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

Percentage Accurate: 99.9% → 99.9%

Time: 11.9s

Alternatives: 12

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. Final simplification 99.9%

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

Alternative 2: 90.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0105:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+40}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0105)
   (+ x (cos y))
   (if (<= x 5.6e+40) (- (cos y) (* z (sin y))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0105) {
		tmp = x + cos(y);
	} else if (x <= 5.6e+40) {
		tmp = cos(y) - (z * sin(y));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.0105d0)) then
        tmp = x + cos(y)
    else if (x <= 5.6d+40) then
        tmp = cos(y) - (z * sin(y))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0105) {
		tmp = x + Math.cos(y);
	} else if (x <= 5.6e+40) {
		tmp = Math.cos(y) - (z * Math.sin(y));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0105:
		tmp = x + math.cos(y)
	elif x <= 5.6e+40:
		tmp = math.cos(y) - (z * math.sin(y))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0105)
		tmp = Float64(x + cos(y));
	elseif (x <= 5.6e+40)
		tmp = Float64(cos(y) - Float64(z * sin(y)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0105)
		tmp = x + cos(y);
	elseif (x <= 5.6e+40)
		tmp = cos(y) - (z * sin(y));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0105], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+40], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0105000000000000007

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 81.3%

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

      1. +-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -0.0105000000000000007 < x < 5.6000000000000003e40

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 98.1%

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

   if 5.6000000000000003e40 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 88.6%

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

      1. +-commutative 88.6%

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

   4. Simplified 88.6%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0105:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+40}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 3: 82.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+172} \lor \neg \left(z \leq 6.2 \cdot 10^{+101}\right):\\ \;\;\;\;\left(1 + \left(x + -0.5 \cdot \left(y \cdot y\right)\right)\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.45e+172) (not (<= z 6.2e+101)))
   (- (+ 1.0 (+ x (* -0.5 (* y y)))) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.45e+172) || !(z <= 6.2e+101)) {
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (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 <= (-1.45d+172)) .or. (.not. (z <= 6.2d+101))) then
        tmp = (1.0d0 + (x + ((-0.5d0) * (y * y)))) - (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 <= -1.45e+172) || !(z <= 6.2e+101)) {
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.45e+172) or not (z <= 6.2e+101):
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.45e+172) || !(z <= 6.2e+101))
		tmp = Float64(Float64(1.0 + Float64(x + Float64(-0.5 * Float64(y * y)))) - 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 <= -1.45e+172) || ~((z <= 6.2e+101)))
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.45e+172], N[Not[LessEqual[z, 6.2e+101]], $MachinePrecision]], N[(N[(1.0 + N[(x + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e172 or 6.19999999999999998e101 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 72.1%

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

      1. unpow2 72.1%

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

   4. Simplified 72.1%

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

   if -1.45e172 < z < 6.19999999999999998e101

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 88.5%

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

      1. +-commutative 88.5%

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

   4. Simplified 88.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+172} \lor \neg \left(z \leq 6.2 \cdot 10^{+101}\right):\\ \;\;\;\;\left(1 + \left(x + -0.5 \cdot \left(y \cdot y\right)\right)\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 4: 80.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -170000000 \lor \neg \left(y \leq 3600000000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \mathsf{fma}\left(-y, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -170000000.0) (not (<= y 3600000000000.0)))
   (+ x (cos y))
   (+ 1.0 (fma (- y) z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -170000000.0) || !(y <= 3600000000000.0)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + fma(-y, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -170000000.0) || !(y <= 3600000000000.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + fma(Float64(-y), z, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -170000000.0], N[Not[LessEqual[y, 3600000000000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[((-y) * z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e8 or 3.6e12 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 64.9%

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

      1. +-commutative 64.9%

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

   4. Simplified 64.9%

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

   if -1.7e8 < y < 3.6e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-*r* 96.6%

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

      3. fma-def 96.6%

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

      4. mul-1-neg 96.6%

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

   4. Simplified 96.6%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -170000000 \lor \neg \left(y \leq 3600000000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \mathsf{fma}\left(-y, z, x\right)\\ \end{array} \]

Alternative 5: 80.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6600000 \lor \neg \left(y \leq 3600000000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6600000.0) (not (<= y 3600000000000.0)))
   (+ x (cos y))
   (- (+ x 1.0) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6600000.0) || !(y <= 3600000000000.0)) {
		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 <= (-6600000.0d0)) .or. (.not. (y <= 3600000000000.0d0))) 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 <= -6600000.0) || !(y <= 3600000000000.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6600000.0) or not (y <= 3600000000000.0):
		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 <= -6600000.0) || !(y <= 3600000000000.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6600000.0) || ~((y <= 3600000000000.0)))
		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, -6600000.0], N[Not[LessEqual[y, 3600000000000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6e6 or 3.6e12 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 64.9%

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

      1. +-commutative 64.9%

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

   4. Simplified 64.9%

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

   if -6.6e6 < y < 3.6e12

   1. Initial program 100.0%

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

      1. flip3-- 49.4%

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

      2. clear-num 49.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + \cos y\right) \cdot \left(x + \cos y\right) + \left(\left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right) + \left(x + \cos y\right) \cdot \left(z \cdot \sin y\right)\right)}{{\left(x + \cos y\right)}^{3} - {\left(z \cdot \sin y\right)}^{3}}}} \]

      3. clear-num 49.3%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(x + \cos y\right)}^{3} - {\left(z \cdot \sin y\right)}^{3}}{\left(x + \cos y\right) \cdot \left(x + \cos y\right) + \left(\left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right) + \left(x + \cos y\right) \cdot \left(z \cdot \sin y\right)\right)}}}} \]

      4. flip3-- 99.7%

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

      5. +-commutative 99.7%

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

      6. associate--l+ 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in y around 0 96.6%

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

      1. associate-+r+ 96.6%

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

      2. mul-1-neg 96.6%

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

   6. Simplified 96.6%

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

      1. unsub-neg 96.6%

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

      2. *-commutative 96.6%

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

   8. Applied egg-rr 96.6%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6600000 \lor \neg \left(y \leq 3600000000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \]

Alternative 6: 71.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-15}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 0.00095:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e-15) (+ x 1.0) (if (<= x 0.00095) (cos y) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e-15) {
		tmp = x + 1.0;
	} else if (x <= 0.00095) {
		tmp = cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.05d-15)) then
        tmp = x + 1.0d0
    else if (x <= 0.00095d0) then
        tmp = cos(y)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e-15) {
		tmp = x + 1.0;
	} else if (x <= 0.00095) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e-15:
		tmp = x + 1.0
	elif x <= 0.00095:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e-15)
		tmp = Float64(x + 1.0);
	elseif (x <= 0.00095)
		tmp = cos(y);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.05e-15)
		tmp = x + 1.0;
	elseif (x <= 0.00095)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e-15], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 0.00095], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0499999999999999e-15 or 9.49999999999999998e-4 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.2%

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

      1. +-commutative 80.2%

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

   4. Simplified 80.2%

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

   if -1.0499999999999999e-15 < x < 9.49999999999999998e-4

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in z around 0 62.1%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-15}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 0.00095:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 7: 69.7% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+57}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 8000000000000:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.5e+57)
   (+ x 1.0)
   (if (<= y 8000000000000.0) (- (+ x 1.0) (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e+57) {
		tmp = x + 1.0;
	} else if (y <= 8000000000000.0) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.5d+57)) then
        tmp = x + 1.0d0
    else if (y <= 8000000000000.0d0) then
        tmp = (x + 1.0d0) - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e+57) {
		tmp = x + 1.0;
	} else if (y <= 8000000000000.0) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.5e+57:
		tmp = x + 1.0
	elif y <= 8000000000000.0:
		tmp = (x + 1.0) - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.5e+57)
		tmp = Float64(x + 1.0);
	elseif (y <= 8000000000000.0)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.5e+57)
		tmp = x + 1.0;
	elseif (y <= 8000000000000.0)
		tmp = (x + 1.0) - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.5e+57], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 8000000000000.0], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999986e57 or 8e12 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 44.5%

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

      1. +-commutative 44.5%

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

   4. Simplified 44.5%

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

   if -2.49999999999999986e57 < y < 8e12

   1. Initial program 99.9%

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

      1. flip3-- 48.7%

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

      2. clear-num 48.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + \cos y\right) \cdot \left(x + \cos y\right) + \left(\left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right) + \left(x + \cos y\right) \cdot \left(z \cdot \sin y\right)\right)}{{\left(x + \cos y\right)}^{3} - {\left(z \cdot \sin y\right)}^{3}}}} \]

      3. clear-num 48.7%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(x + \cos y\right)}^{3} - {\left(z \cdot \sin y\right)}^{3}}{\left(x + \cos y\right) \cdot \left(x + \cos y\right) + \left(\left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right) + \left(x + \cos y\right) \cdot \left(z \cdot \sin y\right)\right)}}}} \]

      4. flip3-- 99.7%

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

      5. +-commutative 99.7%

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

      6. associate--l+ 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in y around 0 92.4%

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

      1. associate-+r+ 92.4%

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

      2. mul-1-neg 92.4%

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

   6. Simplified 92.4%

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

      1. unsub-neg 92.4%

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

      2. *-commutative 92.4%

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

   8. Applied egg-rr 92.4%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+57}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 8000000000000:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8: 65.6% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0066:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+36}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0066) (+ x 1.0) (if (<= x 1.15e+36) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0066) {
		tmp = x + 1.0;
	} else if (x <= 1.15e+36) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.0066d0)) then
        tmp = x + 1.0d0
    else if (x <= 1.15d+36) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0066) {
		tmp = x + 1.0;
	} else if (x <= 1.15e+36) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0066:
		tmp = x + 1.0
	elif x <= 1.15e+36:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0066)
		tmp = Float64(x + 1.0);
	elseif (x <= 1.15e+36)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0066)
		tmp = x + 1.0;
	elseif (x <= 1.15e+36)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0066], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 1.15e+36], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0066 or 1.14999999999999998e36 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.0%

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

      1. +-commutative 83.0%

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

   4. Simplified 83.0%

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

   if -0.0066 < x < 1.14999999999999998e36

   1. Initial program 99.9%

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

      1. flip3-- 75.7%

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

      2. clear-num 75.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + \cos y\right) \cdot \left(x + \cos y\right) + \left(\left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right) + \left(x + \cos y\right) \cdot \left(z \cdot \sin y\right)\right)}{{\left(x + \cos y\right)}^{3} - {\left(z \cdot \sin y\right)}^{3}}}} \]

      3. clear-num 75.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(x + \cos y\right)}^{3} - {\left(z \cdot \sin y\right)}^{3}}{\left(x + \cos y\right) \cdot \left(x + \cos y\right) + \left(\left(z \cdot \sin y\right) \cdot \left(z \cdot \sin y\right) + \left(x + \cos y\right) \cdot \left(z \cdot \sin y\right)\right)}}}} \]

      4. flip3-- 99.7%

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

      5. +-commutative 99.7%

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

      6. associate--l+ 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in y around 0 52.7%

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

      1. associate-+r+ 52.7%

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

      2. mul-1-neg 52.7%

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

   6. Simplified 52.7%

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

   7. Taylor expanded in x around 0 51.1%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0066:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+36}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9: 61.8% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.3 \cdot 10^{+221}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.3e+221) (+ x 1.0) (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.3e+221) {
		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 <= 1.3d+221) 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 <= 1.3e+221) {
		tmp = x + 1.0;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.3e+221:
		tmp = x + 1.0
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.3e+221)
		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 <= 1.3e+221)
		tmp = x + 1.0;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.3e+221], N[(x + 1.0), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.30000000000000002e221

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 66.2%

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

      1. +-commutative 66.2%

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

   4. Simplified 66.2%

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

   if 1.30000000000000002e221 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. distribute-rgt-neg-out 78.2%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in y around 0 49.3%

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

      1. associate-*r* 49.3%

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

      2. mul-1-neg 49.3%

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

   7. Simplified 49.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.3 \cdot 10^{+221}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 10: 60.7% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0065:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0065) x (if (<= x 1.0) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0065) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.0065d0)) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0065) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0065:
		tmp = x
	elif x <= 1.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0065)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0065)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0065], x, If[LessEqual[x, 1.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0064999999999999997 or 1 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 80.3%

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

   if -0.0064999999999999997 < x < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 98.8%

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

   3. Taylor expanded in y around 0 40.0%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0065:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 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. Taylor expanded in y around 0 63.0%

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

   1. +-commutative 63.0%

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

4. Simplified 63.0%

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

5. Final simplification 63.0%

   \[\leadsto x + 1 \]

Alternative 12: 22.0% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 54.6%

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

3. Taylor expanded in y around 0 19.3%

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

4. Final simplification 19.3%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023297 
(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))))