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

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

Alternatives: 13

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. Final simplification 99.9%

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

Alternative 2: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{-7} \lor \neg \left(x \leq 3.55 \cdot 10^{-9}\right):\\ \;\;\;\;\left(x + 1\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -1.15e-7) (not (<= x 3.55e-9)))
     (- (+ 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 <= -1.15e-7) || !(x <= 3.55e-9)) {
		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 <= (-1.15d-7)) .or. (.not. (x <= 3.55d-9))) 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 <= -1.15e-7) || !(x <= 3.55e-9)) {
		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 <= -1.15e-7) or not (x <= 3.55e-9):
		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 <= -1.15e-7) || !(x <= 3.55e-9))
		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 <= -1.15e-7) || ~((x <= 3.55e-9)))
		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, -1.15e-7], N[Not[LessEqual[x, 3.55e-9]], $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 < -1.14999999999999997e-7 or 3.54999999999999994e-9 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 98.4%

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

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

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

   if -1.14999999999999997e-7 < x < 3.54999999999999994e-9

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-7} \lor \neg \left(x \leq 3.55 \cdot 10^{-9}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+81} \lor \neg \left(z \leq 61000 \lor \neg \left(z \leq 9.5 \cdot 10^{+55}\right) \land z \leq 5.2 \cdot 10^{+95}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.15e+81)
         (not (or (<= z 61000.0) (and (not (<= z 9.5e+55)) (<= z 5.2e+95)))))
   (* (sin y) (- z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.15e+81) || !((z <= 61000.0) || (!(z <= 9.5e+55) && (z <= 5.2e+95)))) {
		tmp = sin(y) * -z;
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.15d+81)) .or. (.not. (z <= 61000.0d0) .or. (.not. (z <= 9.5d+55)) .and. (z <= 5.2d+95))) then
        tmp = sin(y) * -z
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.15e+81) || !((z <= 61000.0) || (!(z <= 9.5e+55) && (z <= 5.2e+95)))) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.15e+81) or not ((z <= 61000.0) or (not (z <= 9.5e+55) and (z <= 5.2e+95))):
		tmp = math.sin(y) * -z
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.15e+81) || !((z <= 61000.0) || (!(z <= 9.5e+55) && (z <= 5.2e+95))))
		tmp = Float64(sin(y) * Float64(-z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.15e+81) || ~(((z <= 61000.0) || (~((z <= 9.5e+55)) && (z <= 5.2e+95)))))
		tmp = sin(y) * -z;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.15e+81], N[Not[Or[LessEqual[z, 61000.0], And[N[Not[LessEqual[z, 9.5e+55]], $MachinePrecision], LessEqual[z, 5.2e+95]]]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1500000000000002e81 or 61000 < z < 9.49999999999999989e55 or 5.19999999999999981e95 < 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 76.3%

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

      1. associate-*r* 76.3%

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

      2. neg-mul-1 76.3%

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

      3. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   if -3.1500000000000002e81 < z < 61000 or 9.49999999999999989e55 < z < 5.19999999999999981e95

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 93.3%

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

      1. +-commutative 93.3%

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

   5. Simplified 93.3%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+81} \lor \neg \left(z \leq 61000 \lor \neg \left(z \leq 9.5 \cdot 10^{+55}\right) \land z \leq 5.2 \cdot 10^{+95}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -700000 \lor \neg \left(z \leq 0.05\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -700000.0) (not (<= z 0.05)))
   (- (+ x 1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -700000.0) || !(z <= 0.05)) {
		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 <= (-700000.0d0)) .or. (.not. (z <= 0.05d0))) 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 <= -700000.0) || !(z <= 0.05)) {
		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 <= -700000.0) or not (z <= 0.05):
		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 <= -700000.0) || !(z <= 0.05))
		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 <= -700000.0) || ~((z <= 0.05)))
		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, -700000.0], N[Not[LessEqual[z, 0.05]], $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 < -7e5 or 0.050000000000000003 < 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 -7e5 < z < 0.050000000000000003

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.6%

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

      1. +-commutative 99.6%

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

   5. Simplified 99.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -700000 \lor \neg \left(z \leq 0.05\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -320000000000 \lor \neg \left(z \leq 2500\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -320000000000.0) (not (<= z 2500.0)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -320000000000.0) || !(z <= 2500.0)) {
		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 <= (-320000000000.0d0)) .or. (.not. (z <= 2500.0d0))) 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 <= -320000000000.0) || !(z <= 2500.0)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -320000000000.0) or not (z <= 2500.0):
		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 <= -320000000000.0) || !(z <= 2500.0))
		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 <= -320000000000.0) || ~((z <= 2500.0)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -320000000000.0], N[Not[LessEqual[z, 2500.0]], $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 < -3.2e11 or 2500 < 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 87.3%

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

   if -3.2e11 < z < 2500

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.9%

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

      1. +-commutative 98.9%

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

   5. Simplified 98.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -320000000000 \lor \neg \left(z \leq 2500\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0016 \lor \neg \left(y \leq 0.58\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0016) (not (<= y 0.58)))
   (+ 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 <= -0.0016) || !(y <= 0.58)) {
		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 <= (-0.0016d0)) .or. (.not. (y <= 0.58d0))) 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 <= -0.0016) || !(y <= 0.58)) {
		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 <= -0.0016) or not (y <= 0.58):
		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 <= -0.0016) || !(y <= 0.58))
		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 <= -0.0016) || ~((y <= 0.58)))
		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, -0.0016], N[Not[LessEqual[y, 0.58]], $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 < -0.00160000000000000008 or 0.57999999999999996 < 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 58.7%

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

      1. +-commutative 58.7%

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

   5. Simplified 58.7%

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

   if -0.00160000000000000008 < y < 0.57999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0016 \lor \neg \left(y \leq 0.58\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.7% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -23000000000 \lor \neg \left(y \leq 18\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -23000000000.0) (not (<= y 18.0)))
   (+ 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 <= -23000000000.0) || !(y <= 18.0)) {
		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 <= (-23000000000.0d0)) .or. (.not. (y <= 18.0d0))) 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 <= -23000000000.0) || !(y <= 18.0)) {
		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 <= -23000000000.0) or not (y <= 18.0):
		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 <= -23000000000.0) || !(y <= 18.0))
		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 <= -23000000000.0) || ~((y <= 18.0)))
		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, -23000000000.0], N[Not[LessEqual[y, 18.0]], $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 < -2.3e10 or 18 < y

   1. Initial program 99.9%

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

      1. add-cube-cbrt 97.9%

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

      2. pow3 98.0%

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

      3. associate--l+ 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in y around 0 40.4%

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

      1. +-commutative 40.4%

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

   7. Simplified 40.4%

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

   if -2.3e10 < y < 18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.8%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -23000000000 \lor \neg \left(y \leq 18\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.6% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -140000000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 160000000:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -140000000000.0)
   (+ x 1.0)
   (if (<= y 160000000.0)
     (+ 1.0 (+ x (* y (- (* y -0.5) z))))
     (* x (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -140000000000.0) {
		tmp = x + 1.0;
	} else if (y <= 160000000.0) {
		tmp = 1.0 + (x + (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 <= (-140000000000.0d0)) then
        tmp = x + 1.0d0
    else if (y <= 160000000.0d0) then
        tmp = 1.0d0 + (x + (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 <= -140000000000.0) {
		tmp = x + 1.0;
	} else if (y <= 160000000.0) {
		tmp = 1.0 + (x + (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 <= -140000000000.0:
		tmp = x + 1.0
	elif y <= 160000000.0:
		tmp = 1.0 + (x + (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 <= -140000000000.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 160000000.0)
		tmp = Float64(1.0 + Float64(x + 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 <= -140000000000.0)
		tmp = x + 1.0;
	elseif (y <= 160000000.0)
		tmp = 1.0 + (x + (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, -140000000000.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 160000000.0], N[(1.0 + N[(x + N[(y * N[(N[(y * -0.5), $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 < -1.4e11

   1. Initial program 99.9%

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

      1. add-cube-cbrt 97.8%

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

      2. pow3 97.9%

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

      3. associate--l+ 97.9%

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

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in y around 0 39.7%

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

      1. +-commutative 39.7%

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

   7. Simplified 39.7%

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

   if -1.4e11 < y < 1.6e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.2%

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

   if 1.6e8 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 90.6%

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

      1. associate--l+ 90.6%

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

      2. div-sub 90.6%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in y around 0 41.2%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -140000000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 160000000:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.5% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+21} \lor \neg \left(y \leq 5800\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e+21) (not (<= y 5800.0))) (+ x 1.0) (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+21) || !(y <= 5800.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.2d+21)) .or. (.not. (y <= 5800.0d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+21) || !(y <= 5800.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.2e+21) or not (y <= 5800.0):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.2e+21) || !(y <= 5800.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.2e+21) || ~((y <= 5800.0)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.2e+21], N[Not[LessEqual[y, 5800.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e21 or 5800 < y

   1. Initial program 99.9%

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

      1. add-cube-cbrt 97.9%

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

      2. pow3 98.0%

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

      3. associate--l+ 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in y around 0 40.3%

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

      1. +-commutative 40.3%

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

   7. Simplified 40.3%

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

   if -7.2e21 < y < 5800

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.5%

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

      1. mul-1-neg 94.5%

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

      2. unsub-neg 94.5%

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

   5. Simplified 94.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+21} \lor \neg \left(y \leq 5800\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.6% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-42} \lor \neg \left(x \leq 0.019\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.7e-42) (not (<= x 0.019))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e-42) || !(x <= 0.019)) {
		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 <= (-3.7d-42)) .or. (.not. (x <= 0.019d0))) 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 <= -3.7e-42) || !(x <= 0.019)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.7e-42) or not (x <= 0.019):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.7e-42) || !(x <= 0.019))
		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 <= -3.7e-42) || ~((x <= 0.019)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.7e-42], N[Not[LessEqual[x, 0.019]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7000000000000002e-42 or 0.0189999999999999995 < x

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.1%

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

      2. pow3 98.1%

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

      3. associate--l+ 98.1%

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

   4. Applied egg-rr 98.1%

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

   5. Taylor expanded in y around 0 79.9%

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

      1. +-commutative 79.9%

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

   7. Simplified 79.9%

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

   if -3.7000000000000002e-42 < x < 0.0189999999999999995

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.0%

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

      1. associate--l+ 81.0%

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

      2. div-sub 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in y around 0 46.8%

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

      1. mul-1-neg 46.8%

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

      2. unsub-neg 46.8%

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

   8. Simplified 46.8%

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

   9. Taylor expanded in x around 0 53.0%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-42} \lor \neg \left(x \leq 0.019\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.2% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+210}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;-y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 4e+210) (+ x 1.0) (- (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 4e+210) {
		tmp = x + 1.0;
	} else {
		tmp = -(y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 4d+210) then
        tmp = x + 1.0d0
    else
        tmp = -(y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 4e+210) {
		tmp = x + 1.0;
	} else {
		tmp = -(y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 4e+210:
		tmp = x + 1.0
	else:
		tmp = -(y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 4e+210)
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(-Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 4e+210)
		tmp = x + 1.0;
	else
		tmp = -(y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 4e+210], N[(x + 1.0), $MachinePrecision], (-N[(y * z), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if z < 3.99999999999999971e210

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.4%

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

      2. pow3 98.5%

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

      3. associate--l+ 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in y around 0 62.3%

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

      1. +-commutative 62.3%

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

   7. Simplified 62.3%

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

   if 3.99999999999999971e210 < 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 73.6%

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

      1. associate--l+ 73.6%

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

      2. div-sub 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in y around 0 30.2%

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

      1. mul-1-neg 30.2%

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

      2. unsub-neg 30.2%

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

   8. Simplified 30.2%

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

   9. Taylor expanded in y around inf 35.7%

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

       1. associate-*r* 35.7%

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

       2. mul-1-neg 35.7%

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

   11. Simplified 35.7%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+210}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;-y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.6% 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. add-cube-cbrt 98.4%

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

   2. pow3 98.5%

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

   3. associate--l+ 98.5%

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

4. Applied egg-rr 98.5%

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

5. Taylor expanded in y around 0 58.5%

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

   1. +-commutative 58.5%

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

7. Simplified 58.5%

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

8. Final simplification 58.5%

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

Alternative 13: 42.9% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 98.4%

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

   2. pow3 98.5%

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

   3. associate--l+ 98.5%

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

4. Applied egg-rr 98.5%

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

5. Taylor expanded in x around inf 37.6%

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

6. Final simplification 37.6%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(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))))