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

Percentage Accurate: 99.9% → 99.9%

Time: 7.7s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(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 + sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(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 + sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + \mathsf{fma}\left(z, \cos y, \sin y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 95.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -9.25 \cdot 10^{-21} \lor \neg \left(x \leq 2.5 \cdot 10^{-45}\right):\\ \;\;\;\;x + t\_0\\ \mathbf{else}:\\ \;\;\;\;\sin y + t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (or (<= x -9.25e-21) (not (<= x 2.5e-45))) (+ x t_0) (+ (sin y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if ((x <= -9.25e-21) || !(x <= 2.5e-45)) {
		tmp = x + t_0;
	} else {
		tmp = sin(y) + 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 * cos(y)
    if ((x <= (-9.25d-21)) .or. (.not. (x <= 2.5d-45))) then
        tmp = x + t_0
    else
        tmp = sin(y) + t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if ((x <= -9.25e-21) || !(x <= 2.5e-45)) {
		tmp = x + t_0;
	} else {
		tmp = Math.sin(y) + t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if (x <= -9.25e-21) or not (x <= 2.5e-45):
		tmp = x + t_0
	else:
		tmp = math.sin(y) + t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if ((x <= -9.25e-21) || !(x <= 2.5e-45))
		tmp = Float64(x + t_0);
	else
		tmp = Float64(sin(y) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if ((x <= -9.25e-21) || ~((x <= 2.5e-45)))
		tmp = x + t_0;
	else
		tmp = sin(y) + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -9.25e-21], N[Not[LessEqual[x, 2.5e-45]], $MachinePrecision]], N[(x + t$95$0), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.2500000000000001e-21 or 2.49999999999999988e-45 < x

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 98.5%

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

   if -9.2500000000000001e-21 < x < 2.49999999999999988e-45

   1. Initial program 99.9%

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

      1. expm1-log1p-u 69.3%

         \[\leadsto \left(x + \sin y\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(z \cdot \cos y\right)\right)} \]

      2. expm1-undefine 62.0%

         \[\leadsto \left(x + \sin y\right) + \color{blue}{\left(e^{\mathsf{log1p}\left(z \cdot \cos y\right)} - 1\right)} \]

   4. Applied egg-rr 62.0%

      \[\leadsto \left(x + \sin y\right) + \color{blue}{\left(e^{\mathsf{log1p}\left(z \cdot \cos y\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-define 69.3%

         \[\leadsto \left(x + \sin y\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(z \cdot \cos y\right)\right)} \]

   6. Simplified 69.3%

      \[\leadsto \left(x + \sin y\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(z \cdot \cos y\right)\right)} \]

   7. Taylor expanded in x around 0 98.2%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.25 \cdot 10^{-21} \lor \neg \left(x \leq 2.5 \cdot 10^{-45}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (z * cos(y)) + (x + 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 = (z * cos(y)) + (x + sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 4: 95.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-27} \lor \neg \left(z \leq 1.9 \cdot 10^{-16}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5e-27) (not (<= z 1.9e-16)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5e-27) || !(z <= 1.9e-16)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = x + sin(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.5d-27)) .or. (.not. (z <= 1.9d-16))) then
        tmp = x + (z * cos(y))
    else
        tmp = x + sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5e-27) || !(z <= 1.9e-16)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5e-27) or not (z <= 1.9e-16):
		tmp = x + (z * math.cos(y))
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5e-27) || !(z <= 1.9e-16))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5e-27) || ~((z <= 1.9e-16)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5e-27], N[Not[LessEqual[z, 1.9e-16]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000002e-27 or 1.90000000000000006e-16 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 97.5%

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

   if -5.5000000000000002e-27 < z < 1.90000000000000006e-16

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 94.7%

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

      1. +-commutative 94.7%

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

   7. Simplified 94.7%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-27} \lor \neg \left(z \leq 1.9 \cdot 10^{-16}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.45 \lor \neg \left(y \leq 0.0072\right):\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.45) (not (<= y 0.0072)))
   (+ x (sin y))
   (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.45) || !(y <= 0.0072)) {
		tmp = x + sin(y);
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	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 <= (-0.45d0)) .or. (.not. (y <= 0.0072d0))) then
        tmp = x + sin(y)
    else
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.45) || !(y <= 0.0072)) {
		tmp = x + Math.sin(y);
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.45) or not (y <= 0.0072):
		tmp = x + math.sin(y)
	else:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.45) || !(y <= 0.0072))
		tmp = Float64(x + sin(y));
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.45) || ~((y <= 0.0072)))
		tmp = x + sin(y);
	else
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.45], N[Not[LessEqual[y, 0.0072]], $MachinePrecision]], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.450000000000000011 or 0.0071999999999999998 < y

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 58.7%

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

      1. +-commutative 58.7%

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

   7. Simplified 58.7%

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

   if -0.450000000000000011 < y < 0.0071999999999999998

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.9%

      \[\leadsto x + \color{blue}{\left(z + y \cdot \left(1 + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot y\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.45 \lor \neg \left(y \leq 0.0072\right):\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.1% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13500000000 \lor \neg \left(y \leq 1.35 \cdot 10^{+14}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -13500000000.0) (not (<= y 1.35e+14)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -13500000000.0) || !(y <= 1.35e+14)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	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 <= (-13500000000.0d0)) .or. (.not. (y <= 1.35d+14))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -13500000000.0) || !(y <= 1.35e+14)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -13500000000.0) or not (y <= 1.35e+14):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -13500000000.0) || !(y <= 1.35e+14))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -13500000000.0) || ~((y <= 1.35e+14)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -13500000000.0], N[Not[LessEqual[y, 1.35e+14]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e10 or 1.35e14 < y

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 39.6%

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

      1. +-commutative 39.6%

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

   7. Simplified 39.6%

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

   if -1.35e10 < y < 1.35e14

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.2%

      \[\leadsto x + \color{blue}{\left(z + y \cdot \left(1 + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot y\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13500000000 \lor \neg \left(y \leq 1.35 \cdot 10^{+14}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \lor \neg \left(y \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5) (not (<= y 6.5e+18)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* -0.5 (* z y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5) || !(y <= 6.5e+18)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (-0.5 * (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 <= (-1.5d0)) .or. (.not. (y <= 6.5d+18))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + ((-0.5d0) * (z * y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5) || !(y <= 6.5e+18)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (-0.5 * (z * y)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5) or not (y <= 6.5e+18):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (-0.5 * (z * y)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5) || !(y <= 6.5e+18))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(-0.5 * Float64(z * y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.5) || ~((y <= 6.5e+18)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (-0.5 * (z * y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5], N[Not[LessEqual[y, 6.5e+18]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5 or 6.5e18 < y

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 39.7%

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

      1. +-commutative 39.7%

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

   7. Simplified 39.7%

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

   if -1.5 < y < 6.5e18

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.9%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \lor \neg \left(y \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+52} \lor \neg \left(y \leq 2.45 \cdot 10^{+66}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e+52) (not (<= y 2.45e+66))) (+ x z) (+ y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e+52) || !(y <= 2.45e+66)) {
		tmp = x + z;
	} else {
		tmp = y + (x + 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 <= (-3.2d+52)) .or. (.not. (y <= 2.45d+66))) then
        tmp = x + z
    else
        tmp = y + (x + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e+52) || !(y <= 2.45e+66)) {
		tmp = x + z;
	} else {
		tmp = y + (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e+52) or not (y <= 2.45e+66):
		tmp = x + z
	else:
		tmp = y + (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e+52) || !(y <= 2.45e+66))
		tmp = Float64(x + z);
	else
		tmp = Float64(y + Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.2e+52) || ~((y <= 2.45e+66)))
		tmp = x + z;
	else
		tmp = y + (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e+52], N[Not[LessEqual[y, 2.45e+66]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e52 or 2.44999999999999988e66 < y

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 39.9%

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

      1. +-commutative 39.9%

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

   7. Simplified 39.9%

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

   if -3.2e52 < y < 2.44999999999999988e66

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 88.6%

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

      1. +-commutative 88.6%

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

      2. associate-+l+ 88.6%

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

   7. Simplified 88.6%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+52} \lor \neg \left(y \leq 2.45 \cdot 10^{+66}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.2% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+53} \lor \neg \left(y \leq 3 \cdot 10^{+66}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.45e+53) (not (<= y 3e+66))) x (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.45e+53) || !(y <= 3e+66)) {
		tmp = x;
	} else {
		tmp = x + 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 <= (-1.45d+53)) .or. (.not. (y <= 3d+66))) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.45e+53) || !(y <= 3e+66)) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.45e+53) or not (y <= 3e+66):
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.45e+53) || !(y <= 3e+66))
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.45e+53) || ~((y <= 3e+66)))
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.45e+53], N[Not[LessEqual[y, 3e+66]], $MachinePrecision]], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4500000000000001e53 or 3.00000000000000002e66 < y

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 36.6%

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

   if -1.4500000000000001e53 < y < 3.00000000000000002e66

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in y around 0 86.6%

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

   7. Taylor expanded in z around 0 48.0%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+53} \lor \neg \left(y \leq 3 \cdot 10^{+66}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around 0 64.5%

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

   1. +-commutative 64.5%

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

7. Simplified 64.5%

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

8. Final simplification 64.5%

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

Alternative 11: 42.5% 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%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 39.6%

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))