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

Percentage Accurate: 99.9% → 99.9%

Time: 11.0s

Alternatives: 13

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: 98.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z + \left(x + \sin y\right)\\ t_1 := \mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 40000:\\ \;\;\;\;\mathsf{fma}\left(1, z, \mathsf{fma}\left(x, \frac{\sin y}{x}, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* (cos y) z) (+ x (sin y)))) (t_1 (fma (cos y) z x)))
   (if (<= t_0 -5e+33)
     t_1
     (if (<= t_0 40000.0) (fma 1.0 z (fma x (/ (sin y) x) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (cos(y) * z) + (x + sin(y));
	double t_1 = fma(cos(y), z, x);
	double tmp;
	if (t_0 <= -5e+33) {
		tmp = t_1;
	} else if (t_0 <= 40000.0) {
		tmp = fma(1.0, z, fma(x, (sin(y) / x), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(cos(y) * z) + Float64(x + sin(y)))
	t_1 = fma(cos(y), z, x)
	tmp = 0.0
	if (t_0 <= -5e+33)
		tmp = t_1;
	elseif (t_0 <= 40000.0)
		tmp = fma(1.0, z, fma(x, Float64(sin(y) / x), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision] + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[y], $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+33], t$95$1, If[LessEqual[t$95$0, 40000.0], N[(1.0 * z + N[(x * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -4.99999999999999973e33 or 4e4 < (+.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. 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. 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 -4.99999999999999973e33 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 4e4

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   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 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

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

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

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

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

      6. sin-lowering-sin.f64 99.8

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, z, \mathsf{fma}\left(x, \frac{\sin y}{x}, x\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos y \cdot z + \left(x + \sin y\right) \leq -5 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{elif}\;\cos y \cdot z + \left(x + \sin y\right) \leq 40000:\\ \;\;\;\;\mathsf{fma}\left(1, z, \mathsf{fma}\left(x, \frac{\sin y}{x}, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z + \left(x + \sin y\right)\\ \mathbf{if}\;t\_0 \leq -0.001:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-6}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* (cos y) z) (+ x (sin y)))))
   (if (<= t_0 -0.001) (+ z x) (if (<= t_0 4e-6) (+ y x) (+ z x)))))

C

double code(double x, double y, double z) {
	double t_0 = (cos(y) * z) + (x + sin(y));
	double tmp;
	if (t_0 <= -0.001) {
		tmp = z + x;
	} else if (t_0 <= 4e-6) {
		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 = (cos(y) * z) + (x + sin(y))
    if (t_0 <= (-0.001d0)) then
        tmp = z + x
    else if (t_0 <= 4d-6) 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 = (Math.cos(y) * z) + (x + Math.sin(y));
	double tmp;
	if (t_0 <= -0.001) {
		tmp = z + x;
	} else if (t_0 <= 4e-6) {
		tmp = y + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.cos(y) * z) + (x + math.sin(y))
	tmp = 0
	if t_0 <= -0.001:
		tmp = z + x
	elif t_0 <= 4e-6:
		tmp = y + x
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(cos(y) * z) + Float64(x + sin(y)))
	tmp = 0.0
	if (t_0 <= -0.001)
		tmp = Float64(z + x);
	elseif (t_0 <= 4e-6)
		tmp = Float64(y + x);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (cos(y) * z) + (x + sin(y));
	tmp = 0.0;
	if (t_0 <= -0.001)
		tmp = z + x;
	elseif (t_0 <= 4e-6)
		tmp = y + x;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision] + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.001], N[(z + x), $MachinePrecision], If[LessEqual[t$95$0, 4e-6], 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))) < -1e-3 or 3.99999999999999982e-6 < (+.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 69.5

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

   5. Simplified 69.5%

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

   if -1e-3 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 3.99999999999999982e-6

   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 99.3%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 84.8%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos y \cdot z + \left(x + \sin y\right) \leq -0.001:\\ \;\;\;\;z + x\\ \mathbf{elif}\;\cos y \cdot z + \left(x + \sin y\right) \leq 4 \cdot 10^{-6}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -8 \cdot 10^{+71}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-29}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+134}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -8e+71)
     t_0
     (if (<= z 4.9e-29) (+ x (sin y)) (if (<= z 3.4e+134) (+ z x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -8e+71) {
		tmp = t_0;
	} else if (z <= 4.9e-29) {
		tmp = x + sin(y);
	} else if (z <= 3.4e+134) {
		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 <= (-8d+71)) then
        tmp = t_0
    else if (z <= 4.9d-29) then
        tmp = x + sin(y)
    else if (z <= 3.4d+134) 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 <= -8e+71) {
		tmp = t_0;
	} else if (z <= 4.9e-29) {
		tmp = x + Math.sin(y);
	} else if (z <= 3.4e+134) {
		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 <= -8e+71:
		tmp = t_0
	elif z <= 4.9e-29:
		tmp = x + math.sin(y)
	elif z <= 3.4e+134:
		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 <= -8e+71)
		tmp = t_0;
	elseif (z <= 4.9e-29)
		tmp = Float64(x + sin(y));
	elseif (z <= 3.4e+134)
		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 <= -8e+71)
		tmp = t_0;
	elseif (z <= 4.9e-29)
		tmp = x + sin(y);
	elseif (z <= 3.4e+134)
		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, -8e+71], t$95$0, If[LessEqual[z, 4.9e-29], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+134], N[(z + x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000003e71 or 3.40000000000000018e134 < z

   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. +-rgt-identity N/A

         \[\leadsto \color{blue}{z \cdot \cos y + 0} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, 0\right)} \]

      3. cos-lowering-cos.f64 80.7

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\cos y}, 0\right) \]

   5. Simplified 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

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

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

      4. cos-lowering-cos.f64 80.7

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

   7. Applied egg-rr 80.7%

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

   if -8.0000000000000003e71 < z < 4.8999999999999998e-29

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   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 92.0

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

   5. Simplified 92.0%

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

   if 4.8999999999999998e-29 < z < 3.40000000000000018e134

   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 90.7

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

   5. Simplified 90.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+71}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-29}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+134}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-29}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (cos y) z x)))
   (if (<= z -8.5e-5) t_0 (if (<= z 6.6e-29) (+ 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 <= -8.5e-5) {
		tmp = t_0;
	} else if (z <= 6.6e-29) {
		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 <= -8.5e-5)
		tmp = t_0;
	elseif (z <= 6.6e-29)
		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, -8.5e-5], t$95$0, If[LessEqual[z, 6.6e-29], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.500000000000001e-5 or 6.60000000000000055e-29 < z

   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. Taylor expanded in x around inf

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

   7. Simplified 99.7%

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

   if -8.500000000000001e-5 < z < 6.60000000000000055e-29

   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 97.1

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

   5. Simplified 97.1%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-29}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;y \leq -650000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-6}:\\ \;\;\;\;y + \mathsf{fma}\left(z, \mathsf{fma}\left(y, y \cdot -0.5, 1\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= y -650000000000.0)
     t_0
     (if (<= y 2e-6) (+ y (fma z (fma y (* y -0.5) 1.0) x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (y <= -650000000000.0) {
		tmp = t_0;
	} else if (y <= 2e-6) {
		tmp = y + fma(z, fma(y, (y * -0.5), 1.0), x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + sin(y))
	tmp = 0.0
	if (y <= -650000000000.0)
		tmp = t_0;
	elseif (y <= 2e-6)
		tmp = Float64(y + fma(z, fma(y, Float64(y * -0.5), 1.0), 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, -650000000000.0], t$95$0, If[LessEqual[y, 2e-6], N[(y + N[(z * N[(y * N[(y * -0.5), $MachinePrecision] + 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e11 or 1.99999999999999991e-6 < 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 66.7

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

   5. Simplified 66.7%

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

   if -6.5e11 < y < 1.99999999999999991e-6

   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%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -650000000000:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-6}:\\ \;\;\;\;y + \mathsf{fma}\left(z, \mathsf{fma}\left(y, y \cdot -0.5, 1\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.1% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -980000000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 132000000:\\ \;\;\;\;x + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, -0.16666666666666666, z \cdot -0.5\right), 1\right), z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -980000000000.0)
   (+ z x)
   (if (<= y 132000000.0)
     (+ 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 <= -980000000000.0) {
		tmp = z + x;
	} else if (y <= 132000000.0) {
		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 <= -980000000000.0)
		tmp = Float64(z + x);
	elseif (y <= 132000000.0)
		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, -980000000000.0], N[(z + x), $MachinePrecision], If[LessEqual[y, 132000000.0], 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 < -9.8e11 or 1.32e8 < 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 45.1

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

   5. Simplified 45.1%

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

   if -9.8e11 < y < 1.32e8

   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 99.3

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

   5. Simplified 99.3%

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

Alternative 8: 70.9% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -860000000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;y + \mathsf{fma}\left(z, \mathsf{fma}\left(y, y \cdot -0.5, 1\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -860000000000.0)
   (+ z x)
   (if (<= y 4.6e+33) (+ 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 <= -860000000000.0) {
		tmp = z + x;
	} else if (y <= 4.6e+33) {
		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 <= -860000000000.0)
		tmp = Float64(z + x);
	elseif (y <= 4.6e+33)
		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, -860000000000.0], N[(z + x), $MachinePrecision], If[LessEqual[y, 4.6e+33], 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 < -8.6e11 or 4.60000000000000021e33 < 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 44.5

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

   5. Simplified 44.5%

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

   if -8.6e11 < y < 4.60000000000000021e33

   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 98.4%

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

Alternative 9: 50.0% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+132}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+138}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.18e+132)
   z
   (if (<= z 1.2e-274) x (if (<= z 3.4e+138) (+ y x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.18e+132) {
		tmp = z;
	} else if (z <= 1.2e-274) {
		tmp = x;
	} else if (z <= 3.4e+138) {
		tmp = y + x;
	} else {
		tmp = 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 (z <= (-1.18d+132)) then
        tmp = z
    else if (z <= 1.2d-274) then
        tmp = x
    else if (z <= 3.4d+138) then
        tmp = y + x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.18e+132) {
		tmp = z;
	} else if (z <= 1.2e-274) {
		tmp = x;
	} else if (z <= 3.4e+138) {
		tmp = y + x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.18e+132:
		tmp = z
	elif z <= 1.2e-274:
		tmp = x
	elif z <= 3.4e+138:
		tmp = y + x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.18e+132)
		tmp = z;
	elseif (z <= 1.2e-274)
		tmp = x;
	elseif (z <= 3.4e+138)
		tmp = Float64(y + x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.18e+132)
		tmp = z;
	elseif (z <= 1.2e-274)
		tmp = x;
	elseif (z <= 3.4e+138)
		tmp = y + x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.18e+132], z, If[LessEqual[z, 1.2e-274], x, If[LessEqual[z, 3.4e+138], N[(y + x), $MachinePrecision], z]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.17999999999999997e132 or 3.40000000000000011e138 < z

   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. +-rgt-identity N/A

         \[\leadsto \color{blue}{z \cdot \cos y + 0} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, 0\right)} \]

      3. cos-lowering-cos.f64 86.9

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\cos y}, 0\right) \]

   5. Simplified 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, 0\right)} \]

   6. Taylor expanded in y around 0

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

   8. Simplified 50.1%

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

   if -1.17999999999999997e132 < z < 1.2e-274

   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 61.5%

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

   if 1.2e-274 < z < 3.40000000000000011e138

   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 68.6%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 69.4%

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

Alternative 10: 70.7% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+14) (+ z x) (if (<= y 1.4e+68) (+ y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+14) {
		tmp = z + x;
	} else if (y <= 1.4e+68) {
		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 <= (-2.7d+14)) then
        tmp = z + x
    else if (y <= 1.4d+68) 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 <= -2.7e+14) {
		tmp = z + x;
	} else if (y <= 1.4e+68) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+14:
		tmp = z + x
	elif y <= 1.4e+68:
		tmp = y + (z + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+14)
		tmp = Float64(z + x);
	elseif (y <= 1.4e+68)
		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 <= -2.7e+14)
		tmp = z + x;
	elseif (y <= 1.4e+68)
		tmp = y + (z + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+14], N[(z + x), $MachinePrecision], If[LessEqual[y, 1.4e+68], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e14 or 1.4e68 < 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 45.1

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

   5. Simplified 45.1%

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

   if -2.7e14 < y < 1.4e68

   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 95.1

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

   5. Simplified 95.1%

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

Alternative 11: 52.0% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+131}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.1e+131) z (if (<= z 2.4e+132) x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.1e+131) {
		tmp = z;
	} else if (z <= 2.4e+132) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-6.1d+131)) then
        tmp = z
    else if (z <= 2.4d+132) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.1e+131) {
		tmp = z;
	} else if (z <= 2.4e+132) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.1e+131:
		tmp = z
	elif z <= 2.4e+132:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.1e+131)
		tmp = z;
	elseif (z <= 2.4e+132)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.1e+131)
		tmp = z;
	elseif (z <= 2.4e+132)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.1e+131], z, If[LessEqual[z, 2.4e+132], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0999999999999999e131 or 2.4000000000000001e132 < z

   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. +-rgt-identity N/A

         \[\leadsto \color{blue}{z \cdot \cos y + 0} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, 0\right)} \]

      3. cos-lowering-cos.f64 86.9

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\cos y}, 0\right) \]

   5. Simplified 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, 0\right)} \]

   6. Taylor expanded in y around 0

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

   8. Simplified 50.1%

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

   if -6.0999999999999999e131 < z < 2.4000000000000001e132

   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 62.7%

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

Alternative 12: 45.2% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-194}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-93}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.5e-194) x (if (<= x 6.2e-93) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e-194) {
		tmp = x;
	} else if (x <= 6.2e-93) {
		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 <= (-6.5d-194)) then
        tmp = x
    else if (x <= 6.2d-93) 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 <= -6.5e-194) {
		tmp = x;
	} else if (x <= 6.2e-93) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.5e-194:
		tmp = x
	elif x <= 6.2e-93:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.5e-194)
		tmp = x;
	elseif (x <= 6.2e-93)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.5e-194)
		tmp = x;
	elseif (x <= 6.2e-93)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.5e-194], x, If[LessEqual[x, 6.2e-93], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.50000000000000019e-194 or 6.19999999999999999e-93 < 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 62.5%

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

   if -6.50000000000000019e-194 < x < 6.19999999999999999e-93

   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 55.8%

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

   6. Taylor expanded in y around inf

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

      1. distribute-lft-in N/A

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

      2. *-commutative N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. unpow2 N/A

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

      9. associate-*r* N/A

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

      10. lft-mult-inverse N/A

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

      11. distribute-rgt-in N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

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

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

      17. +-commutative N/A

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

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

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

      24. *-commutative N/A

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

      25. *-lowering-*.f64 23.3

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

   8. Simplified 23.3%

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

   9. Taylor expanded in y around 0

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

   11. Simplified 24.3%

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

Alternative 13: 43.2% 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 51.4%

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

Reproduce

herbie shell --seed 2024195 
(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))))