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

Percentage Accurate: 99.9% → 99.9%

Time: 7.1s

Alternatives: 10

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

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (cos(y) + x) - (sin(y) * z)
end function

Java

public static double code(double x, double y, double z) {
	return (Math.cos(y) + x) - (Math.sin(y) * z);
}

Python

def code(x, y, z):
	return (math.cos(y) + x) - (math.sin(y) * z)

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = (cos(y) + x) - (sin(y) * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\cos y + x\right) - \sin y \cdot z\\ t_1 := x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{if}\;t\_0 \leq -50:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.98:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (cos y) x) (* (sin y) z))) (t_1 (- x (fma z y -1.0))))
   (if (<= t_0 -50.0) t_1 (if (<= t_0 0.98) (cos y) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (cos(y) + x) - (sin(y) * z);
	double t_1 = x - fma(z, y, -1.0);
	double tmp;
	if (t_0 <= -50.0) {
		tmp = t_1;
	} else if (t_0 <= 0.98) {
		tmp = cos(y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(cos(y) + x) - Float64(sin(y) * z))
	t_1 = Float64(x - fma(z, y, -1.0))
	tmp = 0.0
	if (t_0 <= -50.0)
		tmp = t_1;
	elseif (t_0 <= 0.98)
		tmp = cos(y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -50.0], t$95$1, If[LessEqual[t$95$0, 0.98], N[Cos[y], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -50 or 0.97999999999999998 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. sub-neg N/A

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

      7. *-commutative N/A

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

      8. metadata-eval N/A

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

      9. lower-fma.f64 74.5

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

   5. Applied rewrites 74.5%

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

   if -50 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.97999999999999998

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 97.0

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

   5. Applied rewrites 97.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \cos y \]
   7. Step-by-step derivation

   8. Applied rewrites 94.5%

      \[\leadsto \cos y \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\cos y + x\right) - \sin y \cdot z \leq -50:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{elif}\;\left(\cos y + x\right) - \sin y \cdot z \leq 0.98:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + x\right) - \sin y \cdot z\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+45}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-15}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ 1.0 x) (* (sin y) z))))
   (if (<= z -1.05e+45) t_0 (if (<= z 2.1e-15) (+ (cos y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 + x) - (sin(y) * z);
	double tmp;
	if (z <= -1.05e+45) {
		tmp = t_0;
	} else if (z <= 2.1e-15) {
		tmp = cos(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 + x) - (sin(y) * z)
    if (z <= (-1.05d+45)) then
        tmp = t_0
    else if (z <= 2.1d-15) then
        tmp = cos(y) + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 + x) - (Math.sin(y) * z);
	double tmp;
	if (z <= -1.05e+45) {
		tmp = t_0;
	} else if (z <= 2.1e-15) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 + x) - (math.sin(y) * z)
	tmp = 0
	if z <= -1.05e+45:
		tmp = t_0
	elif z <= 2.1e-15:
		tmp = math.cos(y) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 + x) - Float64(sin(y) * z))
	tmp = 0.0
	if (z <= -1.05e+45)
		tmp = t_0;
	elseif (z <= 2.1e-15)
		tmp = Float64(cos(y) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 + x) - (sin(y) * z);
	tmp = 0.0;
	if (z <= -1.05e+45)
		tmp = t_0;
	elseif (z <= 2.1e-15)
		tmp = cos(y) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 + x), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+45], t$95$0, If[LessEqual[z, 2.1e-15], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999997e45 or 2.09999999999999981e-15 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 99.8%

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

   if -1.04999999999999997e45 < z < 2.09999999999999981e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 99.3

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

   5. Applied rewrites 99.3%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+45}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-15}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot \sin y\\ \mathbf{if}\;z \leq -8 \cdot 10^{+138}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+167}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) (sin y))))
   (if (<= z -8e+138) t_0 (if (<= z 3.7e+167) (+ (cos y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -z * sin(y);
	double tmp;
	if (z <= -8e+138) {
		tmp = t_0;
	} else if (z <= 3.7e+167) {
		tmp = cos(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -z * sin(y)
    if (z <= (-8d+138)) then
        tmp = t_0
    else if (z <= 3.7d+167) then
        tmp = cos(y) + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z * Math.sin(y);
	double tmp;
	if (z <= -8e+138) {
		tmp = t_0;
	} else if (z <= 3.7e+167) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z * math.sin(y)
	tmp = 0
	if z <= -8e+138:
		tmp = t_0
	elif z <= 3.7e+167:
		tmp = math.cos(y) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) * sin(y))
	tmp = 0.0
	if (z <= -8e+138)
		tmp = t_0;
	elseif (z <= 3.7e+167)
		tmp = Float64(cos(y) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z * sin(y);
	tmp = 0.0;
	if (z <= -8e+138)
		tmp = t_0;
	elseif (z <= 3.7e+167)
		tmp = cos(y) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+138], t$95$0, If[LessEqual[z, 3.7e+167], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000003e138 or 3.7000000000000001e167 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-neg-in N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-sin.f64 80.7

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

   5. Applied rewrites 80.7%

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

   if -8.0000000000000003e138 < z < 3.7000000000000001e167

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 89.3

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

   5. Applied rewrites 89.3%

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

Alternative 5: 81.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y + x\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-13}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (cos y) x)))
   (if (<= y -1.65e+16) t_0 (if (<= y 3.5e-13) (- x (fma z y -1.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) + x;
	double tmp;
	if (y <= -1.65e+16) {
		tmp = t_0;
	} else if (y <= 3.5e-13) {
		tmp = x - fma(z, y, -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) + x)
	tmp = 0.0
	if (y <= -1.65e+16)
		tmp = t_0;
	elseif (y <= 3.5e-13)
		tmp = Float64(x - fma(z, y, -1.0));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -1.65e+16], t$95$0, If[LessEqual[y, 3.5e-13], N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e16 or 3.5000000000000002e-13 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 63.3

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

   5. Applied rewrites 63.3%

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

   if -1.65e16 < y < 3.5000000000000002e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. sub-neg N/A

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

      7. *-commutative N/A

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

      8. metadata-eval N/A

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

      9. lower-fma.f64 99.3

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

   5. Applied rewrites 99.3%

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

Alternative 6: 71.1% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+20}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 9.1 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot y - z, y, 1 + x\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.35e+20)
   (+ 1.0 x)
   (if (<= y 9.1e+18) (fma (- (* -0.5 y) z) y (+ 1.0 x)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.35e+20) {
		tmp = 1.0 + x;
	} else if (y <= 9.1e+18) {
		tmp = fma(((-0.5 * y) - z), y, (1.0 + x));
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.35e+20)
		tmp = Float64(1.0 + x);
	elseif (y <= 9.1e+18)
		tmp = fma(Float64(Float64(-0.5 * y) - z), y, Float64(1.0 + x));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.35e+20], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 9.1e+18], N[(N[(N[(-0.5 * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(1.0 + x), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.35e20 or 9.1e18 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 38.4

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

   5. Applied rewrites 38.4%

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

   if -2.35e20 < y < 9.1e18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{2} \cdot y - z, y, 1 + x\right)} \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2} \cdot y - z}, y, 1 + x\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2} \cdot y} - z, y, 1 + x\right) \]

      7. lower-+.f64 96.3

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

   5. Applied rewrites 96.3%

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

Alternative 7: 70.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+67}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+115}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+67)
   (+ 1.0 x)
   (if (<= y 1.2e+115) (- x (fma z y -1.0)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+67) {
		tmp = 1.0 + x;
	} else if (y <= 1.2e+115) {
		tmp = x - fma(z, y, -1.0);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+67)
		tmp = Float64(1.0 + x);
	elseif (y <= 1.2e+115)
		tmp = Float64(x - fma(z, y, -1.0));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+67], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 1.2e+115], N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000002e67 or 1.2e115 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 37.7

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

   5. Applied rewrites 37.7%

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

   if -3.8000000000000002e67 < y < 1.2e115

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. sub-neg N/A

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

      7. *-commutative N/A

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

      8. metadata-eval N/A

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

      9. lower-fma.f64 87.2

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

   5. Applied rewrites 87.2%

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

Alternative 8: 63.0% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{+180}:\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 4.5e+180) (+ 1.0 x) (* (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 4.5e+180) {
		tmp = 1.0 + x;
	} 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 <= 4.5d+180) then
        tmp = 1.0d0 + x
    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 <= 4.5e+180) {
		tmp = 1.0 + x;
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 4.5e+180:
		tmp = 1.0 + x
	else:
		tmp = -z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 4.5e+180)
		tmp = Float64(1.0 + x);
	else
		tmp = Float64(Float64(-z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 4.5e+180)
		tmp = 1.0 + x;
	else
		tmp = -z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 4.5e+180], N[(1.0 + x), $MachinePrecision], N[((-z) * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.49999999999999981e180

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 67.1

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

   5. Applied rewrites 67.1%

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

   if 4.49999999999999981e180 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{2} \cdot y - z, y, 1 + x\right)} \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2} \cdot y - z}, y, 1 + x\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2} \cdot y} - z, y, 1 + x\right) \]

      7. lower-+.f64 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 40.5%

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

Alternative 9: 62.8% accurate, 53.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 1.0 + 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 = 1.0d0 + x
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(1.0 + x)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(1.0 + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. lower-+.f64 61.9

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

5. Applied rewrites 61.9%

   \[\leadsto \color{blue}{1 + x} \]
6. Add Preprocessing

Alternative 10: 22.0% accurate, 212.0× 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. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. lower-+.f64 61.9

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

5. Applied rewrites 61.9%

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

6. Taylor expanded in x around 0

   \[\leadsto 1 \]
7. Step-by-step derivation

8. Applied rewrites 20.1%

   \[\leadsto 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024240 
(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))))