Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.2% → 96.2%

Time: 12.4s

Alternatives: 14

Speedup: 0.7×

• 32.4% 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: 92.2% 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: 96.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+243} \lor \neg \left(a \leq 10^{+130}\right):\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.45e+243) (not (<= a 1e+130)))
   (+ (fma y z x) (* a (+ t (* z b))))
   (+ x (+ (* a t) (* z (+ y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.45e+243) || !(a <= 1e+130)) {
		tmp = fma(y, z, x) + (a * (t + (z * b)));
	} else {
		tmp = x + ((a * t) + (z * (y + (a * b))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.45e+243) || !(a <= 1e+130))
		tmp = Float64(fma(y, z, x) + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * Float64(y + Float64(a * b)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.45e+243], N[Not[LessEqual[a, 1e+130]], $MachinePrecision]], N[(N[(y * z + x), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.44999999999999992e243 or 1.0000000000000001e130 < a

   1. Initial program 75.7%

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

      1. associate-+l+ 75.7%

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

      2. +-commutative 75.7%

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

      3. fma-def 75.7%

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

      4. associate-*l* 82.9%

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

      5. *-commutative 82.9%

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

      6. *-commutative 82.9%

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

      7. distribute-rgt-out 99.9%

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

      8. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   if -2.44999999999999992e243 < a < 1.0000000000000001e130

   1. Initial program 92.7%

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

      1. associate-+l+ 92.7%

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

      2. associate-*l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around 0 97.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+243} \lor \neg \left(a \leq 10^{+130}\right):\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 38.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot z\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-9}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-235}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a z))))
   (if (<= a -7.5e+242)
     t_1
     (if (<= a -6.5e-9)
       (* a t)
       (if (<= a -4.4e-296)
         x
         (if (<= a 9.2e-235)
           (* y z)
           (if (<= a 1.08e-220)
             x
             (if (<= a 5.8e-125) (* y z) (if (<= a 9.5e-9) t_1 (* a t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * z);
	double tmp;
	if (a <= -7.5e+242) {
		tmp = t_1;
	} else if (a <= -6.5e-9) {
		tmp = a * t;
	} else if (a <= -4.4e-296) {
		tmp = x;
	} else if (a <= 9.2e-235) {
		tmp = y * z;
	} else if (a <= 1.08e-220) {
		tmp = x;
	} else if (a <= 5.8e-125) {
		tmp = y * z;
	} else if (a <= 9.5e-9) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = b * (a * z)
    if (a <= (-7.5d+242)) then
        tmp = t_1
    else if (a <= (-6.5d-9)) then
        tmp = a * t
    else if (a <= (-4.4d-296)) then
        tmp = x
    else if (a <= 9.2d-235) then
        tmp = y * z
    else if (a <= 1.08d-220) then
        tmp = x
    else if (a <= 5.8d-125) then
        tmp = y * z
    else if (a <= 9.5d-9) then
        tmp = t_1
    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 t_1 = b * (a * z);
	double tmp;
	if (a <= -7.5e+242) {
		tmp = t_1;
	} else if (a <= -6.5e-9) {
		tmp = a * t;
	} else if (a <= -4.4e-296) {
		tmp = x;
	} else if (a <= 9.2e-235) {
		tmp = y * z;
	} else if (a <= 1.08e-220) {
		tmp = x;
	} else if (a <= 5.8e-125) {
		tmp = y * z;
	} else if (a <= 9.5e-9) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a * z)
	tmp = 0
	if a <= -7.5e+242:
		tmp = t_1
	elif a <= -6.5e-9:
		tmp = a * t
	elif a <= -4.4e-296:
		tmp = x
	elif a <= 9.2e-235:
		tmp = y * z
	elif a <= 1.08e-220:
		tmp = x
	elif a <= 5.8e-125:
		tmp = y * z
	elif a <= 9.5e-9:
		tmp = t_1
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * z))
	tmp = 0.0
	if (a <= -7.5e+242)
		tmp = t_1;
	elseif (a <= -6.5e-9)
		tmp = Float64(a * t);
	elseif (a <= -4.4e-296)
		tmp = x;
	elseif (a <= 9.2e-235)
		tmp = Float64(y * z);
	elseif (a <= 1.08e-220)
		tmp = x;
	elseif (a <= 5.8e-125)
		tmp = Float64(y * z);
	elseif (a <= 9.5e-9)
		tmp = t_1;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * z);
	tmp = 0.0;
	if (a <= -7.5e+242)
		tmp = t_1;
	elseif (a <= -6.5e-9)
		tmp = a * t;
	elseif (a <= -4.4e-296)
		tmp = x;
	elseif (a <= 9.2e-235)
		tmp = y * z;
	elseif (a <= 1.08e-220)
		tmp = x;
	elseif (a <= 5.8e-125)
		tmp = y * z;
	elseif (a <= 9.5e-9)
		tmp = t_1;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e+242], t$95$1, If[LessEqual[a, -6.5e-9], N[(a * t), $MachinePrecision], If[LessEqual[a, -4.4e-296], x, If[LessEqual[a, 9.2e-235], N[(y * z), $MachinePrecision], If[LessEqual[a, 1.08e-220], x, If[LessEqual[a, 5.8e-125], N[(y * z), $MachinePrecision], If[LessEqual[a, 9.5e-9], t$95$1, N[(a * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.49999999999999961e242 or 5.8000000000000004e-125 < a < 9.5000000000000007e-9

   1. Initial program 84.5%

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

      1. associate-+l+ 84.5%

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

      2. associate-*l* 79.8%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in z around 0 80.2%

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

   6. Taylor expanded in x around 0 60.9%

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

   7. Taylor expanded in a around inf 68.5%

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

      1. +-commutative 68.5%

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

   9. Simplified 68.5%

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

   10. Taylor expanded in b around inf 50.5%

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

       1. associate-*r* 48.3%

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

       2. *-commutative 48.3%

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

       3. associate-*r* 57.7%

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

   12. Simplified 57.7%

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

   if -7.49999999999999961e242 < a < -6.5000000000000003e-9 or 9.5000000000000007e-9 < a

   1. Initial program 84.6%

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

      1. associate-+l+ 84.6%

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

      2. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around 0 91.1%

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

   6. Taylor expanded in x around 0 78.0%

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

   7. Taylor expanded in t around inf 49.8%

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

   if -6.5000000000000003e-9 < a < -4.40000000000000024e-296 or 9.19999999999999989e-235 < a < 1.08e-220

   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+ 100.0%

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

      2. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in x around inf 55.9%

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

   if -4.40000000000000024e-296 < a < 9.19999999999999989e-235 or 1.08e-220 < a < 5.8000000000000004e-125

   1. Initial program 93.0%

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

      1. associate-+l+ 93.0%

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

      2. associate-*l* 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+242}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-9}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-235}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+244}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-8}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-235}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 0.0038:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.8e+244)
   (* b (* a z))
   (if (<= a -7.5e-8)
     (* a t)
     (if (<= a -5.8e-296)
       x
       (if (<= a 6.2e-235)
         (* y z)
         (if (<= a 3.4e-220)
           x
           (if (<= a 5.7e-117)
             (* y z)
             (if (<= a 0.0038) (* z (* a b)) (* a t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.8e+244) {
		tmp = b * (a * z);
	} else if (a <= -7.5e-8) {
		tmp = a * t;
	} else if (a <= -5.8e-296) {
		tmp = x;
	} else if (a <= 6.2e-235) {
		tmp = y * z;
	} else if (a <= 3.4e-220) {
		tmp = x;
	} else if (a <= 5.7e-117) {
		tmp = y * z;
	} else if (a <= 0.0038) {
		tmp = z * (a * b);
	} 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 (a <= (-3.8d+244)) then
        tmp = b * (a * z)
    else if (a <= (-7.5d-8)) then
        tmp = a * t
    else if (a <= (-5.8d-296)) then
        tmp = x
    else if (a <= 6.2d-235) then
        tmp = y * z
    else if (a <= 3.4d-220) then
        tmp = x
    else if (a <= 5.7d-117) then
        tmp = y * z
    else if (a <= 0.0038d0) then
        tmp = z * (a * b)
    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 (a <= -3.8e+244) {
		tmp = b * (a * z);
	} else if (a <= -7.5e-8) {
		tmp = a * t;
	} else if (a <= -5.8e-296) {
		tmp = x;
	} else if (a <= 6.2e-235) {
		tmp = y * z;
	} else if (a <= 3.4e-220) {
		tmp = x;
	} else if (a <= 5.7e-117) {
		tmp = y * z;
	} else if (a <= 0.0038) {
		tmp = z * (a * b);
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.8e+244:
		tmp = b * (a * z)
	elif a <= -7.5e-8:
		tmp = a * t
	elif a <= -5.8e-296:
		tmp = x
	elif a <= 6.2e-235:
		tmp = y * z
	elif a <= 3.4e-220:
		tmp = x
	elif a <= 5.7e-117:
		tmp = y * z
	elif a <= 0.0038:
		tmp = z * (a * b)
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.8e+244)
		tmp = Float64(b * Float64(a * z));
	elseif (a <= -7.5e-8)
		tmp = Float64(a * t);
	elseif (a <= -5.8e-296)
		tmp = x;
	elseif (a <= 6.2e-235)
		tmp = Float64(y * z);
	elseif (a <= 3.4e-220)
		tmp = x;
	elseif (a <= 5.7e-117)
		tmp = Float64(y * z);
	elseif (a <= 0.0038)
		tmp = Float64(z * Float64(a * b));
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.8e+244)
		tmp = b * (a * z);
	elseif (a <= -7.5e-8)
		tmp = a * t;
	elseif (a <= -5.8e-296)
		tmp = x;
	elseif (a <= 6.2e-235)
		tmp = y * z;
	elseif (a <= 3.4e-220)
		tmp = x;
	elseif (a <= 5.7e-117)
		tmp = y * z;
	elseif (a <= 0.0038)
		tmp = z * (a * b);
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.8e+244], N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e-8], N[(a * t), $MachinePrecision], If[LessEqual[a, -5.8e-296], x, If[LessEqual[a, 6.2e-235], N[(y * z), $MachinePrecision], If[LessEqual[a, 3.4e-220], x, If[LessEqual[a, 5.7e-117], N[(y * z), $MachinePrecision], If[LessEqual[a, 0.0038], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(a * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.79999999999999983e244

   1. Initial program 72.2%

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

      1. associate-+l+ 72.2%

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

      2. associate-*l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in z around 0 57.0%

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

   6. Taylor expanded in x around 0 57.0%

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

   7. Taylor expanded in a around inf 94.4%

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

      1. +-commutative 94.4%

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

   9. Simplified 94.4%

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

   10. Taylor expanded in b around inf 67.0%

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

       1. associate-*r* 51.9%

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

       2. *-commutative 51.9%

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

       3. associate-*r* 72.4%

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

   12. Simplified 72.4%

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

   if -3.79999999999999983e244 < a < -7.4999999999999997e-8 or 0.00379999999999999999 < a

   1. Initial program 84.6%

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

      1. associate-+l+ 84.6%

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

      2. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around 0 91.1%

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

   6. Taylor expanded in x around 0 78.0%

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

   7. Taylor expanded in t around inf 49.8%

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

   if -7.4999999999999997e-8 < a < -5.79999999999999965e-296 or 6.2e-235 < a < 3.39999999999999993e-220

   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+ 100.0%

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

      2. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in x around inf 55.9%

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

   if -5.79999999999999965e-296 < a < 6.2e-235 or 3.39999999999999993e-220 < a < 5.6999999999999999e-117

   1. Initial program 93.0%

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

      1. associate-+l+ 93.0%

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

      2. associate-*l* 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   if 5.6999999999999999e-117 < a < 0.00379999999999999999

   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+ 95.0%

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

      2. associate-*l* 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in z around inf 53.3%

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

   6. Taylor expanded in y around 0 45.3%

      \[\leadsto z \cdot \color{blue}{\left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+244}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-8}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-235}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 0.0038:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{+243}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-7}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-235}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.65e+243)
   (* a (* z b))
   (if (<= a -4.2e-7)
     (* a t)
     (if (<= a -6.2e-296)
       x
       (if (<= a 2.4e-235)
         (* y z)
         (if (<= a 5.5e-221)
           x
           (if (<= a 1.7e-125) (* y z) (if (<= a 6.5e-63) x (* a t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.65e+243) {
		tmp = a * (z * b);
	} else if (a <= -4.2e-7) {
		tmp = a * t;
	} else if (a <= -6.2e-296) {
		tmp = x;
	} else if (a <= 2.4e-235) {
		tmp = y * z;
	} else if (a <= 5.5e-221) {
		tmp = x;
	} else if (a <= 1.7e-125) {
		tmp = y * z;
	} else if (a <= 6.5e-63) {
		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 (a <= (-2.65d+243)) then
        tmp = a * (z * b)
    else if (a <= (-4.2d-7)) then
        tmp = a * t
    else if (a <= (-6.2d-296)) then
        tmp = x
    else if (a <= 2.4d-235) then
        tmp = y * z
    else if (a <= 5.5d-221) then
        tmp = x
    else if (a <= 1.7d-125) then
        tmp = y * z
    else if (a <= 6.5d-63) 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 (a <= -2.65e+243) {
		tmp = a * (z * b);
	} else if (a <= -4.2e-7) {
		tmp = a * t;
	} else if (a <= -6.2e-296) {
		tmp = x;
	} else if (a <= 2.4e-235) {
		tmp = y * z;
	} else if (a <= 5.5e-221) {
		tmp = x;
	} else if (a <= 1.7e-125) {
		tmp = y * z;
	} else if (a <= 6.5e-63) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.65e+243:
		tmp = a * (z * b)
	elif a <= -4.2e-7:
		tmp = a * t
	elif a <= -6.2e-296:
		tmp = x
	elif a <= 2.4e-235:
		tmp = y * z
	elif a <= 5.5e-221:
		tmp = x
	elif a <= 1.7e-125:
		tmp = y * z
	elif a <= 6.5e-63:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.65e+243)
		tmp = Float64(a * Float64(z * b));
	elseif (a <= -4.2e-7)
		tmp = Float64(a * t);
	elseif (a <= -6.2e-296)
		tmp = x;
	elseif (a <= 2.4e-235)
		tmp = Float64(y * z);
	elseif (a <= 5.5e-221)
		tmp = x;
	elseif (a <= 1.7e-125)
		tmp = Float64(y * z);
	elseif (a <= 6.5e-63)
		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 (a <= -2.65e+243)
		tmp = a * (z * b);
	elseif (a <= -4.2e-7)
		tmp = a * t;
	elseif (a <= -6.2e-296)
		tmp = x;
	elseif (a <= 2.4e-235)
		tmp = y * z;
	elseif (a <= 5.5e-221)
		tmp = x;
	elseif (a <= 1.7e-125)
		tmp = y * z;
	elseif (a <= 6.5e-63)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.65e+243], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.2e-7], N[(a * t), $MachinePrecision], If[LessEqual[a, -6.2e-296], x, If[LessEqual[a, 2.4e-235], N[(y * z), $MachinePrecision], If[LessEqual[a, 5.5e-221], x, If[LessEqual[a, 1.7e-125], N[(y * z), $MachinePrecision], If[LessEqual[a, 6.5e-63], x, N[(a * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.6499999999999999e243

   1. Initial program 72.2%

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

      1. associate-+l+ 72.2%

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

      2. associate-*l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in z around inf 57.4%

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

   6. Taylor expanded in y around 0 67.0%

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

   if -2.6499999999999999e243 < a < -4.2e-7 or 6.4999999999999998e-63 < a

   1. Initial program 85.7%

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

      1. associate-+l+ 85.7%

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

      2. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in z around 0 91.7%

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

   6. Taylor expanded in x around 0 78.1%

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

   7. Taylor expanded in t around inf 48.0%

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

   if -4.2e-7 < a < -6.2000000000000004e-296 or 2.40000000000000011e-235 < a < 5.49999999999999966e-221 or 1.69999999999999988e-125 < a < 6.4999999999999998e-63

   1. Initial program 98.4%

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

      1. associate-+l+ 98.4%

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

      2. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in x around inf 54.3%

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

   if -6.2000000000000004e-296 < a < 2.40000000000000011e-235 or 5.49999999999999966e-221 < a < 1.69999999999999988e-125

   1. Initial program 93.0%

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

      1. associate-+l+ 93.0%

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

      2. associate-*l* 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{+243}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-7}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-235}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-8}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -8.1 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-234}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.5e-8)
   (* a t)
   (if (<= a -8.1e-296)
     x
     (if (<= a 1.7e-234)
       (* y z)
       (if (<= a 8.2e-219)
         x
         (if (<= a 1.1e-117) (* y z) (if (<= a 1.15e-58) x (* a t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.5e-8) {
		tmp = a * t;
	} else if (a <= -8.1e-296) {
		tmp = x;
	} else if (a <= 1.7e-234) {
		tmp = y * z;
	} else if (a <= 8.2e-219) {
		tmp = x;
	} else if (a <= 1.1e-117) {
		tmp = y * z;
	} else if (a <= 1.15e-58) {
		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 (a <= (-4.5d-8)) then
        tmp = a * t
    else if (a <= (-8.1d-296)) then
        tmp = x
    else if (a <= 1.7d-234) then
        tmp = y * z
    else if (a <= 8.2d-219) then
        tmp = x
    else if (a <= 1.1d-117) then
        tmp = y * z
    else if (a <= 1.15d-58) 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 (a <= -4.5e-8) {
		tmp = a * t;
	} else if (a <= -8.1e-296) {
		tmp = x;
	} else if (a <= 1.7e-234) {
		tmp = y * z;
	} else if (a <= 8.2e-219) {
		tmp = x;
	} else if (a <= 1.1e-117) {
		tmp = y * z;
	} else if (a <= 1.15e-58) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.5e-8:
		tmp = a * t
	elif a <= -8.1e-296:
		tmp = x
	elif a <= 1.7e-234:
		tmp = y * z
	elif a <= 8.2e-219:
		tmp = x
	elif a <= 1.1e-117:
		tmp = y * z
	elif a <= 1.15e-58:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.5e-8)
		tmp = Float64(a * t);
	elseif (a <= -8.1e-296)
		tmp = x;
	elseif (a <= 1.7e-234)
		tmp = Float64(y * z);
	elseif (a <= 8.2e-219)
		tmp = x;
	elseif (a <= 1.1e-117)
		tmp = Float64(y * z);
	elseif (a <= 1.15e-58)
		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 (a <= -4.5e-8)
		tmp = a * t;
	elseif (a <= -8.1e-296)
		tmp = x;
	elseif (a <= 1.7e-234)
		tmp = y * z;
	elseif (a <= 8.2e-219)
		tmp = x;
	elseif (a <= 1.1e-117)
		tmp = y * z;
	elseif (a <= 1.15e-58)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.5e-8], N[(a * t), $MachinePrecision], If[LessEqual[a, -8.1e-296], x, If[LessEqual[a, 1.7e-234], N[(y * z), $MachinePrecision], If[LessEqual[a, 8.2e-219], x, If[LessEqual[a, 1.1e-117], N[(y * z), $MachinePrecision], If[LessEqual[a, 1.15e-58], x, N[(a * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.49999999999999993e-8 or 1.1499999999999999e-58 < a

   1. Initial program 84.0%

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

      1. associate-+l+ 84.0%

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

      2. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around 0 87.5%

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

   6. Taylor expanded in x around 0 75.6%

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

   7. Taylor expanded in t around inf 45.8%

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

   if -4.49999999999999993e-8 < a < -8.10000000000000051e-296 or 1.69999999999999993e-234 < a < 8.2e-219 or 1.1000000000000001e-117 < a < 1.1499999999999999e-58

   1. Initial program 98.4%

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

      1. associate-+l+ 98.4%

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

      2. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in x around inf 54.3%

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

   if -8.10000000000000051e-296 < a < 1.69999999999999993e-234 or 8.2e-219 < a < 1.1000000000000001e-117

   1. Initial program 93.0%

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

      1. associate-+l+ 93.0%

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

      2. associate-*l* 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-8}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -8.1 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-234}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -1.32 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-88}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-116}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-64}:\\ \;\;\;\;x + b \cdot \left(a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -1.32e+160)
     t_1
     (if (<= a -2.4e-88)
       (+ x (* a t))
       (if (<= a 1.5e-116)
         (+ x (* y z))
         (if (<= a 2.45e-64) (+ x (* b (* a z))) 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 <= -1.32e+160) {
		tmp = t_1;
	} else if (a <= -2.4e-88) {
		tmp = x + (a * t);
	} else if (a <= 1.5e-116) {
		tmp = x + (y * z);
	} else if (a <= 2.45e-64) {
		tmp = x + (b * (a * z));
	} 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 <= (-1.32d+160)) then
        tmp = t_1
    else if (a <= (-2.4d-88)) then
        tmp = x + (a * t)
    else if (a <= 1.5d-116) then
        tmp = x + (y * z)
    else if (a <= 2.45d-64) then
        tmp = x + (b * (a * z))
    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 <= -1.32e+160) {
		tmp = t_1;
	} else if (a <= -2.4e-88) {
		tmp = x + (a * t);
	} else if (a <= 1.5e-116) {
		tmp = x + (y * z);
	} else if (a <= 2.45e-64) {
		tmp = x + (b * (a * z));
	} 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 <= -1.32e+160:
		tmp = t_1
	elif a <= -2.4e-88:
		tmp = x + (a * t)
	elif a <= 1.5e-116:
		tmp = x + (y * z)
	elif a <= 2.45e-64:
		tmp = x + (b * (a * z))
	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 <= -1.32e+160)
		tmp = t_1;
	elseif (a <= -2.4e-88)
		tmp = Float64(x + Float64(a * t));
	elseif (a <= 1.5e-116)
		tmp = Float64(x + Float64(y * z));
	elseif (a <= 2.45e-64)
		tmp = Float64(x + Float64(b * Float64(a * z)));
	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 <= -1.32e+160)
		tmp = t_1;
	elseif (a <= -2.4e-88)
		tmp = x + (a * t);
	elseif (a <= 1.5e-116)
		tmp = x + (y * z);
	elseif (a <= 2.45e-64)
		tmp = x + (b * (a * z));
	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, -1.32e+160], t$95$1, If[LessEqual[a, -2.4e-88], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-116], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e-64], N[(x + N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.32e160 or 2.4500000000000001e-64 < a

   1. Initial program 82.1%

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

      1. associate-+l+ 82.1%

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

      2. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in z around 0 86.5%

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

   6. Taylor expanded in x around 0 79.1%

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

   7. Taylor expanded in a around inf 79.1%

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

      1. +-commutative 79.1%

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

   9. Simplified 79.1%

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

   if -1.32e160 < a < -2.4e-88

   1. Initial program 90.7%

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

      1. associate-+l+ 90.7%

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

      2. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in z around 0 73.6%

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

      1. +-commutative 73.6%

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

   7. Simplified 73.6%

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

   if -2.4e-88 < a < 1.50000000000000013e-116

   1. Initial program 96.6%

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

      1. associate-+l+ 96.6%

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

      2. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in a around 0 90.3%

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

   if 1.50000000000000013e-116 < a < 2.4500000000000001e-64

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. associate-*l* 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in z around 0 100.0%

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

   6. Taylor expanded in y around 0 82.9%

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

      1. distribute-lft-in 82.9%

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

      2. +-commutative 82.9%

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

      3. +-commutative 82.9%

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

   8. Simplified 82.9%

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

   9. Taylor expanded in b around inf 80.4%

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

       1. associate-*r* 47.8%

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

       2. *-commutative 47.8%

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

       3. associate-*r* 47.4%

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

   11. Simplified 97.2%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-88}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-116}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-64}:\\ \;\;\;\;x + b \cdot \left(a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -5.3 \cdot 10^{+243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+151}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -5.3e+243)
     t_1
     (if (<= a 3.6e+151) (+ x (+ (* a t) (* z (+ y (* a b))))) (+ x 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 <= -5.3e+243) {
		tmp = t_1;
	} else if (a <= 3.6e+151) {
		tmp = x + ((a * t) + (z * (y + (a * b))));
	} else {
		tmp = x + 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 <= (-5.3d+243)) then
        tmp = t_1
    else if (a <= 3.6d+151) then
        tmp = x + ((a * t) + (z * (y + (a * b))))
    else
        tmp = x + 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 <= -5.3e+243) {
		tmp = t_1;
	} else if (a <= 3.6e+151) {
		tmp = x + ((a * t) + (z * (y + (a * b))));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -5.3e+243:
		tmp = t_1
	elif a <= 3.6e+151:
		tmp = x + ((a * t) + (z * (y + (a * b))))
	else:
		tmp = x + 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 <= -5.3e+243)
		tmp = t_1;
	elseif (a <= 3.6e+151)
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * Float64(y + Float64(a * b)))));
	else
		tmp = Float64(x + 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 <= -5.3e+243)
		tmp = t_1;
	elseif (a <= 3.6e+151)
		tmp = x + ((a * t) + (z * (y + (a * b))));
	else
		tmp = x + 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, -5.3e+243], t$95$1, If[LessEqual[a, 3.6e+151], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.2999999999999997e243

   1. Initial program 72.2%

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

      1. associate-+l+ 72.2%

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

      2. associate-*l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in z around 0 57.0%

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

   6. Taylor expanded in x around 0 57.0%

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

   7. Taylor expanded in a around inf 94.4%

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

      1. +-commutative 94.4%

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

   9. Simplified 94.4%

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

   if -5.2999999999999997e243 < a < 3.6e151

   1. Initial program 92.8%

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

      1. associate-+l+ 92.8%

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

      2. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around 0 97.6%

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

   if 3.6e151 < a

   1. Initial program 74.6%

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

      1. associate-+l+ 74.6%

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

      2. +-commutative 74.6%

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

      3. fma-def 74.6%

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

      4. associate-*l* 83.8%

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

      5. *-commutative 83.8%

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

      6. *-commutative 83.8%

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

      7. distribute-rgt-out 99.9%

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

      8. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+243}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+151}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-90}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -1.7e+159)
     t_1
     (if (<= a -7.2e-90)
       (+ x (* a t))
       (if (<= a 9.5e-64) (+ x (* y z)) 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 <= -1.7e+159) {
		tmp = t_1;
	} else if (a <= -7.2e-90) {
		tmp = x + (a * t);
	} else if (a <= 9.5e-64) {
		tmp = x + (y * z);
	} 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 <= (-1.7d+159)) then
        tmp = t_1
    else if (a <= (-7.2d-90)) then
        tmp = x + (a * t)
    else if (a <= 9.5d-64) then
        tmp = x + (y * z)
    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 <= -1.7e+159) {
		tmp = t_1;
	} else if (a <= -7.2e-90) {
		tmp = x + (a * t);
	} else if (a <= 9.5e-64) {
		tmp = x + (y * z);
	} 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 <= -1.7e+159:
		tmp = t_1
	elif a <= -7.2e-90:
		tmp = x + (a * t)
	elif a <= 9.5e-64:
		tmp = x + (y * z)
	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 <= -1.7e+159)
		tmp = t_1;
	elseif (a <= -7.2e-90)
		tmp = Float64(x + Float64(a * t));
	elseif (a <= 9.5e-64)
		tmp = Float64(x + Float64(y * z));
	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 <= -1.7e+159)
		tmp = t_1;
	elseif (a <= -7.2e-90)
		tmp = x + (a * t);
	elseif (a <= 9.5e-64)
		tmp = x + (y * z);
	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, -1.7e+159], t$95$1, If[LessEqual[a, -7.2e-90], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-64], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.69999999999999996e159 or 9.50000000000000043e-64 < a

   1. Initial program 82.1%

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

      1. associate-+l+ 82.1%

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

      2. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in z around 0 86.5%

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

   6. Taylor expanded in x around 0 79.1%

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

   7. Taylor expanded in a around inf 79.1%

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

      1. +-commutative 79.1%

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

   9. Simplified 79.1%

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

   if -1.69999999999999996e159 < a < -7.19999999999999961e-90

   1. Initial program 90.7%

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

      1. associate-+l+ 90.7%

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

      2. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in z around 0 73.6%

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

      1. +-commutative 73.6%

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

   7. Simplified 73.6%

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

   if -7.19999999999999961e-90 < a < 9.50000000000000043e-64

   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+ 97.0%

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

      2. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in a around 0 85.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+159}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-90}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+244}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-90} \lor \neg \left(a \leq 1.05 \cdot 10^{-33}\right):\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.5e+244)
   (* b (* a z))
   (if (or (<= a -1.05e-90) (not (<= a 1.05e-33)))
     (+ x (* a t))
     (+ x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.5e+244) {
		tmp = b * (a * z);
	} else if ((a <= -1.05e-90) || !(a <= 1.05e-33)) {
		tmp = x + (a * t);
	} else {
		tmp = x + (y * z);
	}
	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 (a <= (-4.5d+244)) then
        tmp = b * (a * z)
    else if ((a <= (-1.05d-90)) .or. (.not. (a <= 1.05d-33))) then
        tmp = x + (a * t)
    else
        tmp = x + (y * z)
    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 (a <= -4.5e+244) {
		tmp = b * (a * z);
	} else if ((a <= -1.05e-90) || !(a <= 1.05e-33)) {
		tmp = x + (a * t);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.5e+244:
		tmp = b * (a * z)
	elif (a <= -1.05e-90) or not (a <= 1.05e-33):
		tmp = x + (a * t)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.5e+244)
		tmp = Float64(b * Float64(a * z));
	elseif ((a <= -1.05e-90) || !(a <= 1.05e-33))
		tmp = Float64(x + Float64(a * t));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.5e+244)
		tmp = b * (a * z);
	elseif ((a <= -1.05e-90) || ~((a <= 1.05e-33)))
		tmp = x + (a * t);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.5e+244], N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.05e-90], N[Not[LessEqual[a, 1.05e-33]], $MachinePrecision]], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5000000000000003e244

   1. Initial program 72.2%

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

      1. associate-+l+ 72.2%

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

      2. associate-*l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in z around 0 57.0%

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

   6. Taylor expanded in x around 0 57.0%

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

   7. Taylor expanded in a around inf 94.4%

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

      1. +-commutative 94.4%

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

   9. Simplified 94.4%

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

   10. Taylor expanded in b around inf 67.0%

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

       1. associate-*r* 51.9%

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

       2. *-commutative 51.9%

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

       3. associate-*r* 72.4%

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

   12. Simplified 72.4%

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

   if -4.5000000000000003e244 < a < -1.05e-90 or 1.05e-33 < a

   1. Initial program 86.0%

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

      1. associate-+l+ 86.0%

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

      2. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in z around 0 64.6%

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

      1. +-commutative 64.6%

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

   7. Simplified 64.6%

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

   if -1.05e-90 < a < 1.05e-33

   1. Initial program 96.2%

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

      1. associate-+l+ 96.2%

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

      2. associate-*l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in a around 0 82.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+244}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-90} \lor \neg \left(a \leq 1.05 \cdot 10^{-33}\right):\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-88} \lor \neg \left(a \leq 2.5 \cdot 10^{-120}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.8e-88) (not (<= a 2.5e-120)))
   (+ x (* a (+ t (* z b))))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.8e-88) || !(a <= 2.5e-120)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (y * z);
	}
	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 ((a <= (-1.8d-88)) .or. (.not. (a <= 2.5d-120))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + (y * z)
    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 ((a <= -1.8e-88) || !(a <= 2.5e-120)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.8e-88) or not (a <= 2.5e-120):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.8e-88) || !(a <= 2.5e-120))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.8e-88) || ~((a <= 2.5e-120)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.8e-88], N[Not[LessEqual[a, 2.5e-120]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8e-88 or 2.50000000000000003e-120 < a

   1. Initial program 85.4%

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

      1. associate-+l+ 85.4%

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

      2. +-commutative 85.4%

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

      3. fma-def 85.4%

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

      4. associate-*l* 88.2%

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

      5. *-commutative 88.2%

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

      6. *-commutative 88.2%

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

      7. distribute-rgt-out 94.7%

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

      8. *-commutative 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in y around 0 86.3%

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

   if -1.8e-88 < a < 2.50000000000000003e-120

   1. Initial program 96.6%

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

      1. associate-+l+ 96.6%

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

      2. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in a around 0 90.3%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-88} \lor \neg \left(a \leq 2.5 \cdot 10^{-120}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+188} \lor \neg \left(b \leq 2.8 \cdot 10^{+60}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t + \left(x + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.6e+188) (not (<= b 2.8e+60)))
   (+ x (* a (+ t (* z b))))
   (+ (* a t) (+ x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.6e+188) || !(b <= 2.8e+60)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (a * t) + (x + (y * z));
	}
	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 ((b <= (-5.6d+188)) .or. (.not. (b <= 2.8d+60))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (a * t) + (x + (y * z))
    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 ((b <= -5.6e+188) || !(b <= 2.8e+60)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (a * t) + (x + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.6e+188) or not (b <= 2.8e+60):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (a * t) + (x + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.6e+188) || !(b <= 2.8e+60))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(a * t) + Float64(x + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.6e+188) || ~((b <= 2.8e+60)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (a * t) + (x + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.6e+188], N[Not[LessEqual[b, 2.8e+60]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * t), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5999999999999996e188 or 2.8e60 < b

   1. Initial program 83.7%

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

      1. associate-+l+ 83.7%

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

      2. +-commutative 83.7%

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

      3. fma-def 83.7%

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

      4. associate-*l* 79.5%

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

      5. *-commutative 79.5%

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

      6. *-commutative 79.5%

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

      7. distribute-rgt-out 89.1%

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

      8. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in y around 0 89.3%

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

   if -5.5999999999999996e188 < b < 2.8e60

   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+ 91.4%

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

      2. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around inf 89.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+188} \lor \neg \left(b \leq 2.8 \cdot 10^{+60}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t + \left(x + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+137} \lor \neg \left(t \leq 2.2 \cdot 10^{+167}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.9e+137) (not (<= t 2.2e+167))) (* a t) (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.9e+137) || !(t <= 2.2e+167)) {
		tmp = a * t;
	} else {
		tmp = x + (y * z);
	}
	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 <= (-2.9d+137)) .or. (.not. (t <= 2.2d+167))) then
        tmp = a * t
    else
        tmp = x + (y * z)
    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 <= -2.9e+137) || !(t <= 2.2e+167)) {
		tmp = a * t;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.9e+137) or not (t <= 2.2e+167):
		tmp = a * t
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.9e+137) || !(t <= 2.2e+167))
		tmp = Float64(a * t);
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.9e+137) || ~((t <= 2.2e+167)))
		tmp = a * t;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.9e+137], N[Not[LessEqual[t, 2.2e+167]], $MachinePrecision]], N[(a * t), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.89999999999999985e137 or 2.20000000000000003e167 < t

   1. Initial program 82.5%

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

      1. associate-+l+ 82.5%

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

      2. associate-*l* 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in z around 0 87.3%

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

   6. Taylor expanded in x around 0 76.4%

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

   7. Taylor expanded in t around inf 66.0%

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

   if -2.89999999999999985e137 < t < 2.20000000000000003e167

   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+ 91.4%

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

      2. associate-*l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around 0 61.9%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+137} \lor \neg \left(t \leq 2.2 \cdot 10^{+167}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-8} \lor \neg \left(a \leq 7 \cdot 10^{-59}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.2e-8) (not (<= a 7e-59))) (* a t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -5.2e-8) || !(a <= 7e-59)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	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 ((a <= (-5.2d-8)) .or. (.not. (a <= 7d-59))) then
        tmp = a * t
    else
        tmp = x
    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 ((a <= -5.2e-8) || !(a <= 7e-59)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -5.2e-8) or not (a <= 7e-59):
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -5.2e-8) || !(a <= 7e-59))
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -5.2e-8) || ~((a <= 7e-59)))
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -5.2e-8], N[Not[LessEqual[a, 7e-59]], $MachinePrecision]], N[(a * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -5.2000000000000002e-8 or 7.0000000000000002e-59 < a

   1. Initial program 84.0%

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

      1. associate-+l+ 84.0%

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

      2. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around 0 87.5%

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

   6. Taylor expanded in x around 0 75.6%

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

   7. Taylor expanded in t around inf 45.8%

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

   if -5.2000000000000002e-8 < a < 7.0000000000000002e-59

   1. Initial program 96.3%

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

      1. associate-+l+ 96.3%

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

      2. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around inf 44.4%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-8} \lor \neg \left(a \leq 7 \cdot 10^{-59}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.1% 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 89.2%

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

   1. associate-+l+ 89.2%

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

   2. associate-*l* 88.5%

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

3. Simplified 88.5%

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

5. Taylor expanded in x around inf 26.9%

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

6. Final simplification 26.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.4% 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 2024029 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000.0) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))