Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.5% → 95.4%

Time: 8.6s

Alternatives: 12

Speedup: 0.8×

• 32.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + (y * z)) + (t * a)) + ((a * z) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + (y * z)) + (t * a)) + ((a * z) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 92.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + (y * z)) + (t * a)) + ((a * z) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + (y * z)) + (t * a)) + ((a * z) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+110}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a \cdot \left(t + z \cdot b\right)\right) + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1e+110)
   (+ x (* z (+ y (* a b))))
   (+ (+ x (* a (+ t (* z b)))) (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1e+110) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (a * (t + (z * b)))) + (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1d+110)) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = (x + (a * (t + (z * b)))) + (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1e+110) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (a * (t + (z * b)))) + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1e+110:
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = (x + (a * (t + (z * b)))) + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1e+110)
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(x + Float64(a * Float64(t + Float64(z * b)))) + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1e+110)
		tmp = x + (z * (y + (a * b)));
	else
		tmp = (x + (a * (t + (z * b)))) + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1e+110], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e110

   1. Initial program 71.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 80.6%

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

   3. Simplified 80.6%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

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

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

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

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

      7. *-lowering-*.f64 92.8%

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

   7. Simplified 92.8%

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

   if -1e110 < z

   1. Initial program 95.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 99.5%

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

   3. Simplified 99.5%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+110}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a \cdot \left(t + z \cdot b\right)\right) + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 37.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-103}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+72}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= a -5.4e+184)
     t_1
     (if (<= a -1.06e-103)
       (* a t)
       (if (<= a -4.6e-211)
         x
         (if (<= a 5e+72) (* z y) (if (<= a 1.6e+149) (* a t) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (a <= -5.4e+184) {
		tmp = t_1;
	} else if (a <= -1.06e-103) {
		tmp = a * t;
	} else if (a <= -4.6e-211) {
		tmp = x;
	} else if (a <= 5e+72) {
		tmp = z * y;
	} else if (a <= 1.6e+149) {
		tmp = a * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (a * b)
    if (a <= (-5.4d+184)) then
        tmp = t_1
    else if (a <= (-1.06d-103)) then
        tmp = a * t
    else if (a <= (-4.6d-211)) then
        tmp = x
    else if (a <= 5d+72) then
        tmp = z * y
    else if (a <= 1.6d+149) then
        tmp = a * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (a <= -5.4e+184) {
		tmp = t_1;
	} else if (a <= -1.06e-103) {
		tmp = a * t;
	} else if (a <= -4.6e-211) {
		tmp = x;
	} else if (a <= 5e+72) {
		tmp = z * y;
	} else if (a <= 1.6e+149) {
		tmp = a * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if a <= -5.4e+184:
		tmp = t_1
	elif a <= -1.06e-103:
		tmp = a * t
	elif a <= -4.6e-211:
		tmp = x
	elif a <= 5e+72:
		tmp = z * y
	elif a <= 1.6e+149:
		tmp = a * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (a <= -5.4e+184)
		tmp = t_1;
	elseif (a <= -1.06e-103)
		tmp = Float64(a * t);
	elseif (a <= -4.6e-211)
		tmp = x;
	elseif (a <= 5e+72)
		tmp = Float64(z * y);
	elseif (a <= 1.6e+149)
		tmp = Float64(a * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a * b);
	tmp = 0.0;
	if (a <= -5.4e+184)
		tmp = t_1;
	elseif (a <= -1.06e-103)
		tmp = a * t;
	elseif (a <= -4.6e-211)
		tmp = x;
	elseif (a <= 5e+72)
		tmp = z * y;
	elseif (a <= 1.6e+149)
		tmp = a * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e+184], t$95$1, If[LessEqual[a, -1.06e-103], N[(a * t), $MachinePrecision], If[LessEqual[a, -4.6e-211], x, If[LessEqual[a, 5e+72], N[(z * y), $MachinePrecision], If[LessEqual[a, 1.6e+149], N[(a * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.3999999999999998e184 or 1.6000000000000001e149 < a

   1. Initial program 77.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 93.4%

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

   3. Simplified 93.4%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{z} \]

      2. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot z \]

      3. associate-*r* N/A

         \[\leadsto b \cdot \color{blue}{\left(a \cdot z\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot z\right)}\right) \]

      5. *-lowering-*.f64 56.9%

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

   7. Simplified 56.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot z\right)} \]
   8. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot a\right) \cdot \color{blue}{z} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot a\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot b\right), z\right) \]

      4. *-lowering-*.f64 61.4%

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

   9. Applied egg-rr 61.4%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot z} \]

   if -5.3999999999999998e184 < a < -1.06000000000000004e-103 or 4.99999999999999992e72 < a < 1.6000000000000001e149

   1. Initial program 92.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 98.8%

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

   3. Simplified 98.8%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a \cdot t} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 42.1%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{t}\right) \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -1.06000000000000004e-103 < a < -4.59999999999999976e-211

   1. Initial program 100.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

   7. Simplified 91.0%

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

   if -4.59999999999999976e-211 < a < 4.99999999999999992e72

   1. Initial program 98.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 96.0%

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

   3. Simplified 96.0%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 48.4%

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

   7. Simplified 48.4%

      \[\leadsto \color{blue}{z \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+184}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-103}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+72}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+108}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-244}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+15}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.2e+108)
   (* a t)
   (if (<= t -7.5e-48)
     x
     (if (<= t 2.2e-244) (* a (* z b)) (if (<= t 6e+15) (* z y) (* a t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e+108) {
		tmp = a * t;
	} else if (t <= -7.5e-48) {
		tmp = x;
	} else if (t <= 2.2e-244) {
		tmp = a * (z * b);
	} else if (t <= 6e+15) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.2d+108)) then
        tmp = a * t
    else if (t <= (-7.5d-48)) then
        tmp = x
    else if (t <= 2.2d-244) then
        tmp = a * (z * b)
    else if (t <= 6d+15) then
        tmp = z * y
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e+108) {
		tmp = a * t;
	} else if (t <= -7.5e-48) {
		tmp = x;
	} else if (t <= 2.2e-244) {
		tmp = a * (z * b);
	} else if (t <= 6e+15) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.2e+108:
		tmp = a * t
	elif t <= -7.5e-48:
		tmp = x
	elif t <= 2.2e-244:
		tmp = a * (z * b)
	elif t <= 6e+15:
		tmp = z * y
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.2e+108)
		tmp = Float64(a * t);
	elseif (t <= -7.5e-48)
		tmp = x;
	elseif (t <= 2.2e-244)
		tmp = Float64(a * Float64(z * b));
	elseif (t <= 6e+15)
		tmp = Float64(z * y);
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.2e+108)
		tmp = a * t;
	elseif (t <= -7.5e-48)
		tmp = x;
	elseif (t <= 2.2e-244)
		tmp = a * (z * b);
	elseif (t <= 6e+15)
		tmp = z * y;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.2e+108], N[(a * t), $MachinePrecision], If[LessEqual[t, -7.5e-48], x, If[LessEqual[t, 2.2e-244], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+15], N[(z * y), $MachinePrecision], N[(a * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.20000000000000019e108 or 6e15 < t

   1. Initial program 91.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.2%

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

   3. Simplified 95.2%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a \cdot t} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 58.7%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{t}\right) \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -4.20000000000000019e108 < t < -7.50000000000000042e-48

   1. Initial program 89.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

   7. Simplified 45.7%

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

   if -7.50000000000000042e-48 < t < 2.19999999999999985e-244

   1. Initial program 91.7%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 98.3%

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

   3. Simplified 98.3%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{z} \]

      2. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot z \]

      3. associate-*r* N/A

         \[\leadsto b \cdot \color{blue}{\left(a \cdot z\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot z\right)}\right) \]

      5. *-lowering-*.f64 40.2%

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

   7. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto b \cdot \left(z \cdot \color{blue}{a}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{a} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot z\right), \color{blue}{a}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot b\right), a\right) \]

      5. *-lowering-*.f64 43.3%

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

   9. Applied egg-rr 43.3%

      \[\leadsto \color{blue}{\left(z \cdot b\right) \cdot a} \]

   if 2.19999999999999985e-244 < t < 6e15

   1. Initial program 91.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.1%

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

   3. Simplified 95.1%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 44.1%

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

   7. Simplified 44.1%

      \[\leadsto \color{blue}{z \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+108}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-244}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+15}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+109}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+15}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.2e+109)
   (* a t)
   (if (<= t -1.85e-48)
     x
     (if (<= t 2.25e-237) (* b (* z a)) (if (<= t 5.4e+15) (* z y) (* a t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.2e+109) {
		tmp = a * t;
	} else if (t <= -1.85e-48) {
		tmp = x;
	} else if (t <= 2.25e-237) {
		tmp = b * (z * a);
	} else if (t <= 5.4e+15) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6.2d+109)) then
        tmp = a * t
    else if (t <= (-1.85d-48)) then
        tmp = x
    else if (t <= 2.25d-237) then
        tmp = b * (z * a)
    else if (t <= 5.4d+15) then
        tmp = z * y
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.2e+109) {
		tmp = a * t;
	} else if (t <= -1.85e-48) {
		tmp = x;
	} else if (t <= 2.25e-237) {
		tmp = b * (z * a);
	} else if (t <= 5.4e+15) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.2e+109:
		tmp = a * t
	elif t <= -1.85e-48:
		tmp = x
	elif t <= 2.25e-237:
		tmp = b * (z * a)
	elif t <= 5.4e+15:
		tmp = z * y
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.2e+109)
		tmp = Float64(a * t);
	elseif (t <= -1.85e-48)
		tmp = x;
	elseif (t <= 2.25e-237)
		tmp = Float64(b * Float64(z * a));
	elseif (t <= 5.4e+15)
		tmp = Float64(z * y);
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.2e+109)
		tmp = a * t;
	elseif (t <= -1.85e-48)
		tmp = x;
	elseif (t <= 2.25e-237)
		tmp = b * (z * a);
	elseif (t <= 5.4e+15)
		tmp = z * y;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.2e+109], N[(a * t), $MachinePrecision], If[LessEqual[t, -1.85e-48], x, If[LessEqual[t, 2.25e-237], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+15], N[(z * y), $MachinePrecision], N[(a * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.19999999999999985e109 or 5.4e15 < t

   1. Initial program 91.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.2%

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

   3. Simplified 95.2%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a \cdot t} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 58.7%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{t}\right) \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -6.19999999999999985e109 < t < -1.8499999999999999e-48

   1. Initial program 89.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

   7. Simplified 45.7%

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

   if -1.8499999999999999e-48 < t < 2.25000000000000005e-237

   1. Initial program 91.7%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 98.3%

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

   3. Simplified 98.3%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{z} \]

      2. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot z \]

      3. associate-*r* N/A

         \[\leadsto b \cdot \color{blue}{\left(a \cdot z\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot z\right)}\right) \]

      5. *-lowering-*.f64 40.2%

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

   7. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot z\right)} \]

   if 2.25000000000000005e-237 < t < 5.4e15

   1. Initial program 91.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.1%

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

   3. Simplified 95.1%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 44.1%

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

   7. Simplified 44.1%

      \[\leadsto \color{blue}{z \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+109}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+15}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-132}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ y (* a b))))))
   (if (<= z -2.35e-80) t_1 (if (<= z 1.7e-132) (+ x (* a t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -2.35e-80) {
		tmp = t_1;
	} else if (z <= 1.7e-132) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y + (a * b)))
    if (z <= (-2.35d-80)) then
        tmp = t_1
    else if (z <= 1.7d-132) then
        tmp = x + (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -2.35e-80) {
		tmp = t_1;
	} else if (z <= 1.7e-132) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y + (a * b)))
	tmp = 0
	if z <= -2.35e-80:
		tmp = t_1
	elif z <= 1.7e-132:
		tmp = x + (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y + Float64(a * b))))
	tmp = 0.0
	if (z <= -2.35e-80)
		tmp = t_1;
	elseif (z <= 1.7e-132)
		tmp = Float64(x + Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y + (a * b)));
	tmp = 0.0;
	if (z <= -2.35e-80)
		tmp = t_1;
	elseif (z <= 1.7e-132)
		tmp = x + (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e-80], t$95$1, If[LessEqual[z, 1.7e-132], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.34999999999999986e-80 or 1.69999999999999991e-132 < z

   1. Initial program 87.9%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 94.8%

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

   3. Simplified 94.8%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

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

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

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

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

      7. *-lowering-*.f64 88.1%

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

   7. Simplified 88.1%

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

   if -2.34999999999999986e-80 < z < 1.69999999999999991e-132

   1. Initial program 98.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 88.0%

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

   7. Simplified 88.0%

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

Alternative 6: 39.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+108}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+15}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.4e+108)
   (* a t)
   (if (<= t -3.5e-47) x (if (<= t 6.9e+15) (* z y) (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.4e+108) {
		tmp = a * t;
	} else if (t <= -3.5e-47) {
		tmp = x;
	} else if (t <= 6.9e+15) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.4d+108)) then
        tmp = a * t
    else if (t <= (-3.5d-47)) then
        tmp = x
    else if (t <= 6.9d+15) then
        tmp = z * y
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.4e+108) {
		tmp = a * t;
	} else if (t <= -3.5e-47) {
		tmp = x;
	} else if (t <= 6.9e+15) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.4e+108:
		tmp = a * t
	elif t <= -3.5e-47:
		tmp = x
	elif t <= 6.9e+15:
		tmp = z * y
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.4e+108)
		tmp = Float64(a * t);
	elseif (t <= -3.5e-47)
		tmp = x;
	elseif (t <= 6.9e+15)
		tmp = Float64(z * y);
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.4e+108)
		tmp = a * t;
	elseif (t <= -3.5e-47)
		tmp = x;
	elseif (t <= 6.9e+15)
		tmp = z * y;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.4e+108], N[(a * t), $MachinePrecision], If[LessEqual[t, -3.5e-47], x, If[LessEqual[t, 6.9e+15], N[(z * y), $MachinePrecision], N[(a * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4000000000000003e108 or 6.9e15 < t

   1. Initial program 91.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.2%

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

   3. Simplified 95.2%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a \cdot t} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 58.7%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{t}\right) \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -4.4000000000000003e108 < t < -3.4999999999999998e-47

   1. Initial program 89.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

   7. Simplified 45.7%

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

   if -3.4999999999999998e-47 < t < 6.9e15

   1. Initial program 91.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 96.8%

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

   3. Simplified 96.8%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 38.3%

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

   7. Simplified 38.3%

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

Alternative 7: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-23}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -1.55e-7) t_1 (if (<= z 6.5e-23) (+ x (* a t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -1.55e-7) {
		tmp = t_1;
	} else if (z <= 6.5e-23) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y + (a * b))
    if (z <= (-1.55d-7)) then
        tmp = t_1
    else if (z <= 6.5d-23) then
        tmp = x + (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -1.55e-7) {
		tmp = t_1;
	} else if (z <= 6.5e-23) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (a * b))
	tmp = 0
	if z <= -1.55e-7:
		tmp = t_1
	elif z <= 6.5e-23:
		tmp = x + (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -1.55e-7)
		tmp = t_1;
	elseif (z <= 6.5e-23)
		tmp = Float64(x + Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -1.55e-7)
		tmp = t_1;
	elseif (z <= 6.5e-23)
		tmp = x + (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e-7], t$95$1, If[LessEqual[z, 6.5e-23], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e-7 or 6.5e-23 < z

   1. Initial program 84.2%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 93.2%

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

   3. Simplified 93.2%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y + a \cdot b\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      3. *-lowering-*.f64 77.9%

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

   7. Simplified 77.9%

      \[\leadsto \color{blue}{z \cdot \left(y + a \cdot b\right)} \]

   if -1.55e-7 < z < 6.5e-23

   1. Initial program 98.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 79.4%

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

   7. Simplified 79.4%

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

Alternative 8: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+68}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -3.4e+66) t_1 (if (<= a 2.6e+68) (+ x (* z y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -3.4e+66) {
		tmp = t_1;
	} else if (a <= 2.6e+68) {
		tmp = x + (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t + (z * b))
    if (a <= (-3.4d+66)) then
        tmp = t_1
    else if (a <= 2.6d+68) then
        tmp = x + (z * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -3.4e+66) {
		tmp = t_1;
	} else if (a <= 2.6e+68) {
		tmp = x + (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -3.4e+66:
		tmp = t_1
	elif a <= 2.6e+68:
		tmp = x + (z * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -3.4e+66)
		tmp = t_1;
	elseif (a <= 2.6e+68)
		tmp = Float64(x + Float64(z * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -3.4e+66)
		tmp = t_1;
	elseif (a <= 2.6e+68)
		tmp = x + (z * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+66], t$95$1, If[LessEqual[a, 2.6e+68], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.4000000000000003e66 or 2.5999999999999998e68 < a

   1. Initial program 82.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.3%

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

   3. Simplified 95.3%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(t + b \cdot z\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(t + b \cdot z\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{\left(b \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 81.4%

      \[\leadsto \color{blue}{a \cdot \left(t + b \cdot z\right)} \]

   if -3.4000000000000003e66 < a < 2.5999999999999998e68

   1. Initial program 97.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 97.4%

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

   3. Simplified 97.4%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

   7. Simplified 75.5%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+68}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot y\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-31}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z y))))
   (if (<= z -6.5e-60) t_1 (if (<= z 8e-31) (+ x (* a t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * y);
	double tmp;
	if (z <= -6.5e-60) {
		tmp = t_1;
	} else if (z <= 8e-31) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * y)
    if (z <= (-6.5d-60)) then
        tmp = t_1
    else if (z <= 8d-31) then
        tmp = x + (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * y);
	double tmp;
	if (z <= -6.5e-60) {
		tmp = t_1;
	} else if (z <= 8e-31) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * y)
	tmp = 0
	if z <= -6.5e-60:
		tmp = t_1
	elif z <= 8e-31:
		tmp = x + (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * y))
	tmp = 0.0
	if (z <= -6.5e-60)
		tmp = t_1;
	elseif (z <= 8e-31)
		tmp = Float64(x + Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * y);
	tmp = 0.0;
	if (z <= -6.5e-60)
		tmp = t_1;
	elseif (z <= 8e-31)
		tmp = x + (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e-60], t$95$1, If[LessEqual[z, 8e-31], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999995e-60 or 8.000000000000001e-31 < z

   1. Initial program 85.8%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 93.9%

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

   3. Simplified 93.9%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

   7. Simplified 59.4%

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

   if -6.49999999999999995e-60 < z < 8.000000000000001e-31

   1. Initial program 98.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 81.9%

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

   7. Simplified 81.9%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-60}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-31}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+133}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-19}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.22e+133) (* z y) (if (<= z 5.4e-19) (+ x (* a t)) (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.22e+133) {
		tmp = z * y;
	} else if (z <= 5.4e-19) {
		tmp = x + (a * t);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.22d+133)) then
        tmp = z * y
    else if (z <= 5.4d-19) then
        tmp = x + (a * t)
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.22e+133) {
		tmp = z * y;
	} else if (z <= 5.4e-19) {
		tmp = x + (a * t);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.22e+133:
		tmp = z * y
	elif z <= 5.4e-19:
		tmp = x + (a * t)
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.22e+133)
		tmp = Float64(z * y);
	elseif (z <= 5.4e-19)
		tmp = Float64(x + Float64(a * t));
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.22e+133)
		tmp = z * y;
	elseif (z <= 5.4e-19)
		tmp = x + (a * t);
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.22e+133], N[(z * y), $MachinePrecision], If[LessEqual[z, 5.4e-19], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2199999999999999e133 or 5.4000000000000002e-19 < z

   1. Initial program 81.8%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 91.9%

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

   3. Simplified 91.9%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 48.3%

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

   7. Simplified 48.3%

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

   if -1.2199999999999999e133 < z < 5.4000000000000002e-19

   1. Initial program 97.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 70.9%

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

   7. Simplified 70.9%

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

Alternative 11: 39.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+108}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.2e+108) (* a t) (if (<= t 1.4e+23) x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e+108) {
		tmp = a * t;
	} else if (t <= 1.4e+23) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.2d+108)) then
        tmp = a * t
    else if (t <= 1.4d+23) then
        tmp = x
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e+108) {
		tmp = a * t;
	} else if (t <= 1.4e+23) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.2e+108:
		tmp = a * t
	elif t <= 1.4e+23:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.2e+108)
		tmp = Float64(a * t);
	elseif (t <= 1.4e+23)
		tmp = x;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.2e+108)
		tmp = a * t;
	elseif (t <= 1.4e+23)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.2e+108], N[(a * t), $MachinePrecision], If[LessEqual[t, 1.4e+23], x, N[(a * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.20000000000000019e108 or 1.4e23 < t

   1. Initial program 91.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.2%

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

   3. Simplified 95.2%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a \cdot t} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 59.3%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{t}\right) \]

   7. Simplified 59.3%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -4.20000000000000019e108 < t < 1.4e23

   1. Initial program 91.2%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 97.4%

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

   3. Simplified 97.4%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

   7. Simplified 32.3%

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

Alternative 12: 26.0% accurate, 15.0× speedup

Math

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

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 91.2%

   \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
2. Step-by-step derivation

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

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

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

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

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

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

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

   7. *-commutative N/A

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

   8. associate-*l* N/A

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

   9. distribute-lft-out N/A

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

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

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

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

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

   12. *-lowering-*.f64 96.5%

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

3. Simplified 96.5%

   \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

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

7. Simplified 25.9%

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

Developer Target 1: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))