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

Percentage Accurate: 99.9% → 99.9%

Time: 8.6s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{-8} \lor \neg \left(x \leq 5.8 \cdot 10^{-10}\right):\\ \;\;\;\;\left(x + 1\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -3.6e-8) (not (<= x 5.8e-10)))
     (- (+ x 1.0) t_0)
     (- (cos y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if ((x <= -3.6e-8) || !(x <= 5.8e-10)) {
		tmp = (x + 1.0) - t_0;
	} else {
		tmp = cos(y) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * sin(y)
    if ((x <= (-3.6d-8)) .or. (.not. (x <= 5.8d-10))) then
        tmp = (x + 1.0d0) - t_0
    else
        tmp = cos(y) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if ((x <= -3.6e-8) || !(x <= 5.8e-10)) {
		tmp = (x + 1.0) - t_0;
	} else {
		tmp = Math.cos(y) - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if (x <= -3.6e-8) or not (x <= 5.8e-10):
		tmp = (x + 1.0) - t_0
	else:
		tmp = math.cos(y) - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if ((x <= -3.6e-8) || !(x <= 5.8e-10))
		tmp = Float64(Float64(x + 1.0) - t_0);
	else
		tmp = Float64(cos(y) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if ((x <= -3.6e-8) || ~((x <= 5.8e-10)))
		tmp = (x + 1.0) - t_0;
	else
		tmp = cos(y) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -3.6e-8], N[Not[LessEqual[x, 5.8e-10]], $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 < -3.59999999999999981e-8 or 5.79999999999999962e-10 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

   if -3.59999999999999981e-8 < x < 5.79999999999999962e-10

   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 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-8} \lor \neg \left(x \leq 5.8 \cdot 10^{-10}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.21 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.21) (not (<= z 1.0)))
   (- (+ x 1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.21) || !(z <= 1.0)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.21d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.21) || !(z <= 1.0)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.21) or not (z <= 1.0):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.21) || !(z <= 1.0))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.21) || ~((z <= 1.0)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.21], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.209999999999999992 or 1 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 98.7%

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

      1. +-commutative 98.7%

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

   5. Simplified 98.7%

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

   if -0.209999999999999992 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.21 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+29} \lor \neg \left(z \leq 3.4 \cdot 10^{+70}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e+29) (not (<= z 3.4e+70)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+29) || !(z <= 3.4e+70)) {
		tmp = x - (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 <= (-2.5d+29)) .or. (.not. (z <= 3.4d+70))) then
        tmp = x - (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 <= -2.5e+29) || !(z <= 3.4e+70)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e+29) or not (z <= 3.4e+70):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e+29) || !(z <= 3.4e+70))
		tmp = Float64(x - 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 <= -2.5e+29) || ~((z <= 3.4e+70)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e+29], N[Not[LessEqual[z, 3.4e+70]], $MachinePrecision]], N[(x - 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 < -2.5e29 or 3.4000000000000001e70 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 92.0%

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

   if -2.5e29 < z < 3.4000000000000001e70

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.0%

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

      1. +-commutative 97.0%

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

   5. Simplified 97.0%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+29} \lor \neg \left(z \leq 3.4 \cdot 10^{+70}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+99} \lor \neg \left(z \leq 1.32 \cdot 10^{+66}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.1e+99) (not (<= z 1.32e+66)))
   (- 1.0 (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e+99) || !(z <= 1.32e+66)) {
		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 <= (-4.1d+99)) .or. (.not. (z <= 1.32d+66))) 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 <= -4.1e+99) || !(z <= 1.32e+66)) {
		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 <= -4.1e+99) or not (z <= 1.32e+66):
		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 <= -4.1e+99) || !(z <= 1.32e+66))
		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 <= -4.1e+99) || ~((z <= 1.32e+66)))
		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, -4.1e+99], N[Not[LessEqual[z, 1.32e+66]], $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 < -4.09999999999999979e99 or 1.32000000000000009e66 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

      1. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 75.4%

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

   if -4.09999999999999979e99 < z < 1.32000000000000009e66

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.7%

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

      1. +-commutative 94.7%

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

   5. Simplified 94.7%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+99} \lor \neg \left(z \leq 1.32 \cdot 10^{+66}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+100} \lor \neg \left(z \leq 6.6 \cdot 10^{+78}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05e+100) (not (<= z 6.6e+78)))
   (* z (- (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e+100) || !(z <= 6.6e+78)) {
		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 <= (-1.05d+100)) .or. (.not. (z <= 6.6d+78))) 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 <= -1.05e+100) || !(z <= 6.6e+78)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05e+100) or not (z <= 6.6e+78):
		tmp = z * -math.sin(y)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05e+100) || !(z <= 6.6e+78))
		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 <= -1.05e+100) || ~((z <= 6.6e+78)))
		tmp = z * -sin(y);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05e+100], N[Not[LessEqual[z, 6.6e+78]], $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 < -1.0499999999999999e100 or 6.6e78 < 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 68.2%

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

      1. associate-*r* 68.2%

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

      2. neg-mul-1 68.2%

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

      3. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   if -1.0499999999999999e100 < z < 6.6e78

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.7%

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

      1. +-commutative 94.7%

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

   5. Simplified 94.7%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+100} \lor \neg \left(z \leq 6.6 \cdot 10^{+78}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+29} \lor \neg \left(y \leq 750\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.6e+29) (not (<= y 750.0)))
   (+ x (cos y))
   (+ 1.0 (+ x (* y (- (* y (- (* 0.16666666666666666 (* y z)) 0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.6e+29) || !(y <= 750.0)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.6d+29)) .or. (.not. (y <= 750.0d0))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x + (y * ((y * ((0.16666666666666666d0 * (y * z)) - 0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.6e+29) || !(y <= 750.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.6e+29) or not (y <= 750.0):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.6e+29) || !(y <= 750.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(0.16666666666666666 * Float64(y * z)) - 0.5)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.6e+29) || ~((y <= 750.0)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.6e+29], N[Not[LessEqual[y, 750.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999993e29 or 750 < 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 61.9%

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

      1. +-commutative 61.9%

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

   5. Simplified 61.9%

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

   if -1.59999999999999993e29 < y < 750

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+29} \lor \neg \left(y \leq 750\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-18} \lor \neg \left(x \leq 8 \cdot 10^{-10}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.32e-18) (not (<= x 8e-10))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.32e-18) || !(x <= 8e-10)) {
		tmp = x + 1.0;
	} else {
		tmp = cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.32d-18)) .or. (.not. (x <= 8d-10))) then
        tmp = x + 1.0d0
    else
        tmp = cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.32e-18) || !(x <= 8e-10)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.32e-18) or not (x <= 8e-10):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.32e-18) || !(x <= 8e-10))
		tmp = Float64(x + 1.0);
	else
		tmp = cos(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.32e-18) || ~((x <= 8e-10)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.32e-18], N[Not[LessEqual[x, 8e-10]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3199999999999999e-18 or 8.00000000000000029e-10 < x

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. add-cube-cbrt 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. fma-define 99.7%

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

      6. pow2 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right)} \]

   5. Taylor expanded in y around 0 84.5%

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

      1. +-commutative 84.5%

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

   7. Simplified 84.5%

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

   if -1.3199999999999999e-18 < x < 8.00000000000000029e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 59.5%

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

      1. +-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in x around 0 59.4%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-18} \lor \neg \left(x \leq 8 \cdot 10^{-10}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.6% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+30} \lor \neg \left(y \leq 350000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.35e+30) (not (<= y 350000.0)))
   (+ x 1.0)
   (+ 1.0 (+ x (* y (- (* y (- (* 0.16666666666666666 (* y z)) 0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.35e+30) || !(y <= 350000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.35d+30)) .or. (.not. (y <= 350000.0d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x + (y * ((y * ((0.16666666666666666d0 * (y * z)) - 0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.35e+30) || !(y <= 350000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.35e+30) or not (y <= 350000.0):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.35e+30) || !(y <= 350000.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(0.16666666666666666 * Float64(y * z)) - 0.5)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.35e+30) || ~((y <= 350000.0)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.35e+30], N[Not[LessEqual[y, 350000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.34999999999999995e30 or 3.5e5 < y

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. add-cube-cbrt 99.3%

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

      4. distribute-rgt-neg-in 99.3%

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

      5. fma-define 99.3%

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

      6. pow2 99.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right) \]

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right)} \]

   5. Taylor expanded in y around 0 37.0%

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

      1. +-commutative 37.0%

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

   7. Simplified 37.0%

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

   if -2.34999999999999995e30 < y < 3.5e5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+30} \lor \neg \left(y \leq 350000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.5% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+74} \lor \neg \left(y \leq 4.4 \cdot 10^{+15}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.5e+74) (not (<= y 4.4e+15)))
   (+ x 1.0)
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.5e+74) || !(y <= 4.4e+15)) {
		tmp = x + 1.0;
	} 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 <= (-3.5d+74)) .or. (.not. (y <= 4.4d+15))) then
        tmp = x + 1.0d0
    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 <= -3.5e+74) || !(y <= 4.4e+15)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.5e+74) or not (y <= 4.4e+15):
		tmp = x + 1.0
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.5e+74) || !(y <= 4.4e+15))
		tmp = Float64(x + 1.0);
	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 <= -3.5e+74) || ~((y <= 4.4e+15)))
		tmp = x + 1.0;
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.5e+74], N[Not[LessEqual[y, 4.4e+15]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.50000000000000014e74 or 4.4e15 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. add-cube-cbrt 99.3%

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

      4. distribute-rgt-neg-in 99.3%

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

      5. fma-define 99.3%

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

      6. pow2 99.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right) \]

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right)} \]

   5. Taylor expanded in y around 0 36.6%

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

      1. +-commutative 36.6%

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

   7. Simplified 36.6%

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

   if -3.50000000000000014e74 < y < 4.4e15

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.9%

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

      1. associate-+r+ 91.9%

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

      2. +-commutative 91.9%

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

      3. associate-+l+ 91.9%

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

      4. mul-1-neg 91.9%

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

      5. unsub-neg 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+74} \lor \neg \left(y \leq 4.4 \cdot 10^{+15}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.9% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-12} \lor \neg \left(x \leq 8 \cdot 10^{-20}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.65e-12) (not (<= x 8e-20))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e-12) || !(x <= 8e-20)) {
		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 <= (-1.65d-12)) .or. (.not. (x <= 8d-20))) 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 <= -1.65e-12) || !(x <= 8e-20)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.65e-12) or not (x <= 8e-20):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.65e-12) || !(x <= 8e-20))
		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 <= -1.65e-12) || ~((x <= 8e-20)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.65e-12], N[Not[LessEqual[x, 8e-20]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e-12 or 7.99999999999999956e-20 < x

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. add-cube-cbrt 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. fma-define 99.7%

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

      6. pow2 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right)} \]

   5. Taylor expanded in y around 0 84.8%

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

      1. +-commutative 84.8%

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

   7. Simplified 84.8%

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

   if -1.65e-12 < x < 7.99999999999999956e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 49.5%

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

      1. associate-+r+ 49.5%

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

      2. +-commutative 49.5%

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

      3. associate-+l+ 49.5%

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

      4. mul-1-neg 49.5%

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

      5. unsub-neg 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in x around 0 49.5%

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

      1. *-commutative 49.5%

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

   8. Simplified 49.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-12} \lor \neg \left(x \leq 8 \cdot 10^{-20}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.0% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.92:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.8:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -0.92) x (if (<= x 0.8) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.92) {
		tmp = x;
	} else if (x <= 0.8) {
		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 <= (-0.92d0)) then
        tmp = x
    else if (x <= 0.8d0) 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 <= -0.92) {
		tmp = x;
	} else if (x <= 0.8) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.92:
		tmp = x
	elif x <= 0.8:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.92)
		tmp = x;
	elseif (x <= 0.8)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.92)
		tmp = x;
	elseif (x <= 0.8)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.92], x, If[LessEqual[x, 0.8], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.92000000000000004 or 0.80000000000000004 < x

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. add-cube-cbrt 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. fma-define 99.7%

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

      6. pow2 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right)} \]

   5. Taylor expanded in x around inf 83.3%

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

   if -0.92000000000000004 < x < 0.80000000000000004

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 59.3%

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

      1. +-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in x around inf 59.1%

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

   7. Taylor expanded in x around 0 58.5%

      \[\leadsto x \cdot \color{blue}{\frac{\cos y}{x}} \]

   8. Taylor expanded in y around 0 36.5%

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

Alternative 13: 62.6% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8 \cdot 10^{+169}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 8e+169) (+ x 1.0) (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 8e+169) {
		tmp = x + 1.0;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 8d+169) then
        tmp = x + 1.0d0
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 8e+169) {
		tmp = x + 1.0;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 8e+169:
		tmp = x + 1.0
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 8e+169)
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 8e+169)
		tmp = x + 1.0;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 8e+169], N[(x + 1.0), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.99999999999999947e169

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. add-cube-cbrt 99.5%

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

      4. distribute-rgt-neg-in 99.5%

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

      5. fma-define 99.5%

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

      6. pow2 99.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right) \]

   4. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right)} \]

   5. Taylor expanded in y around 0 63.1%

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

      1. +-commutative 63.1%

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

   7. Simplified 63.1%

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

   if 7.99999999999999947e169 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 36.9%

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

      1. associate-+r+ 36.9%

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

      2. +-commutative 36.9%

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

      3. associate-+l+ 36.9%

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

      4. mul-1-neg 36.9%

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

      5. unsub-neg 36.9%

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

   5. Simplified 36.9%

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

   6. Taylor expanded in y around inf 34.2%

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

      1. associate-*r* 34.2%

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

      2. neg-mul-1 34.2%

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

      3. *-commutative 34.2%

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

   8. Simplified 34.2%

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

Alternative 14: 62.8% 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. Step-by-step derivation

   1. sub-neg 99.9%

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

   2. +-commutative 99.9%

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

   3. add-cube-cbrt 99.4%

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

   4. distribute-rgt-neg-in 99.4%

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

   5. fma-define 99.4%

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

   6. pow2 99.4%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right) \]

4. Applied egg-rr 99.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right)} \]

5. Taylor expanded in y around 0 58.9%

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

   1. +-commutative 58.9%

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

7. Simplified 58.9%

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

Alternative 15: 20.8% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around 0 71.3%

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

   1. +-commutative 71.3%

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

5. Simplified 71.3%

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

6. Taylor expanded in x around inf 71.2%

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

7. Taylor expanded in x around 0 33.7%

   \[\leadsto x \cdot \color{blue}{\frac{\cos y}{x}} \]

8. Taylor expanded in y around 0 21.7%

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

Reproduce

herbie shell --seed 2024116 
(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))))