 \cdot {y}^{2}\right)\right)} - z \cdot \sin y \]
   3. Step-by-step derivation

      1. unpow2 79.3%

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

   4. Simplified 79.3%

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

   if -2.4999999999999999e196 < z < -4.9000000000000003e64 or 5.20000000000000022e56 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 72.3%

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

      1. neg-mul-1 72.3%

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

      2. distribute-rgt-neg-in 72.3%

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

   4. Simplified 72.3%

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

   if -4.9000000000000003e64 < z < 5.20000000000000022e56

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 95.0%

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

      1. +-commutative 95.0%

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

   4. Simplified 95.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+196}:\\ \;\;\;\;\left(1 + \left(x + -0.5 \cdot \left(y \cdot y\right)\right)\right) - \sin y \cdot z\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+64} \lor \neg \left(z \leq 5.2 \cdot 10^{+56}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 80.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+63} \lor \neg \left(z \leq 8.5 \cdot 10^{+55}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.2e+63) (not (<= z 8.5e+55)))
   (* (sin y) (- z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2e+63) || !(z <= 8.5e+55)) {
		tmp = sin(y) * -z;
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.2d+63)) .or. (.not. (z <= 8.5d+55))) then
        tmp = sin(y) * -z
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2e+63) || !(z <= 8.5e+55)) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.2e+63) or not (z <= 8.5e+55):
		tmp = math.sin(y) * -z
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.2e+63) || !(z <= 8.5e+55))
		tmp = Float64(sin(y) * Float64(-z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.2e+63) || ~((z <= 8.5e+55)))
		tmp = sin(y) * -z;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.2e+63], N[Not[LessEqual[z, 8.5e+55]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000011e63 or 8.50000000000000002e55 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 70.0%

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

      1. neg-mul-1 70.0%

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

      2. distribute-rgt-neg-in 70.0%

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

   4. Simplified 70.0%

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

   if -3.20000000000000011e63 < z < 8.50000000000000002e55

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 95.0%

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

      1. +-commutative 95.0%

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

   4. Simplified 95.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+63} \lor \neg \left(z \leq 8.5 \cdot 10^{+55}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 6: 72.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-29}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;x \leq 14.5:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.2e+46)
   x
   (if (<= x -1.75e-29)
     (+ x (- 1.0 (* y z)))
     (if (<= x 14.5) (cos y) (+ x 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e+46) {
		tmp = x;
	} else if (x <= -1.75e-29) {
		tmp = x + (1.0 - (y * z));
	} else if (x <= 14.5) {
		tmp = cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-8.2d+46)) then
        tmp = x
    else if (x <= (-1.75d-29)) then
        tmp = x + (1.0d0 - (y * z))
    else if (x <= 14.5d0) then
        tmp = cos(y)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e+46) {
		tmp = x;
	} else if (x <= -1.75e-29) {
		tmp = x + (1.0 - (y * z));
	} else if (x <= 14.5) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.2e+46:
		tmp = x
	elif x <= -1.75e-29:
		tmp = x + (1.0 - (y * z))
	elif x <= 14.5:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.2e+46)
		tmp = x;
	elseif (x <= -1.75e-29)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	elseif (x <= 14.5)
		tmp = cos(y);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.2e+46)
		tmp = x;
	elseif (x <= -1.75e-29)
		tmp = x + (1.0 - (y * z));
	elseif (x <= 14.5)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.2e+46], x, If[LessEqual[x, -1.75e-29], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 14.5], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.19999999999999999e46

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.5%

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

   if -8.19999999999999999e46 < x < -1.7499999999999999e-29

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 60.5%

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

      1. associate-+r+ 60.5%

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

      2. +-commutative 60.5%

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

      3. associate-+l+ 60.5%

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

      4. mul-1-neg 60.5%

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

      5. unsub-neg 60.5%

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

   4. Simplified 60.5%

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

   if -1.7499999999999999e-29 < x < 14.5

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 59.2%

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

      1. +-commutative 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in x around 0 58.5%

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

   if 14.5 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.3%

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

      1. +-commutative 81.3%

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

   4. Simplified 81.3%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-29}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;x \leq 14.5:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 7: 81.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00205 \lor \neg \left(y \leq 0.1\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + \left(y \cdot \left(y \cdot -0.5\right) - y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00205) (not (<= y 0.1)))
   (+ x (cos y))
   (+ x (+ 1.0 (- (* y (* y -0.5)) (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00205) || !(y <= 0.1)) {
		tmp = x + cos(y);
	} else {
		tmp = x + (1.0 + ((y * (y * -0.5)) - (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 <= (-0.00205d0)) .or. (.not. (y <= 0.1d0))) then
        tmp = x + cos(y)
    else
        tmp = x + (1.0d0 + ((y * (y * (-0.5d0))) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00205) || !(y <= 0.1)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 + ((y * (y * -0.5)) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00205) or not (y <= 0.1):
		tmp = x + math.cos(y)
	else:
		tmp = x + (1.0 + ((y * (y * -0.5)) - (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00205) || !(y <= 0.1))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(x + Float64(1.0 + Float64(Float64(y * Float64(y * -0.5)) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00205) || ~((y <= 0.1)))
		tmp = x + cos(y);
	else
		tmp = x + (1.0 + ((y * (y * -0.5)) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00205], N[Not[LessEqual[y, 0.1]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 + N[(N[(y * N[(y * -0.5), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00205000000000000017 or 0.10000000000000001 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 59.9%

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

      1. +-commutative 59.9%

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

   4. Simplified 59.9%

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

   if -0.00205000000000000017 < y < 0.10000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.5%

      \[\leadsto \color{blue}{1 + \left(x + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)\right)} \]
   3. Step-by-step derivation

      1. associate-+r+ 98.5%

         \[\leadsto \color{blue}{\left(1 + x\right) + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)} \]

      2. +-commutative 98.5%

         \[\leadsto \color{blue}{\left(x + 1\right)} + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right) \]

      3. associate-+l+ 98.5%

         \[\leadsto \color{blue}{x + \left(1 + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)\right)} \]

      4. +-commutative 98.5%

         \[\leadsto x + \left(1 + \color{blue}{\left(-0.5 \cdot {y}^{2} + -1 \cdot \left(y \cdot z\right)\right)}\right) \]

      5. mul-1-neg 98.5%

         \[\leadsto x + \left(1 + \left(-0.5 \cdot {y}^{2} + \color{blue}{\left(-y \cdot z\right)}\right)\right) \]

      6. unsub-neg 98.5%

         \[\leadsto x + \left(1 + \color{blue}{\left(-0.5 \cdot {y}^{2} - y \cdot z\right)}\right) \]

      7. *-commutative 98.5%

         \[\leadsto x + \left(1 + \left(\color{blue}{{y}^{2} \cdot -0.5} - y \cdot z\right)\right) \]

      8. unpow2 98.5%

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

      9. associate-*l* 98.5%

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

   4. Simplified 98.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00205 \lor \neg \left(y \leq 0.1\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + \left(y \cdot \left(y \cdot -0.5\right) - y \cdot z\right)\right)\\ \end{array} \]

Alternative 8: 70.5% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1400 \lor \neg \left(y \leq 1900000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + \left(y \cdot \left(y \cdot -0.5\right) - y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1400.0) (not (<= y 1900000.0)))
   (+ x 1.0)
   (+ x (+ 1.0 (- (* y (* y -0.5)) (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1400.0) || !(y <= 1900000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 + ((y * (y * -0.5)) - (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 <= (-1400.0d0)) .or. (.not. (y <= 1900000.0d0))) then
        tmp = x + 1.0d0
    else
        tmp = x + (1.0d0 + ((y * (y * (-0.5d0))) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1400.0) || !(y <= 1900000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 + ((y * (y * -0.5)) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1400.0) or not (y <= 1900000.0):
		tmp = x + 1.0
	else:
		tmp = x + (1.0 + ((y * (y * -0.5)) - (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1400.0) || !(y <= 1900000.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(x + Float64(1.0 + Float64(Float64(y * Float64(y * -0.5)) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1400.0) || ~((y <= 1900000.0)))
		tmp = x + 1.0;
	else
		tmp = x + (1.0 + ((y * (y * -0.5)) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1400.0], N[Not[LessEqual[y, 1900000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(x + N[(1.0 + N[(N[(y * N[(y * -0.5), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1400 or 1.9e6 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 37.4%

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

      1. +-commutative 37.4%

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

   4. Simplified 37.4%

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

   if -1400 < y < 1.9e6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.3%

      \[\leadsto \color{blue}{1 + \left(x + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)\right)} \]
   3. Step-by-step derivation

      1. associate-+r+ 96.3%

         \[\leadsto \color{blue}{\left(1 + x\right) + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)} \]

      2. +-commutative 96.3%

         \[\leadsto \color{blue}{\left(x + 1\right)} + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right) \]

      3. associate-+l+ 96.3%

         \[\leadsto \color{blue}{x + \left(1 + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)\right)} \]

      4. +-commutative 96.3%

         \[\leadsto x + \left(1 + \color{blue}{\left(-0.5 \cdot {y}^{2} + -1 \cdot \left(y \cdot z\right)\right)}\right) \]

      5. mul-1-neg 96.3%

         \[\leadsto x + \left(1 + \left(-0.5 \cdot {y}^{2} + \color{blue}{\left(-y \cdot z\right)}\right)\right) \]

      6. unsub-neg 96.3%

         \[\leadsto x + \left(1 + \color{blue}{\left(-0.5 \cdot {y}^{2} - y \cdot z\right)}\right) \]

      7. *-commutative 96.3%

         \[\leadsto x + \left(1 + \left(\color{blue}{{y}^{2} \cdot -0.5} - y \cdot z\right)\right) \]

      8. unpow2 96.3%

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

      9. associate-*l* 96.3%

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

   4. Simplified 96.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1400 \lor \neg \left(y \leq 1900000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + \left(y \cdot \left(y \cdot -0.5\right) - y \cdot z\right)\right)\\ \end{array} \]

Alternative 9: 70.4% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+26}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 510000:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.4e+26)
   (+ x 1.0)
   (if (<= y 510000.0) (+ x (- 1.0 (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.4e+26) {
		tmp = x + 1.0;
	} else if (y <= 510000.0) {
		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 <= (-4.4d+26)) then
        tmp = x + 1.0d0
    else if (y <= 510000.0d0) 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 <= -4.4e+26) {
		tmp = x + 1.0;
	} else if (y <= 510000.0) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.4e+26:
		tmp = x + 1.0
	elif y <= 510000.0:
		tmp = x + (1.0 - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.4e+26)
		tmp = Float64(x + 1.0);
	elseif (y <= 510000.0)
		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 <= -4.4e+26)
		tmp = x + 1.0;
	elseif (y <= 510000.0)
		tmp = x + (1.0 - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.4e+26], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 510000.0], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.40000000000000014e26 or 5.1e5 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 38.5%

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

      1. +-commutative 38.5%

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

   4. Simplified 38.5%

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

   if -4.40000000000000014e26 < y < 5.1e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.4%

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

      1. associate-+r+ 91.4%

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

      2. +-commutative 91.4%

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

      3. associate-+l+ 91.4%

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

      4. mul-1-neg 91.4%

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

      5. unsub-neg 91.4%

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

   4. Simplified 91.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+26}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 510000:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 10: 66.4% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+14}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e+18) x (if (<= x 2.1e+14) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e+18) {
		tmp = x;
	} else if (x <= 2.1e+14) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.25d+18)) then
        tmp = x
    else if (x <= 2.1d+14) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e+18) {
		tmp = x;
	} else if (x <= 2.1e+14) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e+18:
		tmp = x
	elif x <= 2.1e+14:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e+18)
		tmp = x;
	elseif (x <= 2.1e+14)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.25e+18)
		tmp = x;
	elseif (x <= 2.1e+14)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e+18], x, If[LessEqual[x, 2.1e+14], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25e18

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.0%

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

   if -1.25e18 < x < 2.1e14

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 97.8%

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

   3. Taylor expanded in y around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. unsub-neg 50.7%

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

      3. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   if 2.1e14 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

   4. Simplified 83.9%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+14}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 11: 62.8% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+237}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.7e+237) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.7e+237) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.7d+237)) then
        tmp = y * -z
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.7e+237) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.7e+237:
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.7e+237)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.7e+237)
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.7e+237], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.69999999999999993e237

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 80.1%

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

   3. Taylor expanded in y around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unsub-neg 50.3%

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

      3. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in z around inf 50.3%

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

      1. associate-*r* 50.3%

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

      2. neg-mul-1 50.3%

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

   8. Simplified 50.3%

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

   if -5.69999999999999993e237 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 59.4%

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

      1. +-commutative 59.4%

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

   4. Simplified 59.4%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+237}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 12: 61.5% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.96:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 14.5:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -0.96) x (if (<= x 14.5) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.96) {
		tmp = x;
	} else if (x <= 14.5) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.96d0)) then
        tmp = x
    else if (x <= 14.5d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.96) {
		tmp = x;
	} else if (x <= 14.5) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.96:
		tmp = x
	elif x <= 14.5:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.96)
		tmp = x;
	elseif (x <= 14.5)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.96)
		tmp = x;
	elseif (x <= 14.5)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.96], x, If[LessEqual[x, 14.5], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.95999999999999996 or 14.5 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.4%

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

   if -0.95999999999999996 < x < 14.5

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.1%

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

   3. Taylor expanded in y around 0 36.5%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.96:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 14.5:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 62.3% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 57.2%

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

   1. +-commutative 57.2%

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

4. Simplified 57.2%

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

5. Final simplification 57.2%

   \[\leadsto x + 1 \]

Alternative 14: 22.3% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 62.4%

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

3. Taylor expanded in y around 0 20.7%

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

4. Final simplification 20.7%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023290 
(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))))