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

Percentage Accurate: 99.9% → 99.9%

Time: 9.1s

Alternatives: 14

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 71.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -4 \cdot 10^{+169}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-134}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-257}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+104}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -4e+169)
     t_0
     (if (<= z -1.75e-134)
       (+ x z)
       (if (<= z -4.2e-257) (sin y) (if (<= z 1.12e+104) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -4e+169) {
		tmp = t_0;
	} else if (z <= -1.75e-134) {
		tmp = x + z;
	} else if (z <= -4.2e-257) {
		tmp = sin(y);
	} else if (z <= 1.12e+104) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-4d+169)) then
        tmp = t_0
    else if (z <= (-1.75d-134)) then
        tmp = x + z
    else if (z <= (-4.2d-257)) then
        tmp = sin(y)
    else if (z <= 1.12d+104) then
        tmp = x + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -4e+169) {
		tmp = t_0;
	} else if (z <= -1.75e-134) {
		tmp = x + z;
	} else if (z <= -4.2e-257) {
		tmp = Math.sin(y);
	} else if (z <= 1.12e+104) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -4e+169:
		tmp = t_0
	elif z <= -1.75e-134:
		tmp = x + z
	elif z <= -4.2e-257:
		tmp = math.sin(y)
	elif z <= 1.12e+104:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -4e+169)
		tmp = t_0;
	elseif (z <= -1.75e-134)
		tmp = Float64(x + z);
	elseif (z <= -4.2e-257)
		tmp = sin(y);
	elseif (z <= 1.12e+104)
		tmp = Float64(x + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -4e+169)
		tmp = t_0;
	elseif (z <= -1.75e-134)
		tmp = x + z;
	elseif (z <= -4.2e-257)
		tmp = sin(y);
	elseif (z <= 1.12e+104)
		tmp = x + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+169], t$95$0, If[LessEqual[z, -1.75e-134], N[(x + z), $MachinePrecision], If[LessEqual[z, -4.2e-257], N[Sin[y], $MachinePrecision], If[LessEqual[z, 1.12e+104], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999974e169 or 1.12000000000000003e104 < 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right) \]

      2. cos-lowering-cos.f64 83.3%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right) \]

   5. Simplified 83.3%

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

   if -3.99999999999999974e169 < z < -1.7499999999999999e-134 or -4.2000000000000002e-257 < z < 1.12000000000000003e104

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 74.8%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 74.8%

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

   if -1.7499999999999999e-134 < z < -4.2000000000000002e-257

   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

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

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

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 96.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 96.4%

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

   6. Taylor expanded in x around 0

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

      1. sin-lowering-sin.f64 78.7%

         \[\leadsto \mathsf{sin.f64}\left(y\right) \]

   8. Simplified 78.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-134}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-257}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+104}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+76}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -165:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 1.05:\\ \;\;\;\;\left(x + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right) + \left(z + \left(y \cdot \left(y \cdot z\right)\right) \cdot \left(-0.5 + y \cdot \left(y \cdot 0.041666666666666664\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= y -6.2e+76)
     t_0
     (if (<= y -165.0)
       (* z (cos y))
       (if (<= y 1.05)
         (+
          (+ x (* y (+ 1.0 (* y (* y -0.16666666666666666)))))
          (+ z (* (* y (* y z)) (+ -0.5 (* y (* y 0.041666666666666664))))))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (y <= -6.2e+76) {
		tmp = t_0;
	} else if (y <= -165.0) {
		tmp = z * cos(y);
	} else if (y <= 1.05) {
		tmp = (x + (y * (1.0 + (y * (y * -0.16666666666666666))))) + (z + ((y * (y * z)) * (-0.5 + (y * (y * 0.041666666666666664)))));
	} 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 = x + sin(y)
    if (y <= (-6.2d+76)) then
        tmp = t_0
    else if (y <= (-165.0d0)) then
        tmp = z * cos(y)
    else if (y <= 1.05d0) then
        tmp = (x + (y * (1.0d0 + (y * (y * (-0.16666666666666666d0)))))) + (z + ((y * (y * z)) * ((-0.5d0) + (y * (y * 0.041666666666666664d0)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.sin(y);
	double tmp;
	if (y <= -6.2e+76) {
		tmp = t_0;
	} else if (y <= -165.0) {
		tmp = z * Math.cos(y);
	} else if (y <= 1.05) {
		tmp = (x + (y * (1.0 + (y * (y * -0.16666666666666666))))) + (z + ((y * (y * z)) * (-0.5 + (y * (y * 0.041666666666666664)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.sin(y)
	tmp = 0
	if y <= -6.2e+76:
		tmp = t_0
	elif y <= -165.0:
		tmp = z * math.cos(y)
	elif y <= 1.05:
		tmp = (x + (y * (1.0 + (y * (y * -0.16666666666666666))))) + (z + ((y * (y * z)) * (-0.5 + (y * (y * 0.041666666666666664)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + sin(y))
	tmp = 0.0
	if (y <= -6.2e+76)
		tmp = t_0;
	elseif (y <= -165.0)
		tmp = Float64(z * cos(y));
	elseif (y <= 1.05)
		tmp = Float64(Float64(x + Float64(y * Float64(1.0 + Float64(y * Float64(y * -0.16666666666666666))))) + Float64(z + Float64(Float64(y * Float64(y * z)) * Float64(-0.5 + Float64(y * Float64(y * 0.041666666666666664))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + sin(y);
	tmp = 0.0;
	if (y <= -6.2e+76)
		tmp = t_0;
	elseif (y <= -165.0)
		tmp = z * cos(y);
	elseif (y <= 1.05)
		tmp = (x + (y * (1.0 + (y * (y * -0.16666666666666666))))) + (z + ((y * (y * z)) * (-0.5 + (y * (y * 0.041666666666666664)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+76], t$95$0, If[LessEqual[y, -165.0], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05], N[(N[(x + N[(y * N[(1.0 + N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z + N[(N[(y * N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(-0.5 + N[(y * N[(y * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000023e76 or 1.05000000000000004 < y

   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

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

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

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 67.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 67.7%

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

   if -6.20000000000000023e76 < y < -165

   1. Initial program 99.6%

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

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right) \]

      2. cos-lowering-cos.f64 73.3%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right) \]

   5. Simplified 73.3%

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

   if -165 < y < 1.05000000000000004

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x + y \cdot \left(1 + \frac{-1}{6} \cdot {y}^{2}\right)\right)}, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(y \cdot \left(1 + \frac{-1}{6} \cdot {y}^{2}\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{cos.f64}\left(y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(1 + \frac{-1}{6} \cdot {y}^{2}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(\frac{-1}{6} \cdot {y}^{2}\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(\left(\frac{-1}{6} \cdot y\right) \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(y \cdot \left(\frac{-1}{6} \cdot y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(\frac{-1}{6} \cdot y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(y \cdot \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

      9. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \color{blue}{\left(z + {y}^{2} \cdot \left(\frac{-1}{2} \cdot z + \frac{1}{24} \cdot \left({y}^{2} \cdot z\right)\right)\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \color{blue}{\left({y}^{2} \cdot \left(\frac{-1}{2} \cdot z + \frac{1}{24} \cdot \left({y}^{2} \cdot z\right)\right)\right)}\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \left({y}^{2} \cdot \left(\frac{-1}{2} \cdot z\right) + \color{blue}{{y}^{2} \cdot \left(\frac{1}{24} \cdot \left({y}^{2} \cdot z\right)\right)}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \left({y}^{2} \cdot \left(z \cdot \frac{-1}{2}\right) + {y}^{\color{blue}{2}} \cdot \left(\frac{1}{24} \cdot \left({y}^{2} \cdot z\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \left(\left({y}^{2} \cdot z\right) \cdot \frac{-1}{2} + \color{blue}{{y}^{2}} \cdot \left(\frac{1}{24} \cdot \left({y}^{2} \cdot z\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \left(\frac{-1}{2} \cdot \left({y}^{2} \cdot z\right) + \color{blue}{{y}^{2}} \cdot \left(\frac{1}{24} \cdot \left({y}^{2} \cdot z\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \left(\frac{-1}{2} \cdot \left({y}^{2} \cdot z\right) + \left({y}^{2} \cdot \frac{1}{24}\right) \cdot \color{blue}{\left({y}^{2} \cdot z\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \left(\frac{-1}{2} \cdot \left({y}^{2} \cdot z\right) + \left(\frac{1}{24} \cdot {y}^{2}\right) \cdot \left(\color{blue}{{y}^{2}} \cdot z\right)\right)\right)\right) \]

      8. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \left(\left({y}^{2} \cdot z\right) \cdot \color{blue}{\left(\frac{-1}{2} + \frac{1}{24} \cdot {y}^{2}\right)}\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \left(\left({y}^{2} \cdot z\right) \cdot \left(\frac{1}{24} \cdot {y}^{2} + \color{blue}{\frac{-1}{2}}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\left({y}^{2} \cdot z\right), \color{blue}{\left(\frac{1}{24} \cdot {y}^{2} + \frac{-1}{2}\right)}\right)\right)\right) \]

      11. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\left(\left(y \cdot y\right) \cdot z\right), \left(\color{blue}{\frac{1}{24}} \cdot {y}^{2} + \frac{-1}{2}\right)\right)\right)\right) \]

      12. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\left(y \cdot \left(y \cdot z\right)\right), \left(\color{blue}{\frac{1}{24} \cdot {y}^{2}} + \frac{-1}{2}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(y \cdot z\right)\right), \left(\color{blue}{\frac{1}{24} \cdot {y}^{2}} + \frac{-1}{2}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, z\right)\right), \left(\frac{1}{24} \cdot \color{blue}{{y}^{2}} + \frac{-1}{2}\right)\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, z\right)\right), \left(\frac{-1}{2} + \color{blue}{\frac{1}{24} \cdot {y}^{2}}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{-1}{2}, \color{blue}{\left(\frac{1}{24} \cdot {y}^{2}\right)}\right)\right)\right)\right) \]

      17. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{-1}{2}, \left(\frac{1}{24} \cdot \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

      18. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{-1}{2}, \left(\left(\frac{1}{24} \cdot y\right) \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{-1}{2}, \left(y \cdot \color{blue}{\left(\frac{1}{24} \cdot y\right)}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{24} \cdot y\right)}\right)\right)\right)\right)\right) \]

      21. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\frac{1}{24}}\right)\right)\right)\right)\right)\right) \]

      22. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\frac{1}{24}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 100.0%

      \[\leadsto \left(x + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right) + \color{blue}{\left(z + \left(y \cdot \left(y \cdot z\right)\right) \cdot \left(-0.5 + y \cdot \left(y \cdot 0.041666666666666664\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+76}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;y \leq -165:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 1.05:\\ \;\;\;\;\left(x + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right) + \left(z + \left(y \cdot \left(y \cdot z\right)\right) \cdot \left(-0.5 + y \cdot \left(y \cdot 0.041666666666666664\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -1.25:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.9:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (cos y)))))
   (if (<= z -1.25) t_0 (if (<= z 1.9) (+ z (+ x (sin y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z * cos(y));
	double tmp;
	if (z <= -1.25) {
		tmp = t_0;
	} else if (z <= 1.9) {
		tmp = z + (x + sin(y));
	} 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 = x + (z * cos(y))
    if (z <= (-1.25d0)) then
        tmp = t_0
    else if (z <= 1.9d0) then
        tmp = z + (x + sin(y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (z * Math.cos(y));
	double tmp;
	if (z <= -1.25) {
		tmp = t_0;
	} else if (z <= 1.9) {
		tmp = z + (x + Math.sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z * math.cos(y))
	tmp = 0
	if z <= -1.25:
		tmp = t_0
	elif z <= 1.9:
		tmp = z + (x + math.sin(y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(z * cos(y)))
	tmp = 0.0
	if (z <= -1.25)
		tmp = t_0;
	elseif (z <= 1.9)
		tmp = Float64(z + Float64(x + sin(y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (z * cos(y));
	tmp = 0.0;
	if (z <= -1.25)
		tmp = t_0;
	elseif (z <= 1.9)
		tmp = z + (x + sin(y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25], t$95$0, If[LessEqual[z, 1.9], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25 or 1.8999999999999999 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 97.6%

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

   if -1.25 < z < 1.8999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \color{blue}{z}\right) \]
   4. Step-by-step derivation

   5. Simplified 99.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25:\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{elif}\;z \leq 1.9:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{-37}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-81}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (cos y)))))
   (if (<= z -6.8e-37) t_0 (if (<= z 1.9e-81) (+ x (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z * cos(y));
	double tmp;
	if (z <= -6.8e-37) {
		tmp = t_0;
	} else if (z <= 1.9e-81) {
		tmp = x + sin(y);
	} 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 = x + (z * cos(y))
    if (z <= (-6.8d-37)) then
        tmp = t_0
    else if (z <= 1.9d-81) then
        tmp = x + sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (z * Math.cos(y));
	double tmp;
	if (z <= -6.8e-37) {
		tmp = t_0;
	} else if (z <= 1.9e-81) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z * math.cos(y))
	tmp = 0
	if z <= -6.8e-37:
		tmp = t_0
	elif z <= 1.9e-81:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(z * cos(y)))
	tmp = 0.0
	if (z <= -6.8e-37)
		tmp = t_0;
	elseif (z <= 1.9e-81)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (z * cos(y));
	tmp = 0.0;
	if (z <= -6.8e-37)
		tmp = t_0;
	elseif (z <= 1.9e-81)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e-37], t$95$0, If[LessEqual[z, 1.9e-81], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000037e-37 or 1.8999999999999999e-81 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 94.9%

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

   if -6.80000000000000037e-37 < z < 1.8999999999999999e-81

   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

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

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

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 92.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 92.7%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-37}:\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-81}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -130:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+41}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666 + z \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -130.0)
   (+ x z)
   (if (<= y 2.8e+41)
     (+ (+ x z) (* y (+ 1.0 (* y (+ (* y -0.16666666666666666) (* z -0.5))))))
     (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -130.0) {
		tmp = x + z;
	} else if (y <= 2.8e+41) {
		tmp = (x + z) + (y * (1.0 + (y * ((y * -0.16666666666666666) + (z * -0.5)))));
	} else {
		tmp = sin(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-130.0d0)) then
        tmp = x + z
    else if (y <= 2.8d+41) then
        tmp = (x + z) + (y * (1.0d0 + (y * ((y * (-0.16666666666666666d0)) + (z * (-0.5d0))))))
    else
        tmp = sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -130.0) {
		tmp = x + z;
	} else if (y <= 2.8e+41) {
		tmp = (x + z) + (y * (1.0 + (y * ((y * -0.16666666666666666) + (z * -0.5)))));
	} else {
		tmp = Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -130.0:
		tmp = x + z
	elif y <= 2.8e+41:
		tmp = (x + z) + (y * (1.0 + (y * ((y * -0.16666666666666666) + (z * -0.5)))))
	else:
		tmp = math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -130.0)
		tmp = Float64(x + z);
	elseif (y <= 2.8e+41)
		tmp = Float64(Float64(x + z) + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(y * -0.16666666666666666) + Float64(z * -0.5))))));
	else
		tmp = sin(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -130.0)
		tmp = x + z;
	elseif (y <= 2.8e+41)
		tmp = (x + z) + (y * (1.0 + (y * ((y * -0.16666666666666666) + (z * -0.5)))));
	else
		tmp = sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -130.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.8e+41], N[(N[(x + z), $MachinePrecision] + N[(y * N[(1.0 + N[(y * N[(N[(y * -0.16666666666666666), $MachinePrecision] + N[(z * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sin[y], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -130

   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

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

      2. +-lowering-+.f64 44.4%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 44.4%

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

   if -130 < y < 2.7999999999999999e41

   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. associate-+r+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x + z\right), \color{blue}{\left(y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z + x\right), \left(\color{blue}{y} \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\color{blue}{y} \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \color{blue}{\left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-1}{2} \cdot z\right), \color{blue}{\left(\frac{-1}{6} \cdot y\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \frac{-1}{2}\right), \left(\color{blue}{\frac{-1}{6}} \cdot y\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \left(\color{blue}{\frac{-1}{6}} \cdot y\right)\right)\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \left(y \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 98.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \mathsf{*.f64}\left(y, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   5. Simplified 98.0%

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

   if 2.7999999999999999e41 < y

   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

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

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

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 62.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 62.7%

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

   6. Taylor expanded in x around 0

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

      1. sin-lowering-sin.f64 41.4%

         \[\leadsto \mathsf{sin.f64}\left(y\right) \]

   8. Simplified 41.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -130:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+41}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666 + z \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -180:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 17000000000000:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666 + z \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -180.0)
   (+ x z)
   (if (<= y 17000000000000.0)
     (+ (+ x z) (* y (+ 1.0 (* y (+ (* y -0.16666666666666666) (* z -0.5))))))
     (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -180.0) {
		tmp = x + z;
	} else if (y <= 17000000000000.0) {
		tmp = (x + z) + (y * (1.0 + (y * ((y * -0.16666666666666666) + (z * -0.5)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-180.0d0)) then
        tmp = x + z
    else if (y <= 17000000000000.0d0) then
        tmp = (x + z) + (y * (1.0d0 + (y * ((y * (-0.16666666666666666d0)) + (z * (-0.5d0))))))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -180.0) {
		tmp = x + z;
	} else if (y <= 17000000000000.0) {
		tmp = (x + z) + (y * (1.0 + (y * ((y * -0.16666666666666666) + (z * -0.5)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -180.0:
		tmp = x + z
	elif y <= 17000000000000.0:
		tmp = (x + z) + (y * (1.0 + (y * ((y * -0.16666666666666666) + (z * -0.5)))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -180.0)
		tmp = Float64(x + z);
	elseif (y <= 17000000000000.0)
		tmp = Float64(Float64(x + z) + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(y * -0.16666666666666666) + Float64(z * -0.5))))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -180.0)
		tmp = x + z;
	elseif (y <= 17000000000000.0)
		tmp = (x + z) + (y * (1.0 + (y * ((y * -0.16666666666666666) + (z * -0.5)))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -180.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 17000000000000.0], N[(N[(x + z), $MachinePrecision] + N[(y * N[(1.0 + N[(y * N[(N[(y * -0.16666666666666666), $MachinePrecision] + N[(z * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -180 or 1.7e13 < 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

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

      2. +-lowering-+.f64 37.5%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 37.5%

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

   if -180 < y < 1.7e13

   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. associate-+r+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x + z\right), \color{blue}{\left(y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z + x\right), \left(\color{blue}{y} \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\color{blue}{y} \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \color{blue}{\left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-1}{2} \cdot z\right), \color{blue}{\left(\frac{-1}{6} \cdot y\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \frac{-1}{2}\right), \left(\color{blue}{\frac{-1}{6}} \cdot y\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \left(\color{blue}{\frac{-1}{6}} \cdot y\right)\right)\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \left(y \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), \mathsf{*.f64}\left(y, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   5. Simplified 99.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -180:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 17000000000000:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666 + z \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -160:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1200000000000:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 + y \cdot \left(y \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -160.0)
   (+ x z)
   (if (<= y 1200000000000.0)
     (+ (+ x y) (* z (+ 1.0 (* y (* y -0.5)))))
     (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -160.0) {
		tmp = x + z;
	} else if (y <= 1200000000000.0) {
		tmp = (x + y) + (z * (1.0 + (y * (y * -0.5))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-160.0d0)) then
        tmp = x + z
    else if (y <= 1200000000000.0d0) then
        tmp = (x + y) + (z * (1.0d0 + (y * (y * (-0.5d0)))))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -160.0) {
		tmp = x + z;
	} else if (y <= 1200000000000.0) {
		tmp = (x + y) + (z * (1.0 + (y * (y * -0.5))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -160.0:
		tmp = x + z
	elif y <= 1200000000000.0:
		tmp = (x + y) + (z * (1.0 + (y * (y * -0.5))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -160.0)
		tmp = Float64(x + z);
	elseif (y <= 1200000000000.0)
		tmp = Float64(Float64(x + y) + Float64(z * Float64(1.0 + Float64(y * Float64(y * -0.5)))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -160.0)
		tmp = x + z;
	elseif (y <= 1200000000000.0)
		tmp = (x + y) + (z * (1.0 + (y * (y * -0.5))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -160.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 1200000000000.0], N[(N[(x + y), $MachinePrecision] + N[(z * N[(1.0 + N[(y * N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -160 or 1.2e12 < 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

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

      2. +-lowering-+.f64 37.5%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 37.5%

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

   if -160 < y < 1.2e12

   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. distribute-rgt-in N/A

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

      2. *-lft-identity N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. unpow2 N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)}\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y + x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \left({y}^{2} \cdot \color{blue}{z}\right)\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(1 \cdot z + \color{blue}{\frac{-1}{2}} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(1 \cdot z + \left(\frac{-1}{2} \cdot {y}^{2}\right) \cdot \color{blue}{z}\right)\right) \]

      18. distribute-rgt-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z \cdot \color{blue}{\left(1 + \frac{-1}{2} \cdot {y}^{2}\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 + \frac{-1}{2} \cdot {y}^{2}\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{2} \cdot {y}^{2}\right)}\right)\right)\right) \]

      21. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \left(\frac{-1}{2} \cdot \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

   5. Simplified 99.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -160:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1200000000000:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 + y \cdot \left(y \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1200000000000:\\ \;\;\;\;z + \left(x + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7000.0)
   (+ x z)
   (if (<= y 1200000000000.0)
     (+ z (+ x (* y (+ 1.0 (* y (* y -0.16666666666666666))))))
     (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7000.0) {
		tmp = x + z;
	} else if (y <= 1200000000000.0) {
		tmp = z + (x + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-7000.0d0)) then
        tmp = x + z
    else if (y <= 1200000000000.0d0) then
        tmp = z + (x + (y * (1.0d0 + (y * (y * (-0.16666666666666666d0))))))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7000.0) {
		tmp = x + z;
	} else if (y <= 1200000000000.0) {
		tmp = z + (x + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7000.0:
		tmp = x + z
	elif y <= 1200000000000.0:
		tmp = z + (x + (y * (1.0 + (y * (y * -0.16666666666666666)))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7000.0)
		tmp = Float64(x + z);
	elseif (y <= 1200000000000.0)
		tmp = Float64(z + Float64(x + Float64(y * Float64(1.0 + Float64(y * Float64(y * -0.16666666666666666))))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7000.0)
		tmp = x + z;
	elseif (y <= 1200000000000.0)
		tmp = z + (x + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 1200000000000.0], N[(z + N[(x + N[(y * N[(1.0 + N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7e3 or 1.2e12 < 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

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

      2. +-lowering-+.f64 37.7%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 37.7%

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

   if -7e3 < y < 1.2e12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x + y \cdot \left(1 + \frac{-1}{6} \cdot {y}^{2}\right)\right)}, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(y \cdot \left(1 + \frac{-1}{6} \cdot {y}^{2}\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{cos.f64}\left(y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(1 + \frac{-1}{6} \cdot {y}^{2}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(\frac{-1}{6} \cdot {y}^{2}\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(\left(\frac{-1}{6} \cdot y\right) \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(y \cdot \left(\frac{-1}{6} \cdot y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(\frac{-1}{6} \cdot y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(y \cdot \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

      9. *-lowering-*.f64 99.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   5. Simplified 99.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \frac{-1}{6}\right)\right)\right)\right)\right), \color{blue}{z}\right) \]
   7. Step-by-step derivation

   8. Simplified 98.4%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1200000000000:\\ \;\;\;\;z + \left(x + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+46}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.2:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7e+46) (+ x z) (if (<= y 3.2) (+ z (+ x y)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+46) {
		tmp = x + z;
	} else if (y <= 3.2) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-7d+46)) then
        tmp = x + z
    else if (y <= 3.2d0) then
        tmp = z + (x + y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+46) {
		tmp = x + z;
	} else if (y <= 3.2) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7e+46:
		tmp = x + z
	elif y <= 3.2:
		tmp = z + (x + y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7e+46)
		tmp = Float64(x + z);
	elseif (y <= 3.2)
		tmp = Float64(z + Float64(x + y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7e+46)
		tmp = x + z;
	elseif (y <= 3.2)
		tmp = z + (x + y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7e+46], N[(x + z), $MachinePrecision], If[LessEqual[y, 3.2], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999997e46 or 3.2000000000000002 < 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

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

      2. +-lowering-+.f64 38.0%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 38.0%

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

   if -6.9999999999999997e46 < y < 3.2000000000000002

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + y\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(y + \color{blue}{x}\right)\right) \]

      5. +-lowering-+.f64 97.2%

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 97.2%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+46}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.2:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.8% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -75:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 130000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -75.0) x (if (<= x 130000000.0) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -75.0) {
		tmp = x;
	} else if (x <= 130000000.0) {
		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 <= (-75.0d0)) then
        tmp = x
    else if (x <= 130000000.0d0) 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 <= -75.0) {
		tmp = x;
	} else if (x <= 130000000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -75.0:
		tmp = x
	elif x <= 130000000.0:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -75.0)
		tmp = x;
	elseif (x <= 130000000.0)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -75.0)
		tmp = x;
	elseif (x <= 130000000.0)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -75.0], x, If[LessEqual[x, 130000000.0], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -75 or 1.3e8 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 80.6%

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

   if -75 < x < 1.3e8

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \color{blue}{z}\right) \]
   4. Step-by-step derivation

   5. Simplified 79.4%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 40.4%

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

Alternative 12: 44.7% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-133}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e-106) x (if (<= x 6.8e-133) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-106) {
		tmp = x;
	} else if (x <= 6.8e-133) {
		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 <= (-2.1d-106)) then
        tmp = x
    else if (x <= 6.8d-133) 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 <= -2.1e-106) {
		tmp = x;
	} else if (x <= 6.8e-133) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e-106:
		tmp = x
	elif x <= 6.8e-133:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e-106)
		tmp = x;
	elseif (x <= 6.8e-133)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e-106)
		tmp = x;
	elseif (x <= 6.8e-133)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e-106], x, If[LessEqual[x, 6.8e-133], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.10000000000000003e-106 or 6.80000000000000012e-133 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 57.9%

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

   if -2.10000000000000003e-106 < x < 6.80000000000000012e-133

   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. distribute-rgt-in N/A

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

      2. *-lft-identity N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. unpow2 N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(z + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)}\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y + x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\color{blue}{z} + \left(\frac{-1}{2} \cdot z\right) \cdot {y}^{2}\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z + \frac{-1}{2} \cdot \left({y}^{2} \cdot \color{blue}{z}\right)\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(1 \cdot z + \color{blue}{\frac{-1}{2}} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(1 \cdot z + \left(\frac{-1}{2} \cdot {y}^{2}\right) \cdot \color{blue}{z}\right)\right) \]

      18. distribute-rgt-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(z \cdot \color{blue}{\left(1 + \frac{-1}{2} \cdot {y}^{2}\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 + \frac{-1}{2} \cdot {y}^{2}\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{2} \cdot {y}^{2}\right)}\right)\right)\right) \]

      21. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(1, \left(\frac{-1}{2} \cdot \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

   5. Simplified 56.3%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 18.9%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   8. Simplified 18.9%

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

   9. Taylor expanded in y around inf

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

   11. Simplified 16.8%

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

Alternative 13: 66.8% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 64.9%

      \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

5. Simplified 64.9%

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

6. Final simplification 64.9%

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

Alternative 14: 42.5% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf

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

5. Simplified 40.7%

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

Reproduce

herbie shell --seed 2024152 
(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))))