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

Percentage Accurate: 99.9% → 99.9%

Time: 9.6s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -4 \cdot 10^{-6} \lor \neg \left(x \leq 4.8 \cdot 10^{-33}\right):\\ \;\;\;\;\left(x + 1\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -4e-6) (not (<= x 4.8e-33)))
     (- (+ x 1.0) t_0)
     (- (cos y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if ((x <= -4e-6) || !(x <= 4.8e-33)) {
		tmp = (x + 1.0) - t_0;
	} else {
		tmp = cos(y) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * sin(y)
    if ((x <= (-4d-6)) .or. (.not. (x <= 4.8d-33))) then
        tmp = (x + 1.0d0) - t_0
    else
        tmp = cos(y) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if ((x <= -4e-6) || !(x <= 4.8e-33)) {
		tmp = (x + 1.0) - t_0;
	} else {
		tmp = Math.cos(y) - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if (x <= -4e-6) or not (x <= 4.8e-33):
		tmp = (x + 1.0) - t_0
	else:
		tmp = math.cos(y) - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if ((x <= -4e-6) || !(x <= 4.8e-33))
		tmp = Float64(Float64(x + 1.0) - t_0);
	else
		tmp = Float64(cos(y) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if ((x <= -4e-6) || ~((x <= 4.8e-33)))
		tmp = (x + 1.0) - t_0;
	else
		tmp = cos(y) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -4e-6], N[Not[LessEqual[x, 4.8e-33]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999982e-6 or 4.8e-33 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.1%

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

   if -3.99999999999999982e-6 < x < 4.8e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-6} \lor \neg \left(x \leq 4.8 \cdot 10^{-33}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -115000000 \lor \neg \left(z \leq 2.4 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -115000000.0) (not (<= z 2.4e-6)))
   (- (+ x 1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -115000000.0) || !(z <= 2.4e-6)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-115000000.0d0)) .or. (.not. (z <= 2.4d-6))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -115000000.0) || !(z <= 2.4e-6)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -115000000.0) or not (z <= 2.4e-6):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -115000000.0) || !(z <= 2.4e-6))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -115000000.0) || ~((z <= 2.4e-6)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -115000000.0], N[Not[LessEqual[z, 2.4e-6]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e8 or 2.3999999999999999e-6 < 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 98.7%

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

   if -1.15e8 < z < 2.3999999999999999e-6

   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%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -115000000 \lor \neg \left(z \leq 2.4 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+77} \lor \neg \left(z \leq 2.7 \cdot 10^{+128}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.4e+77) (not (<= z 2.7e+128)))
   (- 1.0 (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.4e+77) || !(z <= 2.7e+128)) {
		tmp = 1.0 - (z * sin(y));
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8.4d+77)) .or. (.not. (z <= 2.7d+128))) then
        tmp = 1.0d0 - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.4e+77) || !(z <= 2.7e+128)) {
		tmp = 1.0 - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.4e+77) or not (z <= 2.7e+128):
		tmp = 1.0 - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.4e+77) || !(z <= 2.7e+128))
		tmp = Float64(1.0 - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.4e+77) || ~((z <= 2.7e+128)))
		tmp = 1.0 - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.4e+77], N[Not[LessEqual[z, 2.7e+128]], $MachinePrecision]], N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.3999999999999995e77 or 2.70000000000000001e128 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 72.2%

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

   4. Taylor expanded in y around 0 72.2%

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

   if -8.3999999999999995e77 < z < 2.70000000000000001e128

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 91.7%

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

      1. +-commutative 91.7%

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

   5. Simplified 91.7%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+77} \lor \neg \left(z \leq 2.7 \cdot 10^{+128}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+160} \lor \neg \left(z \leq 1.02 \cdot 10^{+130}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.6e+160) (not (<= z 1.02e+130)))
   (* z (- (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e+160) || !(z <= 1.02e+130)) {
		tmp = z * -sin(y);
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.6d+160)) .or. (.not. (z <= 1.02d+130))) then
        tmp = z * -sin(y)
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e+160) || !(z <= 1.02e+130)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.6e+160) or not (z <= 1.02e+130):
		tmp = z * -math.sin(y)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.6e+160) || !(z <= 1.02e+130))
		tmp = Float64(z * Float64(-sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.6e+160) || ~((z <= 1.02e+130)))
		tmp = z * -sin(y);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.6e+160], N[Not[LessEqual[z, 1.02e+130]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.60000000000000021e160 or 1.01999999999999999e130 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. distribute-rgt-neg-out 70.5%

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

   5. Simplified 70.5%

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

   if -3.60000000000000021e160 < z < 1.01999999999999999e130

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.6%

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

      1. +-commutative 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+160} \lor \neg \left(z \leq 1.02 \cdot 10^{+130}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-6} \lor \neg \left(y \leq 1.32 \cdot 10^{+14}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e-6) (not (<= y 1.32e+14)))
   (+ x (cos y))
   (+ 1.0 (+ x (* y (- (* y (* (* y z) 0.16666666666666666)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e-6) || !(y <= 1.32e+14)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * ((y * z) * 0.16666666666666666)) - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.2d-6)) .or. (.not. (y <= 1.32d+14))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x + (y * ((y * ((y * z) * 0.16666666666666666d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e-6) || !(y <= 1.32e+14)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * ((y * z) * 0.16666666666666666)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e-6) or not (y <= 1.32e+14):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x + (y * ((y * ((y * z) * 0.16666666666666666)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e-6) || !(y <= 1.32e+14))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(y * z) * 0.16666666666666666)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.2e-6) || ~((y <= 1.32e+14)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x + (y * ((y * ((y * z) * 0.16666666666666666)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e-6], N[Not[LessEqual[y, 1.32e+14]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(y * z), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999999e-6 or 1.32e14 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 68.2%

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

      1. +-commutative 68.2%

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

   5. Simplified 68.2%

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

   if -6.1999999999999999e-6 < y < 1.32e14

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.1%

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

   4. Taylor expanded in y around inf 97.1%

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

      1. *-commutative 97.1%

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

   6. Simplified 97.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-6} \lor \neg \left(y \leq 1.32 \cdot 10^{+14}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.8% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8200000000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8200000000000.0)
   (+ x 1.0)
   (if (<= y 1.32e+14)
     (+ 1.0 (+ x (* y (- (* y (- (* (* y z) 0.16666666666666666) 0.5)) z))))
     (* x (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8200000000000.0) {
		tmp = x + 1.0;
	} else if (y <= 1.32e+14) {
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - 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 (y <= (-8200000000000.0d0)) then
        tmp = x + 1.0d0
    else if (y <= 1.32d+14) then
        tmp = 1.0d0 + (x + (y * ((y * (((y * z) * 0.16666666666666666d0) - 0.5d0)) - 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 (y <= -8200000000000.0) {
		tmp = x + 1.0;
	} else if (y <= 1.32e+14) {
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)));
	} else {
		tmp = x * (1.0 + (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8200000000000.0:
		tmp = x + 1.0
	elif y <= 1.32e+14:
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)))
	else:
		tmp = x * (1.0 + (1.0 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8200000000000.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.32e+14)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(Float64(y * z) * 0.16666666666666666) - 0.5)) - 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 (y <= -8200000000000.0)
		tmp = x + 1.0;
	elseif (y <= 1.32e+14)
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)));
	else
		tmp = x * (1.0 + (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8200000000000.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.32e+14], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(N[(y * z), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.2e12

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 48.4%

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

      1. +-commutative 48.4%

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

   5. Simplified 48.4%

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

   if -8.2e12 < y < 1.32e14

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.5%

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

   if 1.32e14 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.5%

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

      1. associate--l+ 83.5%

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

      2. div-sub 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in y around 0 47.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8200000000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.2% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+73}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 12000000:\\ \;\;\;\;\left(x + 1\right) + y \cdot \left(y \cdot -0.5 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.1e+73)
   (+ x 1.0)
   (if (<= y 12000000.0)
     (+ (+ x 1.0) (* y (- (* y -0.5) z)))
     (* x (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.1e+73) {
		tmp = x + 1.0;
	} else if (y <= 12000000.0) {
		tmp = (x + 1.0) + (y * ((y * -0.5) - 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 (y <= (-1.1d+73)) then
        tmp = x + 1.0d0
    else if (y <= 12000000.0d0) then
        tmp = (x + 1.0d0) + (y * ((y * (-0.5d0)) - 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 (y <= -1.1e+73) {
		tmp = x + 1.0;
	} else if (y <= 12000000.0) {
		tmp = (x + 1.0) + (y * ((y * -0.5) - z));
	} else {
		tmp = x * (1.0 + (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.1e+73:
		tmp = x + 1.0
	elif y <= 12000000.0:
		tmp = (x + 1.0) + (y * ((y * -0.5) - z))
	else:
		tmp = x * (1.0 + (1.0 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.1e+73)
		tmp = Float64(x + 1.0);
	elseif (y <= 12000000.0)
		tmp = Float64(Float64(x + 1.0) + Float64(y * Float64(Float64(y * -0.5) - 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 (y <= -1.1e+73)
		tmp = x + 1.0;
	elseif (y <= 12000000.0)
		tmp = (x + 1.0) + (y * ((y * -0.5) - z));
	else
		tmp = x * (1.0 + (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.1e+73], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 12000000.0], N[(N[(x + 1.0), $MachinePrecision] + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e73

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 52.9%

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

      1. +-commutative 52.9%

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

   5. Simplified 52.9%

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

   if -1.1e73 < y < 1.2e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.3%

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

      1. associate-+r+ 91.3%

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

      2. +-commutative 91.3%

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

      3. *-commutative 91.3%

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

   5. Simplified 91.3%

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

   if 1.2e7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.7%

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

      1. associate--l+ 82.7%

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

      2. div-sub 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around 0 45.0%

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

Alternative 9: 69.4% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+105}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 26000000:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.05e+105)
   (+ x 1.0)
   (if (<= y 26000000.0) (+ 1.0 (- x (* y z))) (* x (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.05e+105) {
		tmp = x + 1.0;
	} else if (y <= 26000000.0) {
		tmp = 1.0 + (x - (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 (y <= (-2.05d+105)) then
        tmp = x + 1.0d0
    else if (y <= 26000000.0d0) then
        tmp = 1.0d0 + (x - (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 (y <= -2.05e+105) {
		tmp = x + 1.0;
	} else if (y <= 26000000.0) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = x * (1.0 + (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.05e+105:
		tmp = x + 1.0
	elif y <= 26000000.0:
		tmp = 1.0 + (x - (y * z))
	else:
		tmp = x * (1.0 + (1.0 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.05e+105)
		tmp = Float64(x + 1.0);
	elseif (y <= 26000000.0)
		tmp = Float64(1.0 + Float64(x - 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 (y <= -2.05e+105)
		tmp = x + 1.0;
	elseif (y <= 26000000.0)
		tmp = 1.0 + (x - (y * z));
	else
		tmp = x * (1.0 + (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.05e+105], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 26000000.0], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0500000000000001e105

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 54.9%

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

      1. +-commutative 54.9%

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

   5. Simplified 54.9%

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

   if -2.0500000000000001e105 < y < 2.6e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.5%

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

      1. mul-1-neg 88.5%

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

      2. unsub-neg 88.5%

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

   5. Simplified 88.5%

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

   if 2.6e7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.7%

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

      1. associate--l+ 82.7%

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

      2. div-sub 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around 0 45.0%

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

Alternative 10: 66.2% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -550000000000 \lor \neg \left(x \leq 2600000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -550000000000.0) (not (<= x 2600000.0)))
   (+ x 1.0)
   (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -550000000000.0) || !(x <= 2600000.0)) {
		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 <= (-550000000000.0d0)) .or. (.not. (x <= 2600000.0d0))) 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 <= -550000000000.0) || !(x <= 2600000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -550000000000.0) or not (x <= 2600000.0):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -550000000000.0) || !(x <= 2600000.0))
		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 <= -550000000000.0) || ~((x <= 2600000.0)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -550000000000.0], N[Not[LessEqual[x, 2600000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e11 or 2.6e6 < 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 87.8%

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

      1. +-commutative 87.8%

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

   5. Simplified 87.8%

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

   if -5.5e11 < x < 2.6e6

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.1%

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

   4. Taylor expanded in y around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

   6. Simplified 52.3%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -550000000000 \lor \neg \left(x \leq 2600000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.1% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -550000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2600000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -550000000000.0) x (if (<= x 2600000.0) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -550000000000.0) {
		tmp = x;
	} else if (x <= 2600000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-550000000000.0d0)) then
        tmp = x
    else if (x <= 2600000.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -550000000000.0) {
		tmp = x;
	} else if (x <= 2600000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -550000000000.0:
		tmp = x
	elif x <= 2600000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -550000000000.0)
		tmp = x;
	elseif (x <= 2600000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -550000000000.0)
		tmp = x;
	elseif (x <= 2600000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -550000000000.0], x, If[LessEqual[x, 2600000.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e11 or 2.6e6 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.5%

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

   if -5.5e11 < x < 2.6e6

   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 42.3%

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

      1. +-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in x around 0 41.4%

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

Alternative 12: 62.1% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+259}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.4e+259) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4e+259) {
		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 <= (-1.4d+259)) 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 <= -1.4e+259) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.4e+259:
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.4e+259)
		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 <= -1.4e+259)
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.4e+259], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e259

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-rgt-neg-out 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 49.0%

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

      1. mul-1-neg 49.0%

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

   8. Simplified 49.0%

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

   if -1.4e259 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.3%

      \[\leadsto \color{blue}{1 + x} \]
   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 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+259}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.3% 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 100.0%

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

3. Taylor expanded in y around 0 64.0%

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

   1. +-commutative 64.0%

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

5. Simplified 64.0%

   \[\leadsto \color{blue}{x + 1} \]
6. Add Preprocessing

Alternative 14: 21.6% 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 100.0%

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

3. Taylor expanded in z around -inf 86.3%

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

   1. mul-1-neg 86.3%

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

   2. distribute-rgt-neg-in 86.3%

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

   3. distribute-lft-out-- 86.3%

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

   4. mul-1-neg 86.3%

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

   5. remove-double-neg 86.3%

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

   6. +-commutative 86.3%

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

5. Simplified 86.3%

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

6. Taylor expanded in y around 0 50.5%

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

   1. +-commutative 50.5%

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

8. Simplified 50.5%

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

9. Taylor expanded in x around 0 23.1%

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

Reproduce

herbie shell --seed 2024139 
(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))))