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

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(z * (-N[Sin[y], $MachinePrecision]) + N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]), $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. distribute-lft-neg-out 99.9%

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

   4. distribute-rgt-neg-in 99.9%

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

   5. sin-neg 99.9%

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

   6. fma-def 99.9%

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

   7. sin-neg 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 90.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0068:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0068)
   (+ x (cos y))
   (if (<= x 2.1e+41) (- (cos y) (* z (sin y))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0068) {
		tmp = x + cos(y);
	} else if (x <= 2.1e+41) {
		tmp = cos(y) - (z * sin(y));
	} 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 <= (-0.0068d0)) then
        tmp = x + cos(y)
    else if (x <= 2.1d+41) then
        tmp = cos(y) - (z * sin(y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0068) {
		tmp = x + Math.cos(y);
	} else if (x <= 2.1e+41) {
		tmp = Math.cos(y) - (z * Math.sin(y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0068:
		tmp = x + math.cos(y)
	elif x <= 2.1e+41:
		tmp = math.cos(y) - (z * math.sin(y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0068)
		tmp = Float64(x + cos(y));
	elseif (x <= 2.1e+41)
		tmp = Float64(cos(y) - Float64(z * sin(y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0068)
		tmp = x + cos(y);
	elseif (x <= 2.1e+41)
		tmp = cos(y) - (z * sin(y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0068], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+41], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00679999999999999962

   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. Taylor expanded in z around 0 90.6%

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

      1. +-commutative 90.6%

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

   6. Simplified 90.6%

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

   if -0.00679999999999999962 < x < 2.1e41

   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. Taylor expanded in x around 0 96.7%

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

   if 2.1e41 < x

   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. Taylor expanded in x around inf 84.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0068:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 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+ 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. Final simplification 99.9%

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

Alternative 4: 81.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.024 \lor \neg \left(y \leq 1.8 \cdot 10^{-5}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, x + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.024) (not (<= y 1.8e-5)))
   (+ x (cos y))
   (fma (- y) z (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.024) || !(y <= 1.8e-5)) {
		tmp = x + cos(y);
	} else {
		tmp = fma(-y, z, (x + 1.0));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.024) || !(y <= 1.8e-5))
		tmp = Float64(x + cos(y));
	else
		tmp = fma(Float64(-y), z, Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.024], N[Not[LessEqual[y, 1.8e-5]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[((-y) * z + N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.024 or 1.80000000000000005e-5 < y

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 62.0%

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

      1. +-commutative 62.0%

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

   6. Simplified 62.0%

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

   if -0.024 < y < 1.80000000000000005e-5

   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. Taylor expanded in y around 0 99.6%

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

      1. associate-+r+ 99.6%

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

      2. +-commutative 99.6%

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

      3. mul-1-neg 99.6%

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

   6. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. distribute-lft-neg-in 99.6%

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

      3. fma-def 99.6%

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

   8. Applied egg-rr 99.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.024 \lor \neg \left(y \leq 1.8 \cdot 10^{-5}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, x + 1\right)\\ \end{array} \]

Alternative 5: 81.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0235 \lor \neg \left(y \leq 1.8 \cdot 10^{-5}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0235) (not (<= y 1.8e-5)))
   (+ x (cos y))
   (- (+ x 1.0) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0235) || !(y <= 1.8e-5)) {
		tmp = x + cos(y);
	} else {
		tmp = (x + 1.0) - (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 ((y <= (-0.0235d0)) .or. (.not. (y <= 1.8d-5))) then
        tmp = x + cos(y)
    else
        tmp = (x + 1.0d0) - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0235) || !(y <= 1.8e-5)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = (x + 1.0) - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0235) or not (y <= 1.8e-5):
		tmp = x + math.cos(y)
	else:
		tmp = (x + 1.0) - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0235) || !(y <= 1.8e-5))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(Float64(x + 1.0) - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0235) || ~((y <= 1.8e-5)))
		tmp = x + cos(y);
	else
		tmp = (x + 1.0) - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0235], N[Not[LessEqual[y, 1.8e-5]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0235 or 1.80000000000000005e-5 < y

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 62.0%

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

      1. +-commutative 62.0%

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

   6. Simplified 62.0%

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

   if -0.0235 < y < 1.80000000000000005e-5

   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. Taylor expanded in y around 0 99.6%

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

      1. associate-+r+ 99.6%

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

      2. +-commutative 99.6%

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

      3. mul-1-neg 99.6%

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

   6. Simplified 99.6%

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

      1. unsub-neg 99.6%

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

      2. *-commutative 99.6%

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

   8. Applied egg-rr 99.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0235 \lor \neg \left(y \leq 1.8 \cdot 10^{-5}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \end{array} \]

Alternative 6: 72.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-11} \lor \neg \left(x \leq 10.8\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.55e-11) (not (<= x 10.8))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e-11) || !(x <= 10.8)) {
		tmp = x + 1.0;
	} else {
		tmp = cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.55d-11)) .or. (.not. (x <= 10.8d0))) then
        tmp = x + 1.0d0
    else
        tmp = cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e-11) || !(x <= 10.8)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.55e-11) or not (x <= 10.8):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.55e-11) || !(x <= 10.8))
		tmp = Float64(x + 1.0);
	else
		tmp = cos(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.55e-11) || ~((x <= 10.8)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.55e-11], N[Not[LessEqual[x, 10.8]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000014e-11 or 10.800000000000001 < x

   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. Taylor expanded in y around 0 82.0%

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

      1. +-commutative 82.0%

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

   6. Simplified 82.0%

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

   if -1.55000000000000014e-11 < x < 10.800000000000001

   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. Taylor expanded in x around 0 99.1%

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

   5. Taylor expanded in z around 0 64.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-11} \lor \neg \left(x \leq 10.8\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]

Alternative 7: 67.2% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-14} \lor \neg \left(x \leq 4.5 \cdot 10^{-14}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.6e-14) (not (<= x 4.5e-14))) (+ x 1.0) (- 1.0 (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.6e-14) || !(x <= 4.5e-14)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (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 ((x <= (-6.6d-14)) .or. (.not. (x <= 4.5d-14))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.6e-14) || !(x <= 4.5e-14)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.6e-14) or not (x <= 4.5e-14):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.6e-14) || !(x <= 4.5e-14))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.6e-14) || ~((x <= 4.5e-14)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.6e-14], N[Not[LessEqual[x, 4.5e-14]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5999999999999996e-14 or 4.4999999999999998e-14 < x

   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. Taylor expanded in y around 0 79.0%

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

      1. +-commutative 79.0%

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

   6. Simplified 79.0%

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

   if -6.5999999999999996e-14 < x < 4.4999999999999998e-14

   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. Taylor expanded in y around 0 57.6%

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

      1. associate-+r+ 57.6%

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

      2. +-commutative 57.6%

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

      3. mul-1-neg 57.6%

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

   6. Simplified 57.6%

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

   7. Taylor expanded in x around 0 57.5%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-14} \lor \neg \left(x \leq 4.5 \cdot 10^{-14}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot y\\ \end{array} \]

Alternative 8: 66.9% accurate, 22.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.25 \cdot 10^{+18}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.25e+18) (- (+ x 1.0) (* z y)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.25e+18) {
		tmp = (x + 1.0) - (z * 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 (y <= 2.25d+18) then
        tmp = (x + 1.0d0) - (z * 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 (y <= 2.25e+18) {
		tmp = (x + 1.0) - (z * y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.25e+18:
		tmp = (x + 1.0) - (z * y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.25e+18)
		tmp = Float64(Float64(x + 1.0) - Float64(z * y));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.25e+18)
		tmp = (x + 1.0) - (z * y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.25e+18], N[(N[(x + 1.0), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.25e18

   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. Taylor expanded in y around 0 79.0%

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

      1. associate-+r+ 79.0%

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

      2. +-commutative 79.0%

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

      3. mul-1-neg 79.0%

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

   6. Simplified 79.0%

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

      1. unsub-neg 79.0%

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

      2. *-commutative 79.0%

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

   8. Applied egg-rr 79.0%

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

   if 2.25e18 < y

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 34.4%

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

      1. +-commutative 34.4%

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

   6. Simplified 34.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.25 \cdot 10^{+18}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9: 61.2% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.75) x (if (<= x 1.45e-9) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.75) {
		tmp = x;
	} else if (x <= 1.45e-9) {
		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 <= (-0.75d0)) then
        tmp = x
    else if (x <= 1.45d-9) 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 <= -0.75) {
		tmp = x;
	} else if (x <= 1.45e-9) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.75:
		tmp = x
	elif x <= 1.45e-9:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.75)
		tmp = x;
	elseif (x <= 1.45e-9)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = x;
	elseif (x <= 1.45e-9)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.75], x, If[LessEqual[x, 1.45e-9], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.75 or 1.44999999999999996e-9 < x

   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. Taylor expanded in x around inf 81.1%

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

   if -0.75 < x < 1.44999999999999996e-9

   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. Taylor expanded in x around 0 99.0%

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

   5. Taylor expanded in y around 0 43.7%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 61.9% 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+ 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. Taylor expanded in y around 0 61.1%

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

   1. +-commutative 61.1%

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

6. Simplified 61.1%

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

7. Final simplification 61.1%

   \[\leadsto x + 1 \]

Alternative 11: 21.7% 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+ 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. Taylor expanded in x around 0 61.6%

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

5. Taylor expanded in y around 0 24.8%

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

6. Final simplification 24.8%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023322 
(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))))