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

Percentage Accurate: 99.9% → 99.9%

Time: 11.4s

Alternatives: 11

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

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

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(x + Float64(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[(x + N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 90.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-10} \lor \neg \left(x \leq 1.55 \cdot 10^{-9}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e-10) (not (<= x 1.55e-9)))
   (+ x (cos y))
   (- (cos y) (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-10) || !(x <= 1.55e-9)) {
		tmp = x + cos(y);
	} else {
		tmp = cos(y) - (z * sin(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 <= (-5.5d-10)) .or. (.not. (x <= 1.55d-9))) then
        tmp = x + cos(y)
    else
        tmp = cos(y) - (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-10) || !(x <= 1.55e-9)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = Math.cos(y) - (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e-10) or not (x <= 1.55e-9):
		tmp = x + math.cos(y)
	else:
		tmp = math.cos(y) - (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e-10) || !(x <= 1.55e-9))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(cos(y) - Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5e-10) || ~((x <= 1.55e-9)))
		tmp = x + cos(y);
	else
		tmp = cos(y) - (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e-10], N[Not[LessEqual[x, 1.55e-9]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4999999999999996e-10 or 1.55000000000000002e-9 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 83.6%

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

      1. +-commutative 83.6%

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

   7. Simplified 83.6%

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

   if -5.4999999999999996e-10 < x < 1.55000000000000002e-9

   1. Initial program 99.9%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.6%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-10} \lor \neg \left(x \leq 1.55 \cdot 10^{-9}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+147} \lor \neg \left(z \leq 4.6 \cdot 10^{+136}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e+147) (not (<= z 4.6e+136)))
   (* z (- (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e+147) || !(z <= 4.6e+136)) {
		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 <= (-1.3d+147)) .or. (.not. (z <= 4.6d+136))) 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 <= -1.3e+147) || !(z <= 4.6e+136)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e+147) or not (z <= 4.6e+136):
		tmp = z * -math.sin(y)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.3e+147) || !(z <= 4.6e+136))
		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 <= -1.3e+147) || ~((z <= 4.6e+136)))
		tmp = z * -sin(y);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e+147], N[Not[LessEqual[z, 4.6e+136]], $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 < -1.2999999999999999e147 or 4.6e136 < z

   1. Initial program 99.8%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 82.4%

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

      1. associate-*r* 82.4%

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

      2. neg-mul-1 82.4%

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

      3. *-commutative 82.4%

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

   7. Simplified 82.4%

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

   if -1.2999999999999999e147 < z < 4.6e136

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 91.8%

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

      1. +-commutative 91.8%

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

   7. Simplified 91.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+147} \lor \neg \left(z \leq 4.6 \cdot 10^{+136}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -135 \lor \neg \left(y \leq 250000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -135.0) (not (<= y 250000.0)))
   (+ x (cos y))
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -135.0) || !(y <= 250000.0)) {
		tmp = x + cos(y);
	} 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 <= (-135.0d0)) .or. (.not. (y <= 250000.0d0))) then
        tmp = x + cos(y)
    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 <= -135.0) || !(y <= 250000.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -135.0) or not (y <= 250000.0):
		tmp = x + math.cos(y)
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -135.0) || !(y <= 250000.0))
		tmp = Float64(x + cos(y));
	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 <= -135.0) || ~((y <= 250000.0)))
		tmp = x + cos(y);
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -135.0], N[Not[LessEqual[y, 250000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -135 or 2.5e5 < y

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 68.8%

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

      1. +-commutative 68.8%

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

   7. Simplified 68.8%

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

   if -135 < y < 2.5e5

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.3%

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

      1. associate-+r+ 98.3%

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

      2. +-commutative 98.3%

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

      3. associate-+l+ 98.3%

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

      4. mul-1-neg 98.3%

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

      5. unsub-neg 98.3%

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

   7. Simplified 98.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -135 \lor \neg \left(y \leq 250000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.5% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+41} \lor \neg \left(y \leq 3700000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e+41) (not (<= y 3700000.0)))
   (+ x 1.0)
   (+ x (+ 1.0 (* y (- (* y -0.5) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+41) || !(y <= 3700000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 + (y * ((y * -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 <= (-4.2d+41)) .or. (.not. (y <= 3700000.0d0))) then
        tmp = x + 1.0d0
    else
        tmp = x + (1.0d0 + (y * ((y * (-0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+41) || !(y <= 3700000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 + (y * ((y * -0.5) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e+41) or not (y <= 3700000.0):
		tmp = x + 1.0
	else:
		tmp = x + (1.0 + (y * ((y * -0.5) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e+41) || !(y <= 3700000.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(x + Float64(1.0 + Float64(y * Float64(Float64(y * -0.5) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.2e+41) || ~((y <= 3700000.0)))
		tmp = x + 1.0;
	else
		tmp = x + (1.0 + (y * ((y * -0.5) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e+41], N[Not[LessEqual[y, 3700000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(x + N[(1.0 + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999999e41 or 3.7e6 < y

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 47.9%

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

      1. +-commutative 47.9%

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

   7. Simplified 47.9%

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

   if -4.1999999999999999e41 < y < 3.7e6

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-+l+ 95.5%

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

      3. +-commutative 95.5%

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

      4. mul-1-neg 95.5%

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

      5. unsub-neg 95.5%

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

      6. *-commutative 95.5%

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

      7. unpow2 95.5%

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

      8. associate-*l* 95.5%

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

      9. distribute-lft-out-- 95.5%

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

   7. Simplified 95.5%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+41} \lor \neg \left(y \leq 3700000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.6% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3900 \lor \neg \left(y \leq 3900000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3900.0) (not (<= y 3900000.0)))
   (+ x 1.0)
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3900.0) || !(y <= 3900000.0)) {
		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 <= (-3900.0d0)) .or. (.not. (y <= 3900000.0d0))) 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 <= -3900.0) || !(y <= 3900000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3900.0) or not (y <= 3900000.0):
		tmp = x + 1.0
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3900.0) || !(y <= 3900000.0))
		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 <= -3900.0) || ~((y <= 3900000.0)))
		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, -3900.0], N[Not[LessEqual[y, 3900000.0]], $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 < -3900 or 3.9e6 < y

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 46.9%

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

      1. +-commutative 46.9%

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

   7. Simplified 46.9%

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

   if -3900 < y < 3.9e6

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.3%

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

      1. associate-+r+ 98.3%

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

      2. +-commutative 98.3%

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

      3. associate-+l+ 98.3%

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

      4. mul-1-neg 98.3%

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

      5. unsub-neg 98.3%

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

   7. Simplified 98.3%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3900 \lor \neg \left(y \leq 3900000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+204} \lor \neg \left(z \leq 7 \cdot 10^{+165}\right):\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.9e+204) (not (<= z 7e+165))) (- 1.0 (* y z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e+204) || !(z <= 7e+165)) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.9d+204)) .or. (.not. (z <= 7d+165))) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e+204) || !(z <= 7e+165)) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.9e+204) or not (z <= 7e+165):
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.9e+204) || !(z <= 7e+165))
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.9e+204) || ~((z <= 7e+165)))
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.9e+204], N[Not[LessEqual[z, 7e+165]], $MachinePrecision]], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e204 or 6.99999999999999991e165 < z

   1. Initial program 99.8%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

      1. add-cube-cbrt 98.2%

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

      2. pow3 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in x around 0 47.0%

      \[\leadsto {\color{blue}{\left({\left(\cos y - z \cdot \sin y\right)}^{0.3333333333333333}\right)}}^{3} \]
   8. Step-by-step derivation

      1. unpow1/3 91.9%

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

   9. Simplified 91.9%

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

   10. Taylor expanded in y around 0 49.1%

       \[\leadsto \color{blue}{1 + y \cdot \left(-0.6666666666666666 \cdot z + -0.3333333333333333 \cdot z\right)} \]
   11. Step-by-step derivation

       1. distribute-rgt-out 49.4%

          \[\leadsto 1 + y \cdot \color{blue}{\left(z \cdot \left(-0.6666666666666666 + -0.3333333333333333\right)\right)} \]

       2. metadata-eval 49.4%

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

       3. *-commutative 49.4%

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

       4. mul-1-neg 49.4%

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

   12. Simplified 49.4%

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

   if -1.8999999999999999e204 < z < 6.99999999999999991e165

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 75.0%

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

      1. +-commutative 75.0%

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

   7. Simplified 75.0%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+204} \lor \neg \left(z \leq 7 \cdot 10^{+165}\right):\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.8% accurate, 14.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+203} \lor \neg \left(z \leq 6.2 \cdot 10^{+165}\right):\\ \;\;\;\;-y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e+203) (not (<= z 6.2e+165))) (- (* y z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e+203) || !(z <= 6.2e+165)) {
		tmp = -(y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.5d+203)) .or. (.not. (z <= 6.2d+165))) then
        tmp = -(y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e+203) || !(z <= 6.2e+165)) {
		tmp = -(y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e+203) or not (z <= 6.2e+165):
		tmp = -(y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e+203) || !(z <= 6.2e+165))
		tmp = Float64(-Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e+203) || ~((z <= 6.2e+165)))
		tmp = -(y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e+203], N[Not[LessEqual[z, 6.2e+165]], $MachinePrecision]], (-N[(y * z), $MachinePrecision]), N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000003e203 or 6.2000000000000003e165 < z

   1. Initial program 99.8%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 89.5%

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

      1. associate-*r* 89.5%

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

      2. neg-mul-1 89.5%

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

      3. *-commutative 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in y around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. distribute-rgt-neg-in 45.4%

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

   10. Simplified 45.4%

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

   if -4.5000000000000003e203 < z < 6.2000000000000003e165

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 75.0%

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

      1. +-commutative 75.0%

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

   7. Simplified 75.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+203} \lor \neg \left(z \leq 6.2 \cdot 10^{+165}\right):\\ \;\;\;\;-y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.7% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.49:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -0.49) x (if (<= x 1.3) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.49) {
		tmp = x;
	} else if (x <= 1.3) {
		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 <= (-0.49d0)) then
        tmp = x
    else if (x <= 1.3d0) 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 <= -0.49) {
		tmp = x;
	} else if (x <= 1.3) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.49:
		tmp = x
	elif x <= 1.3:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.49)
		tmp = x;
	elseif (x <= 1.3)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.49)
		tmp = x;
	elseif (x <= 1.3)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.49], x, If[LessEqual[x, 1.3], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.48999999999999999 or 1.30000000000000004 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 80.3%

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

   if -0.48999999999999999 < x < 1.30000000000000004

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

      1. add-cube-cbrt 98.7%

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

      2. pow3 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in x around 0 71.7%

      \[\leadsto {\color{blue}{\left({\left(\cos y - z \cdot \sin y\right)}^{0.3333333333333333}\right)}}^{3} \]
   8. Step-by-step derivation

      1. unpow1/3 95.5%

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

   9. Simplified 95.5%

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

   10. Taylor expanded in y around 0 43.3%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.49:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.4% 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. Step-by-step derivation

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 62.8%

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

   1. +-commutative 62.8%

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

7. Simplified 62.8%

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

8. Final simplification 62.8%

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

Alternative 11: 21.3% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

   1. add-cube-cbrt 98.3%

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

   2. pow3 98.3%

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

6. Applied egg-rr 98.3%

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

7. Taylor expanded in x around 0 42.7%

   \[\leadsto {\color{blue}{\left({\left(\cos y - z \cdot \sin y\right)}^{0.3333333333333333}\right)}}^{3} \]
8. Step-by-step derivation

   1. unpow1/3 58.6%

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

9. Simplified 58.6%

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

10. Taylor expanded in y around 0 23.8%

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

11. Final simplification 23.8%

    \[\leadsto 1 \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(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))))