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

Percentage Accurate: 99.9% → 99.9%

Time: 8.0s

Alternatives: 8

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: 90.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-16}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-13}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.8e-16)
   (+ x 1.0)
   (if (<= x 3.4e-13) (- (cos y) (* z (sin y))) (+ x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.8e-16) {
		tmp = x + 1.0;
	} else if (x <= 3.4e-13) {
		tmp = cos(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 (x <= (-7.8d-16)) then
        tmp = x + 1.0d0
    else if (x <= 3.4d-13) then
        tmp = cos(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 (x <= -7.8e-16) {
		tmp = x + 1.0;
	} else if (x <= 3.4e-13) {
		tmp = Math.cos(y) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.8e-16:
		tmp = x + 1.0
	elif x <= 3.4e-13:
		tmp = math.cos(y) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.8e-16)
		tmp = Float64(x + 1.0);
	elseif (x <= 3.4e-13)
		tmp = Float64(cos(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 (x <= -7.8e-16)
		tmp = x + 1.0;
	elseif (x <= 3.4e-13)
		tmp = cos(y) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.8e-16], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 3.4e-13], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.79999999999999954e-16

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 83.8%

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

   if -7.79999999999999954e-16 < x < 3.40000000000000015e-13

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. neg-mul-1 99.9%

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

      3. unsub-neg 99.9%

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

   6. Simplified 99.9%

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

   if 3.40000000000000015e-13 < x

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 79.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-16}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-13}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 3: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+140} \lor \neg \left(z \leq 1.6 \cdot 10^{+212}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e+140) (not (<= z 1.6e+212)))
   (* (sin y) (- z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e+140) || !(z <= 1.6e+212)) {
		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 <= (-1.1d+140)) .or. (.not. (z <= 1.6d+212))) 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 <= -1.1e+140) || !(z <= 1.6e+212)) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1e+140) or not (z <= 1.6e+212):
		tmp = math.sin(y) * -z
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1e+140) || !(z <= 1.6e+212))
		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 <= -1.1e+140) || ~((z <= 1.6e+212)))
		tmp = sin(y) * -z;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e+140], N[Not[LessEqual[z, 1.6e+212]], $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 < -1.0999999999999999e140 or 1.5999999999999999e212 < z

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 75.4%

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

      1. neg-mul-1 75.4%

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

      2. distribute-rgt-neg-in 75.4%

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

   6. Simplified 75.4%

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

   if -1.0999999999999999e140 < z < 1.5999999999999999e212

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 87.3%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+140} \lor \neg \left(z \leq 1.6 \cdot 10^{+212}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 4: 80.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+19} \lor \neg \left(y \leq 50000000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e+19) (not (<= y 50000000000.0)))
   (+ x (cos y))
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+19) || !(y <= 50000000000.0)) {
		tmp = x + cos(y);
	} 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 <= (-5.2d+19)) .or. (.not. (y <= 50000000000.0d0))) then
        tmp = x + cos(y)
    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 <= -5.2e+19) || !(y <= 50000000000.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+19) or not (y <= 50000000000.0):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+19) || !(y <= 50000000000.0))
		tmp = Float64(x + cos(y));
	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 <= -5.2e+19) || ~((y <= 50000000000.0)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+19], N[Not[LessEqual[y, 50000000000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e19 or 5e10 < y

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 68.0%

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

   if -5.2e19 < y < 5e10

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 95.6%

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

      1. +-commutative 95.6%

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

      2. mul-1-neg 95.6%

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

      3. unsub-neg 95.6%

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

   6. Simplified 95.6%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+19} \lor \neg \left(y \leq 50000000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]

Alternative 5: 69.6% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+33}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+69}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.9e+33)
   (+ x 1.0)
   (if (<= y 1.55e+69) (+ 1.0 (- x (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e+33) {
		tmp = x + 1.0;
	} else if (y <= 1.55e+69) {
		tmp = 1.0 + (x - (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 <= (-3.9d+33)) then
        tmp = x + 1.0d0
    else if (y <= 1.55d+69) then
        tmp = 1.0d0 + (x - (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 <= -3.9e+33) {
		tmp = x + 1.0;
	} else if (y <= 1.55e+69) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.9e+33:
		tmp = x + 1.0
	elif y <= 1.55e+69:
		tmp = 1.0 + (x - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.9e+33)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.55e+69)
		tmp = Float64(1.0 + Float64(x - 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 <= -3.9e+33)
		tmp = x + 1.0;
	elseif (y <= 1.55e+69)
		tmp = 1.0 + (x - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.9e+33], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.55e+69], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9000000000000002e33 or 1.5499999999999999e69 < y

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 44.6%

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

   if -3.9000000000000002e33 < y < 1.5499999999999999e69

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 90.8%

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

      1. +-commutative 90.8%

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

      2. mul-1-neg 90.8%

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

      3. unsub-neg 90.8%

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

   6. Simplified 90.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+33}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+69}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 6: 62.0% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+214}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 2.5e+214) (+ x 1.0) (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.5e+214) {
		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 <= 2.5d+214) 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 <= 2.5e+214) {
		tmp = x + 1.0;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.5e+214:
		tmp = x + 1.0
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.5e+214)
		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 <= 2.5e+214)
		tmp = x + 1.0;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.5e+214], N[(x + 1.0), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.49999999999999977e214

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 67.3%

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

   if 2.49999999999999977e214 < z

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. neg-mul-1 86.8%

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

      2. distribute-rgt-neg-in 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in y around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. *-commutative 43.6%

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

      3. distribute-rgt-neg-in 43.6%

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

   9. Simplified 43.6%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+214}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 7: 61.2% 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. cancel-sign-sub-inv 99.9%

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

   2. +-commutative 99.9%

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

   3. *-commutative 99.9%

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

   4. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 63.8%

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

5. Final simplification 63.8%

   \[\leadsto x + 1 \]

Alternative 8: 42.3% 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. Step-by-step derivation

   1. cancel-sign-sub-inv 99.9%

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

   2. +-commutative 99.9%

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

   3. *-commutative 99.9%

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

   4. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 40.7%

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

5. Final simplification 40.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(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))))