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

Percentage Accurate: 99.9% → 99.9%

Time: 10.5s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(N[Cos[y], $MachinePrecision] * z + 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. Step-by-step derivation

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. accelerator-lowering-fma.f64 N/A

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

   4. cos-lowering-cos.f64 N/A

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

   5. +-lowering-+.f64 N/A

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

   6. sin-lowering-sin.f64 99.9

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

4. Applied egg-rr 99.9%

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

Alternative 2: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \sin y\right) + \cos y \cdot z\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-20}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-21}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (+ x (sin y)) (* (cos y) z))))
   (if (<= t_0 -2e-20) (+ z x) (if (<= t_0 5e-21) (+ y x) (+ z x)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + sin(y)) + (cos(y) * z);
	double tmp;
	if (t_0 <= -2e-20) {
		tmp = z + x;
	} else if (t_0 <= 5e-21) {
		tmp = y + x;
	} else {
		tmp = z + 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) :: t_0
    real(8) :: tmp
    t_0 = (x + sin(y)) + (cos(y) * z)
    if (t_0 <= (-2d-20)) then
        tmp = z + x
    else if (t_0 <= 5d-21) then
        tmp = y + x
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + Math.sin(y)) + (Math.cos(y) * z);
	double tmp;
	if (t_0 <= -2e-20) {
		tmp = z + x;
	} else if (t_0 <= 5e-21) {
		tmp = y + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + math.sin(y)) + (math.cos(y) * z)
	tmp = 0
	if t_0 <= -2e-20:
		tmp = z + x
	elif t_0 <= 5e-21:
		tmp = y + x
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + sin(y)) + Float64(cos(y) * z))
	tmp = 0.0
	if (t_0 <= -2e-20)
		tmp = Float64(z + x);
	elseif (t_0 <= 5e-21)
		tmp = Float64(y + x);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + sin(y)) + (cos(y) * z);
	tmp = 0.0;
	if (t_0 <= -2e-20)
		tmp = z + x;
	elseif (t_0 <= 5e-21)
		tmp = y + x;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e-20], N[(z + x), $MachinePrecision], If[LessEqual[t$95$0, 5e-21], N[(y + x), $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -1.99999999999999989e-20 or 4.99999999999999973e-21 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 71.8

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

   5. Simplified 71.8%

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

   if -1.99999999999999989e-20 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 4.99999999999999973e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. distribute-rgt-in N/A

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

      6. associate-*r* N/A

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

      7. unpow2 N/A

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

      8. *-lft-identity N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. +-lowering-+.f64 N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. distribute-rgt1-in N/A

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

      18. *-commutative N/A

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

      19. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 85.4%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \sin y\right) + \cos y \cdot z \leq -2 \cdot 10^{-20}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;\left(x + \sin y\right) + \cos y \cdot z \leq 5 \cdot 10^{-21}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+202}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-24}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-27}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+122}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -1.65e+202)
     t_0
     (if (<= z -3.8e-24)
       (+ z x)
       (if (<= z 6.4e-27) (+ x (sin y)) (if (<= z 3.15e+122) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -1.65e+202) {
		tmp = t_0;
	} else if (z <= -3.8e-24) {
		tmp = z + x;
	} else if (z <= 6.4e-27) {
		tmp = x + sin(y);
	} else if (z <= 3.15e+122) {
		tmp = z + 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 = cos(y) * z
    if (z <= (-1.65d+202)) then
        tmp = t_0
    else if (z <= (-3.8d-24)) then
        tmp = z + x
    else if (z <= 6.4d-27) then
        tmp = x + sin(y)
    else if (z <= 3.15d+122) then
        tmp = z + 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 = Math.cos(y) * z;
	double tmp;
	if (z <= -1.65e+202) {
		tmp = t_0;
	} else if (z <= -3.8e-24) {
		tmp = z + x;
	} else if (z <= 6.4e-27) {
		tmp = x + Math.sin(y);
	} else if (z <= 3.15e+122) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	tmp = 0
	if z <= -1.65e+202:
		tmp = t_0
	elif z <= -3.8e-24:
		tmp = z + x
	elif z <= 6.4e-27:
		tmp = x + math.sin(y)
	elif z <= 3.15e+122:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (z <= -1.65e+202)
		tmp = t_0;
	elseif (z <= -3.8e-24)
		tmp = Float64(z + x);
	elseif (z <= 6.4e-27)
		tmp = Float64(x + sin(y));
	elseif (z <= 3.15e+122)
		tmp = Float64(z + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * z;
	tmp = 0.0;
	if (z <= -1.65e+202)
		tmp = t_0;
	elseif (z <= -3.8e-24)
		tmp = z + x;
	elseif (z <= 6.4e-27)
		tmp = x + sin(y);
	elseif (z <= 3.15e+122)
		tmp = z + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.65e+202], t$95$0, If[LessEqual[z, -3.8e-24], N[(z + x), $MachinePrecision], If[LessEqual[z, 6.4e-27], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.15e+122], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6499999999999999e202 or 3.1500000000000001e122 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

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

      2. cos-lowering-cos.f64 89.2

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

   5. Simplified 89.2%

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

   if -1.6499999999999999e202 < z < -3.80000000000000026e-24 or 6.39999999999999982e-27 < z < 3.1500000000000001e122

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 80.6

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

   5. Simplified 80.6%

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

   if -3.80000000000000026e-24 < z < 6.39999999999999982e-27

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

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

      3. sin-lowering-sin.f64 95.8

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

   5. Simplified 95.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+202}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-24}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-27}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+122}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-28}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (cos y) z x)))
   (if (<= z -2.2e-33) t_0 (if (<= z 4.9e-28) (+ x (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(cos(y), z, x);
	double tmp;
	if (z <= -2.2e-33) {
		tmp = t_0;
	} else if (z <= 4.9e-28) {
		tmp = x + sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(cos(y), z, x)
	tmp = 0.0
	if (z <= -2.2e-33)
		tmp = t_0;
	elseif (z <= 4.9e-28)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[z, -2.2e-33], t$95$0, If[LessEqual[z, 4.9e-28], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000005e-33 or 4.9000000000000003e-28 < z

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. cos-lowering-cos.f64 N/A

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

      5. +-lowering-+.f64 N/A

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

      6. sin-lowering-sin.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 99.8%

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

   if -2.20000000000000005e-33 < z < 4.9000000000000003e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

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

      3. sin-lowering-sin.f64 95.8

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

   5. Simplified 95.8%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-28}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;y \leq -0.36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.108:\\ \;\;\;\;y + \mathsf{fma}\left(z \cdot \left(y \cdot -0.5\right), y, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= y -0.36)
     t_0
     (if (<= y 0.108) (+ y (fma (* z (* y -0.5)) y (+ z x))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (y <= -0.36) {
		tmp = t_0;
	} else if (y <= 0.108) {
		tmp = y + fma((z * (y * -0.5)), y, (z + x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + sin(y))
	tmp = 0.0
	if (y <= -0.36)
		tmp = t_0;
	elseif (y <= 0.108)
		tmp = Float64(y + fma(Float64(z * Float64(y * -0.5)), y, Float64(z + x)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.36], t$95$0, If[LessEqual[y, 0.108], N[(y + N[(N[(z * N[(y * -0.5), $MachinePrecision]), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.35999999999999999 or 0.107999999999999999 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

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

      3. sin-lowering-sin.f64 64.0

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

   5. Simplified 64.0%

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

   if -0.35999999999999999 < y < 0.107999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. distribute-rgt-in N/A

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

      6. associate-*r* N/A

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

      7. unpow2 N/A

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

      8. *-lft-identity N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. +-lowering-+.f64 N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. distribute-rgt1-in N/A

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

      18. *-commutative N/A

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

      19. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 99.7%

      \[\leadsto \color{blue}{y + \mathsf{fma}\left(z, \mathsf{fma}\left(y, y \cdot -0.5, 1\right), x\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. +-lowering-+.f64 99.7

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

   7. Applied egg-rr 99.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.36:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;y \leq 0.108:\\ \;\;\;\;y + \mathsf{fma}\left(z \cdot \left(y \cdot -0.5\right), y, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.3% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 13000:\\ \;\;\;\;x + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, -0.16666666666666666, z \cdot -0.5\right), 1\right), z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8)
   (+ z x)
   (if (<= y 13000.0)
     (+ x (fma y (fma y (fma y -0.16666666666666666 (* z -0.5)) 1.0) z))
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8) {
		tmp = z + x;
	} else if (y <= 13000.0) {
		tmp = x + fma(y, fma(y, fma(y, -0.16666666666666666, (z * -0.5)), 1.0), z);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8)
		tmp = Float64(z + x);
	elseif (y <= 13000.0)
		tmp = Float64(x + fma(y, fma(y, fma(y, -0.16666666666666666, Float64(z * -0.5)), 1.0), z));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8], N[(z + x), $MachinePrecision], If[LessEqual[y, 13000.0], N[(x + N[(y * N[(y * N[(y * -0.16666666666666666 + N[(z * -0.5), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999982 or 13000 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 49.8

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

   5. Simplified 49.8%

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

   if -4.79999999999999982 < y < 13000

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto x + \color{blue}{\left(y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right) + z\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(y, 1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right), z\right)} \]

      4. +-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(y, \color{blue}{y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right) + 1}, z\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y, 1\right)}, z\right) \]

      6. +-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\frac{-1}{6} \cdot y + \frac{-1}{2} \cdot z}, 1\right), z\right) \]

      7. *-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \frac{-1}{6}} + \frac{-1}{2} \cdot z, 1\right), z\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{-1}{6}, \frac{-1}{2} \cdot z\right)}, 1\right), z\right) \]

      9. *-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \frac{-1}{6}, \color{blue}{z \cdot \frac{-1}{2}}\right), 1\right), z\right) \]

      10. *-lowering-*.f64 98.6

          \[\leadsto x + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, -0.16666666666666666, \color{blue}{z \cdot -0.5}\right), 1\right), z\right) \]

   5. Simplified 98.6%

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

Alternative 7: 71.2% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 13000:\\ \;\;\;\;y + \mathsf{fma}\left(z, \mathsf{fma}\left(y, y \cdot -0.5, 1\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8)
   (+ z x)
   (if (<= y 13000.0) (+ y (fma z (fma y (* y -0.5) 1.0) x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8) {
		tmp = z + x;
	} else if (y <= 13000.0) {
		tmp = y + fma(z, fma(y, (y * -0.5), 1.0), x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8)
		tmp = Float64(z + x);
	elseif (y <= 13000.0)
		tmp = Float64(y + fma(z, fma(y, Float64(y * -0.5), 1.0), x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8], N[(z + x), $MachinePrecision], If[LessEqual[y, 13000.0], N[(y + N[(z * N[(y * N[(y * -0.5), $MachinePrecision] + 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999982 or 13000 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 49.8

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

   5. Simplified 49.8%

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

   if -4.79999999999999982 < y < 13000

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. distribute-rgt-in N/A

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

      6. associate-*r* N/A

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

      7. unpow2 N/A

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

      8. *-lft-identity N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. +-lowering-+.f64 N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. distribute-rgt1-in N/A

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

      18. *-commutative N/A

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

      19. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 98.5%

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

Alternative 8: 70.2% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+141}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e+141) (+ z x) (if (<= y 6.5e+58) (+ y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+141) {
		tmp = z + x;
	} else if (y <= 6.5e+58) {
		tmp = y + (z + x);
	} else {
		tmp = z + 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 (y <= (-1.65d+141)) then
        tmp = z + x
    else if (y <= 6.5d+58) then
        tmp = y + (z + x)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+141) {
		tmp = z + x;
	} else if (y <= 6.5e+58) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e+141:
		tmp = z + x
	elif y <= 6.5e+58:
		tmp = y + (z + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e+141)
		tmp = Float64(z + x);
	elseif (y <= 6.5e+58)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.65e+141)
		tmp = z + x;
	elseif (y <= 6.5e+58)
		tmp = y + (z + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e+141], N[(z + x), $MachinePrecision], If[LessEqual[y, 6.5e+58], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6499999999999998e141 or 6.49999999999999998e58 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 49.7

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

   5. Simplified 49.7%

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

   if -1.6499999999999998e141 < y < 6.49999999999999998e58

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. +-lowering-+.f64 88.2

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

   5. Simplified 88.2%

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

Alternative 9: 56.0% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2550:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.0068:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2550.0) x (if (<= x 0.0068) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2550.0) {
		tmp = x;
	} else if (x <= 0.0068) {
		tmp = z;
	} 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 <= (-2550.0d0)) then
        tmp = x
    else if (x <= 0.0068d0) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2550.0) {
		tmp = x;
	} else if (x <= 0.0068) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2550.0:
		tmp = x
	elif x <= 0.0068:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2550.0)
		tmp = x;
	elseif (x <= 0.0068)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2550.0)
		tmp = x;
	elseif (x <= 0.0068)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2550.0], x, If[LessEqual[x, 0.0068], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2550 or 0.00679999999999999962 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 75.9%

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

   if -2550 < x < 0.00679999999999999962

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

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

      2. cos-lowering-cos.f64 61.7

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

   5. Simplified 61.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 41.7%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 44.1% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.2e-48) x (if (<= x 3.2e-144) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e-48) {
		tmp = x;
	} else if (x <= 3.2e-144) {
		tmp = 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 <= (-5.2d-48)) then
        tmp = x
    else if (x <= 3.2d-144) then
        tmp = 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 <= -5.2e-48) {
		tmp = x;
	} else if (x <= 3.2e-144) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.2e-48:
		tmp = x
	elif x <= 3.2e-144:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.2e-48)
		tmp = x;
	elseif (x <= 3.2e-144)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.2e-48)
		tmp = x;
	elseif (x <= 3.2e-144)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.2e-48], x, If[LessEqual[x, 3.2e-144], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.19999999999999975e-48 or 3.19999999999999973e-144 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 59.5%

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

   if -5.19999999999999975e-48 < x < 3.19999999999999973e-144

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. distribute-rgt-in N/A

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

      6. associate-*r* N/A

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

      7. unpow2 N/A

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

      8. *-lft-identity N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. +-lowering-+.f64 N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. distribute-rgt1-in N/A

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

      18. *-commutative N/A

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

      19. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 60.9%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 28.6%

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

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   10. Step-by-step derivation

   11. Simplified 25.3%

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

Alternative 11: 42.1% accurate, 212.0× 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. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Simplified 44.0%

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

Reproduce

herbie shell --seed 2024199 
(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))))