Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.4% → 96.0%

Time: 11.2s

Alternatives: 14

Speedup: 0.7×

• 32.6% 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: 92.4% 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: 96.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3500000000:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 3500000000.0)
   (+ (+ x (* z y)) (+ (* t a) (* a (* z b))))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3500000000.0) {
		tmp = (x + (z * y)) + ((t * a) + (a * (z * b)));
	} else {
		tmp = z * (y + ((x / z) + (a * (b + (t / 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 (z <= 3500000000.0d0) then
        tmp = (x + (z * y)) + ((t * a) + (a * (z * b)))
    else
        tmp = z * (y + ((x / z) + (a * (b + (t / 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 (z <= 3500000000.0) {
		tmp = (x + (z * y)) + ((t * a) + (a * (z * b)));
	} else {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 3500000000.0:
		tmp = (x + (z * y)) + ((t * a) + (a * (z * b)))
	else:
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 3500000000.0)
		tmp = Float64(Float64(x + Float64(z * y)) + Float64(Float64(t * a) + Float64(a * Float64(z * b))));
	else
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 3500000000.0)
		tmp = (x + (z * y)) + ((t * a) + (a * (z * b)));
	else
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 3500000000.0], N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.5e9

   1. Initial program 97.3%

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

      1. associate-+l+ 97.3%

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

      2. associate-*l* 98.5%

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

   3. Simplified 98.5%

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

   if 3.5e9 < z

   1. Initial program 89.5%

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

      1. associate-+l+ 89.5%

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

      2. associate-*l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in z around inf 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-+l+ 95.8%

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

      3. +-commutative 95.8%

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

      4. associate-/l* 99.9%

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

      5. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3500000000:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-80}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-119}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (* a (+ t (* z b)))))
   (if (<= a -4e+76)
     t_2
     (if (<= a -6.2e-13)
       t_1
       (if (<= a -3.4e-80)
         (+ x (* a (* z b)))
         (if (<= a 2.45e-119) (+ x (* z y)) (if (<= a 6.5e+58) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -4e+76) {
		tmp = t_2;
	} else if (a <= -6.2e-13) {
		tmp = t_1;
	} else if (a <= -3.4e-80) {
		tmp = x + (a * (z * b));
	} else if (a <= 2.45e-119) {
		tmp = x + (z * y);
	} else if (a <= 6.5e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x + (t * a)
    t_2 = a * (t + (z * b))
    if (a <= (-4d+76)) then
        tmp = t_2
    else if (a <= (-6.2d-13)) then
        tmp = t_1
    else if (a <= (-3.4d-80)) then
        tmp = x + (a * (z * b))
    else if (a <= 2.45d-119) then
        tmp = x + (z * y)
    else if (a <= 6.5d+58) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -4e+76) {
		tmp = t_2;
	} else if (a <= -6.2e-13) {
		tmp = t_1;
	} else if (a <= -3.4e-80) {
		tmp = x + (a * (z * b));
	} else if (a <= 2.45e-119) {
		tmp = x + (z * y);
	} else if (a <= 6.5e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	t_2 = a * (t + (z * b))
	tmp = 0
	if a <= -4e+76:
		tmp = t_2
	elif a <= -6.2e-13:
		tmp = t_1
	elif a <= -3.4e-80:
		tmp = x + (a * (z * b))
	elif a <= 2.45e-119:
		tmp = x + (z * y)
	elif a <= 6.5e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	t_2 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -4e+76)
		tmp = t_2;
	elseif (a <= -6.2e-13)
		tmp = t_1;
	elseif (a <= -3.4e-80)
		tmp = Float64(x + Float64(a * Float64(z * b)));
	elseif (a <= 2.45e-119)
		tmp = Float64(x + Float64(z * y));
	elseif (a <= 6.5e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * a);
	t_2 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -4e+76)
		tmp = t_2;
	elseif (a <= -6.2e-13)
		tmp = t_1;
	elseif (a <= -3.4e-80)
		tmp = x + (a * (z * b));
	elseif (a <= 2.45e-119)
		tmp = x + (z * y);
	elseif (a <= 6.5e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+76], t$95$2, If[LessEqual[a, -6.2e-13], t$95$1, If[LessEqual[a, -3.4e-80], N[(x + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e-119], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+58], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.0000000000000002e76 or 6.49999999999999998e58 < a

   1. Initial program 90.6%

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

      1. associate-+l+ 90.6%

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

      2. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in a around inf 83.6%

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

   if -4.0000000000000002e76 < a < -6.1999999999999998e-13 or 2.45e-119 < a < 6.49999999999999998e58

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around 0 69.5%

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

      1. +-commutative 69.5%

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

   7. Simplified 69.5%

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

   if -6.1999999999999998e-13 < a < -3.4000000000000001e-80

   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* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.9%

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

   6. Taylor expanded in t around 0 73.6%

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

   if -3.4000000000000001e-80 < a < 2.45e-119

   1. Initial program 97.7%

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

      1. associate-+l+ 97.7%

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

      2. associate-*l* 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 a around 0 82.9%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-13}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-80}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-119}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot a\right)\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+68}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+134} \lor \neg \left(a \leq 5.8 \cdot 10^{+179}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* z a))))
   (if (<= a -4.4e+65)
     t_1
     (if (<= a 9e+68)
       (+ x (* z y))
       (if (or (<= a 4.8e+134) (not (<= a 5.8e+179))) (* t a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (z * a);
	double tmp;
	if (a <= -4.4e+65) {
		tmp = t_1;
	} else if (a <= 9e+68) {
		tmp = x + (z * y);
	} else if ((a <= 4.8e+134) || !(a <= 5.8e+179)) {
		tmp = t * a;
	} 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 = b * (z * a)
    if (a <= (-4.4d+65)) then
        tmp = t_1
    else if (a <= 9d+68) then
        tmp = x + (z * y)
    else if ((a <= 4.8d+134) .or. (.not. (a <= 5.8d+179))) then
        tmp = t * a
    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 = b * (z * a);
	double tmp;
	if (a <= -4.4e+65) {
		tmp = t_1;
	} else if (a <= 9e+68) {
		tmp = x + (z * y);
	} else if ((a <= 4.8e+134) || !(a <= 5.8e+179)) {
		tmp = t * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (z * a)
	tmp = 0
	if a <= -4.4e+65:
		tmp = t_1
	elif a <= 9e+68:
		tmp = x + (z * y)
	elif (a <= 4.8e+134) or not (a <= 5.8e+179):
		tmp = t * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(z * a))
	tmp = 0.0
	if (a <= -4.4e+65)
		tmp = t_1;
	elseif (a <= 9e+68)
		tmp = Float64(x + Float64(z * y));
	elseif ((a <= 4.8e+134) || !(a <= 5.8e+179))
		tmp = Float64(t * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (z * a);
	tmp = 0.0;
	if (a <= -4.4e+65)
		tmp = t_1;
	elseif (a <= 9e+68)
		tmp = x + (z * y);
	elseif ((a <= 4.8e+134) || ~((a <= 5.8e+179)))
		tmp = t * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.4e+65], t$95$1, If[LessEqual[a, 9e+68], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 4.8e+134], N[Not[LessEqual[a, 5.8e+179]], $MachinePrecision]], N[(t * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.3999999999999997e65 or 4.80000000000000011e134 < a < 5.80000000000000038e179

   1. Initial program 89.9%

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

      1. associate-+l+ 89.9%

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

      2. +-commutative 89.9%

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

      3. fma-define 89.9%

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

      4. associate-*l* 91.8%

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

      5. *-commutative 91.8%

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

      6. *-commutative 91.8%

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

      7. distribute-rgt-out 95.9%

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

      8. *-commutative 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 86.2%

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

   6. Taylor expanded in b around inf 63.0%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. associate-*r* 66.8%

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

   8. Simplified 66.8%

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

   if -4.3999999999999997e65 < a < 9.0000000000000007e68

   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* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in a around 0 67.5%

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

   if 9.0000000000000007e68 < a < 4.80000000000000011e134 or 5.80000000000000038e179 < a

   1. Initial program 91.3%

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

      1. associate-+l+ 91.3%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 68.2%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+68}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+134} \lor \neg \left(a \leq 5.8 \cdot 10^{+179}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.95 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-90}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-140}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+19}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.95e+39)
   x
   (if (<= x -8.5e-90)
     (* z y)
     (if (<= x 3.9e-140) (* t a) (if (<= x 2.75e+19) (* a (* z b)) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.95e+39) {
		tmp = x;
	} else if (x <= -8.5e-90) {
		tmp = z * y;
	} else if (x <= 3.9e-140) {
		tmp = t * a;
	} else if (x <= 2.75e+19) {
		tmp = a * (z * b);
	} 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 (x <= (-3.95d+39)) then
        tmp = x
    else if (x <= (-8.5d-90)) then
        tmp = z * y
    else if (x <= 3.9d-140) then
        tmp = t * a
    else if (x <= 2.75d+19) then
        tmp = a * (z * b)
    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 (x <= -3.95e+39) {
		tmp = x;
	} else if (x <= -8.5e-90) {
		tmp = z * y;
	} else if (x <= 3.9e-140) {
		tmp = t * a;
	} else if (x <= 2.75e+19) {
		tmp = a * (z * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.95e+39:
		tmp = x
	elif x <= -8.5e-90:
		tmp = z * y
	elif x <= 3.9e-140:
		tmp = t * a
	elif x <= 2.75e+19:
		tmp = a * (z * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.95e+39)
		tmp = x;
	elseif (x <= -8.5e-90)
		tmp = Float64(z * y);
	elseif (x <= 3.9e-140)
		tmp = Float64(t * a);
	elseif (x <= 2.75e+19)
		tmp = Float64(a * Float64(z * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.95e+39)
		tmp = x;
	elseif (x <= -8.5e-90)
		tmp = z * y;
	elseif (x <= 3.9e-140)
		tmp = t * a;
	elseif (x <= 2.75e+19)
		tmp = a * (z * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.95e+39], x, If[LessEqual[x, -8.5e-90], N[(z * y), $MachinePrecision], If[LessEqual[x, 3.9e-140], N[(t * a), $MachinePrecision], If[LessEqual[x, 2.75e+19], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.95000000000000022e39 or 2.75e19 < x

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in x around inf 57.8%

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

   if -3.95000000000000022e39 < x < -8.5000000000000001e-90

   1. Initial program 85.5%

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

      1. associate-+l+ 85.5%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in y around inf 46.4%

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

      1. *-commutative 46.4%

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

   7. Simplified 46.4%

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

   if -8.5000000000000001e-90 < x < 3.90000000000000019e-140

   1. Initial program 95.3%

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

      1. associate-+l+ 95.3%

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

      2. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 46.7%

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

   if 3.90000000000000019e-140 < x < 2.75e19

   1. Initial program 94.0%

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

      1. associate-+l+ 94.0%

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

      2. +-commutative 94.0%

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

      3. fma-define 94.0%

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

      4. associate-*l* 96.8%

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

      5. *-commutative 96.8%

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

      6. *-commutative 96.8%

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

      7. distribute-rgt-out 96.8%

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

      8. *-commutative 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around inf 79.9%

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

   6. Taylor expanded in b around inf 45.3%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.95 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-90}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-140}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+19}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-93}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-140}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.5e+38)
   x
   (if (<= x -5e-93)
     (* z y)
     (if (<= x 7e-140) (* t a) (if (<= x 1.7e+19) (* b (* z a)) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+38) {
		tmp = x;
	} else if (x <= -5e-93) {
		tmp = z * y;
	} else if (x <= 7e-140) {
		tmp = t * a;
	} else if (x <= 1.7e+19) {
		tmp = b * (z * a);
	} 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 (x <= (-9.5d+38)) then
        tmp = x
    else if (x <= (-5d-93)) then
        tmp = z * y
    else if (x <= 7d-140) then
        tmp = t * a
    else if (x <= 1.7d+19) then
        tmp = b * (z * a)
    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 (x <= -9.5e+38) {
		tmp = x;
	} else if (x <= -5e-93) {
		tmp = z * y;
	} else if (x <= 7e-140) {
		tmp = t * a;
	} else if (x <= 1.7e+19) {
		tmp = b * (z * a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.5e+38:
		tmp = x
	elif x <= -5e-93:
		tmp = z * y
	elif x <= 7e-140:
		tmp = t * a
	elif x <= 1.7e+19:
		tmp = b * (z * a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.5e+38)
		tmp = x;
	elseif (x <= -5e-93)
		tmp = Float64(z * y);
	elseif (x <= 7e-140)
		tmp = Float64(t * a);
	elseif (x <= 1.7e+19)
		tmp = Float64(b * Float64(z * a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.5e+38)
		tmp = x;
	elseif (x <= -5e-93)
		tmp = z * y;
	elseif (x <= 7e-140)
		tmp = t * a;
	elseif (x <= 1.7e+19)
		tmp = b * (z * a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.5e+38], x, If[LessEqual[x, -5e-93], N[(z * y), $MachinePrecision], If[LessEqual[x, 7e-140], N[(t * a), $MachinePrecision], If[LessEqual[x, 1.7e+19], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.4999999999999995e38 or 1.7e19 < x

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in x around inf 57.8%

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

   if -9.4999999999999995e38 < x < -4.99999999999999994e-93

   1. Initial program 85.5%

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

      1. associate-+l+ 85.5%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in y around inf 46.4%

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

      1. *-commutative 46.4%

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

   7. Simplified 46.4%

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

   if -4.99999999999999994e-93 < x < 6.9999999999999996e-140

   1. Initial program 95.3%

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

      1. associate-+l+ 95.3%

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

      2. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 46.7%

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

   if 6.9999999999999996e-140 < x < 1.7e19

   1. Initial program 94.0%

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

      1. associate-+l+ 94.0%

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

      2. +-commutative 94.0%

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

      3. fma-define 94.0%

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

      4. associate-*l* 96.8%

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

      5. *-commutative 96.8%

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

      6. *-commutative 96.8%

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

      7. distribute-rgt-out 96.8%

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

      8. *-commutative 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around inf 79.9%

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

   6. Taylor expanded in b around inf 45.3%

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

      1. associate-*r* 45.3%

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

      2. *-commutative 45.3%

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

      3. associate-*r* 48.2%

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

   8. Simplified 48.2%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-93}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-140}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-89} \lor \neg \left(z \leq 2.3 \cdot 10^{-56}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot y + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e-89) (not (<= z 2.3e-56)))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))
   (+ x (+ (* z y) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-89) || !(z <= 2.3e-56)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = x + ((z * y) + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2d-89)) .or. (.not. (z <= 2.3d-56))) then
        tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
    else
        tmp = x + ((z * y) + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-89) || !(z <= 2.3e-56)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = x + ((z * y) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e-89) or not (z <= 2.3e-56):
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	else:
		tmp = x + ((z * y) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e-89) || !(z <= 2.3e-56))
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	else
		tmp = Float64(x + Float64(Float64(z * y) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2e-89) || ~((z <= 2.3e-56)))
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	else
		tmp = x + ((z * y) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e-89], N[Not[LessEqual[z, 2.3e-56]], $MachinePrecision]], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000008e-89 or 2.30000000000000002e-56 < z

   1. Initial program 93.1%

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

      1. associate-+l+ 93.1%

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

      2. associate-*l* 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 inf 97.1%

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

      1. +-commutative 97.1%

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

      2. associate-+l+ 97.1%

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

      3. +-commutative 97.1%

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

      4. associate-/l* 97.1%

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

      5. distribute-lft-out 97.1%

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

   7. Simplified 97.1%

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

   if -2.00000000000000008e-89 < z < 2.30000000000000002e-56

   1. Initial program 99.1%

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

      1. associate-+l+ 99.1%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around 0 93.4%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-89} \lor \neg \left(z \leq 2.3 \cdot 10^{-56}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot y + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-120}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+56}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -4.5e+34)
     t_1
     (if (<= a 5.9e-120) (+ x (* z y)) (if (<= a 8e+56) (+ x (* t a)) 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 <= -4.5e+34) {
		tmp = t_1;
	} else if (a <= 5.9e-120) {
		tmp = x + (z * y);
	} else if (a <= 8e+56) {
		tmp = x + (t * a);
	} 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 <= (-4.5d+34)) then
        tmp = t_1
    else if (a <= 5.9d-120) then
        tmp = x + (z * y)
    else if (a <= 8d+56) then
        tmp = x + (t * a)
    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 <= -4.5e+34) {
		tmp = t_1;
	} else if (a <= 5.9e-120) {
		tmp = x + (z * y);
	} else if (a <= 8e+56) {
		tmp = x + (t * a);
	} 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 <= -4.5e+34:
		tmp = t_1
	elif a <= 5.9e-120:
		tmp = x + (z * y)
	elif a <= 8e+56:
		tmp = x + (t * a)
	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 <= -4.5e+34)
		tmp = t_1;
	elseif (a <= 5.9e-120)
		tmp = Float64(x + Float64(z * y));
	elseif (a <= 8e+56)
		tmp = Float64(x + Float64(t * a));
	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 <= -4.5e+34)
		tmp = t_1;
	elseif (a <= 5.9e-120)
		tmp = x + (z * y);
	elseif (a <= 8e+56)
		tmp = x + (t * a);
	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, -4.5e+34], t$95$1, If[LessEqual[a, 5.9e-120], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+56], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5e34 or 8.00000000000000074e56 < a

   1. Initial program 91.6%

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

      1. associate-+l+ 91.6%

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

      2. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in a around inf 81.1%

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

   if -4.5e34 < a < 5.89999999999999979e-120

   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* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in a around 0 77.3%

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

   if 5.89999999999999979e-120 < a < 8.00000000000000074e56

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around 0 66.9%

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

      1. +-commutative 66.9%

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

   7. Simplified 66.9%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-120}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+56}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -27500:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-39}:\\ \;\;\;\;x + \left(z \cdot y + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -27500.0)
   (+ x (* a (+ t (* z b))))
   (if (<= b 9e-39)
     (+ x (+ (* z y) (* t a)))
     (+ x (+ (* t a) (* a (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -27500.0) {
		tmp = x + (a * (t + (z * b)));
	} else if (b <= 9e-39) {
		tmp = x + ((z * y) + (t * a));
	} else {
		tmp = x + ((t * a) + (a * (z * b)));
	}
	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 <= (-27500.0d0)) then
        tmp = x + (a * (t + (z * b)))
    else if (b <= 9d-39) then
        tmp = x + ((z * y) + (t * a))
    else
        tmp = x + ((t * a) + (a * (z * b)))
    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 <= -27500.0) {
		tmp = x + (a * (t + (z * b)));
	} else if (b <= 9e-39) {
		tmp = x + ((z * y) + (t * a));
	} else {
		tmp = x + ((t * a) + (a * (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -27500.0:
		tmp = x + (a * (t + (z * b)))
	elif b <= 9e-39:
		tmp = x + ((z * y) + (t * a))
	else:
		tmp = x + ((t * a) + (a * (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -27500.0)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	elseif (b <= 9e-39)
		tmp = Float64(x + Float64(Float64(z * y) + Float64(t * a)));
	else
		tmp = Float64(x + Float64(Float64(t * a) + Float64(a * Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -27500.0)
		tmp = x + (a * (t + (z * b)));
	elseif (b <= 9e-39)
		tmp = x + ((z * y) + (t * a));
	else
		tmp = x + ((t * a) + (a * (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -27500.0], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-39], N[(x + N[(N[(z * y), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -27500

   1. Initial program 97.1%

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

      1. associate-+l+ 97.1%

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

      2. +-commutative 97.1%

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

      3. fma-define 97.1%

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

      4. associate-*l* 95.8%

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

      5. *-commutative 95.8%

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

      6. *-commutative 95.8%

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

      7. distribute-rgt-out 98.6%

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

      8. *-commutative 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around 0 87.1%

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

   if -27500 < b < 9.0000000000000002e-39

   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* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in b around 0 95.1%

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

   if 9.0000000000000002e-39 < b

   1. Initial program 95.8%

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

      1. associate-+l+ 95.8%

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

      2. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around 0 86.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -27500:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-39}:\\ \;\;\;\;x + \left(z \cdot y + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-46} \lor \neg \left(a \leq 1.12 \cdot 10^{-119}\right):\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.7e+100)
   (* b (* z a))
   (if (or (<= a -2.65e-46) (not (<= a 1.12e-119)))
     (+ x (* t a))
     (+ x (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.7e+100) {
		tmp = b * (z * a);
	} else if ((a <= -2.65e-46) || !(a <= 1.12e-119)) {
		tmp = x + (t * a);
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.7d+100)) then
        tmp = b * (z * a)
    else if ((a <= (-2.65d-46)) .or. (.not. (a <= 1.12d-119))) then
        tmp = x + (t * a)
    else
        tmp = x + (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.7e+100) {
		tmp = b * (z * a);
	} else if ((a <= -2.65e-46) || !(a <= 1.12e-119)) {
		tmp = x + (t * a);
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.7e+100:
		tmp = b * (z * a)
	elif (a <= -2.65e-46) or not (a <= 1.12e-119):
		tmp = x + (t * a)
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.7e+100)
		tmp = Float64(b * Float64(z * a));
	elseif ((a <= -2.65e-46) || !(a <= 1.12e-119))
		tmp = Float64(x + Float64(t * a));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.7e+100)
		tmp = b * (z * a);
	elseif ((a <= -2.65e-46) || ~((a <= 1.12e-119)))
		tmp = x + (t * a);
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.7e+100], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -2.65e-46], N[Not[LessEqual[a, 1.12e-119]], $MachinePrecision]], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.69999999999999997e100

   1. Initial program 89.0%

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

      1. associate-+l+ 89.0%

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

      2. +-commutative 89.0%

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

      3. fma-define 89.0%

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

      4. associate-*l* 89.1%

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

      5. *-commutative 89.1%

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

      6. *-commutative 89.1%

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

      7. distribute-rgt-out 94.5%

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

      8. *-commutative 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in y around inf 94.8%

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

   6. Taylor expanded in b around inf 61.2%

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

      1. associate-*r* 55.9%

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

      2. *-commutative 55.9%

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

      3. associate-*r* 66.2%

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

   8. Simplified 66.2%

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

   if -1.69999999999999997e100 < a < -2.65000000000000009e-46 or 1.11999999999999998e-119 < a

   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* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 66.7%

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

      1. +-commutative 66.7%

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

   7. Simplified 66.7%

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

   if -2.65000000000000009e-46 < a < 1.11999999999999998e-119

   1. Initial program 98.0%

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

      1. associate-+l+ 98.0%

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

      2. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in a around 0 83.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-46} \lor \neg \left(a \leq 1.12 \cdot 10^{-119}\right):\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-48} \lor \neg \left(a \leq 5 \cdot 10^{-121}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.9e-48) (not (<= a 5e-121)))
   (+ x (* a (+ t (* z b))))
   (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.9e-48) || !(a <= 5e-121)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-3.9d-48)) .or. (.not. (a <= 5d-121))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.9e-48) || !(a <= 5e-121)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.9e-48) or not (a <= 5e-121):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.9e-48) || !(a <= 5e-121))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.9e-48) || ~((a <= 5e-121)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.9e-48], N[Not[LessEqual[a, 5e-121]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9e-48 or 4.99999999999999989e-121 < a

   1. Initial program 94.7%

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

      1. associate-+l+ 94.7%

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

      2. +-commutative 94.7%

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

      3. fma-define 94.7%

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

      4. associate-*l* 96.4%

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

      5. *-commutative 96.4%

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

      6. *-commutative 96.4%

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

      7. distribute-rgt-out 97.6%

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

      8. *-commutative 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around 0 88.1%

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

   if -3.9e-48 < a < 4.99999999999999989e-121

   1. Initial program 98.0%

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

      1. associate-+l+ 98.0%

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

      2. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in a around 0 83.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-48} \lor \neg \left(a \leq 5 \cdot 10^{-121}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -300000 \lor \neg \left(b \leq 8 \cdot 10^{-39}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot y + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -300000.0) (not (<= b 8e-39)))
   (+ x (* a (+ t (* z b))))
   (+ x (+ (* z y) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -300000.0) || !(b <= 8e-39)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + ((z * y) + (t * a));
	}
	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 <= (-300000.0d0)) .or. (.not. (b <= 8d-39))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + ((z * y) + (t * a))
    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 <= -300000.0) || !(b <= 8e-39)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + ((z * y) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -300000.0) or not (b <= 8e-39):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + ((z * y) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -300000.0) || !(b <= 8e-39))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(Float64(z * y) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -300000.0) || ~((b <= 8e-39)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + ((z * y) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -300000.0], N[Not[LessEqual[b, 8e-39]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3e5 or 7.99999999999999943e-39 < b

   1. Initial program 96.5%

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

      1. associate-+l+ 96.5%

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

      2. +-commutative 96.5%

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

      3. fma-define 96.5%

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

      4. associate-*l* 94.2%

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

      5. *-commutative 94.2%

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

      6. *-commutative 94.2%

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

      7. distribute-rgt-out 95.7%

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

      8. *-commutative 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in y around 0 87.0%

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

   if -3e5 < b < 7.99999999999999943e-39

   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* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in b around 0 95.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -300000 \lor \neg \left(b \leq 8 \cdot 10^{-39}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot y + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-88}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-42}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.2e+39)
   x
   (if (<= x -3.4e-88) (* z y) (if (<= x 9.6e-42) (* t a) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.2e+39) {
		tmp = x;
	} else if (x <= -3.4e-88) {
		tmp = z * y;
	} else if (x <= 9.6e-42) {
		tmp = t * a;
	} 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 (x <= (-3.2d+39)) then
        tmp = x
    else if (x <= (-3.4d-88)) then
        tmp = z * y
    else if (x <= 9.6d-42) then
        tmp = t * a
    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 (x <= -3.2e+39) {
		tmp = x;
	} else if (x <= -3.4e-88) {
		tmp = z * y;
	} else if (x <= 9.6e-42) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.2e+39:
		tmp = x
	elif x <= -3.4e-88:
		tmp = z * y
	elif x <= 9.6e-42:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.2e+39)
		tmp = x;
	elseif (x <= -3.4e-88)
		tmp = Float64(z * y);
	elseif (x <= 9.6e-42)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.2e+39)
		tmp = x;
	elseif (x <= -3.4e-88)
		tmp = z * y;
	elseif (x <= 9.6e-42)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.2e+39], x, If[LessEqual[x, -3.4e-88], N[(z * y), $MachinePrecision], If[LessEqual[x, 9.6e-42], N[(t * a), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.19999999999999993e39 or 9.60000000000000011e-42 < x

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in x around inf 54.6%

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

   if -3.19999999999999993e39 < x < -3.39999999999999975e-88

   1. Initial program 85.5%

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

      1. associate-+l+ 85.5%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in y around inf 46.4%

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

      1. *-commutative 46.4%

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

   7. Simplified 46.4%

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

   if -3.39999999999999975e-88 < x < 9.60000000000000011e-42

   1. Initial program 94.5%

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

      1. associate-+l+ 94.5%

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

      2. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around inf 42.3%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-88}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-42}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.1e-80) x (if (<= x 7.2e-42) (* t a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.1e-80) {
		tmp = x;
	} else if (x <= 7.2e-42) {
		tmp = t * a;
	} 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 (x <= (-1.1d-80)) then
        tmp = x
    else if (x <= 7.2d-42) then
        tmp = t * a
    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 (x <= -1.1e-80) {
		tmp = x;
	} else if (x <= 7.2e-42) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.1e-80:
		tmp = x
	elif x <= 7.2e-42:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.1e-80)
		tmp = x;
	elseif (x <= 7.2e-42)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.1e-80)
		tmp = x;
	elseif (x <= 7.2e-42)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.1e-80], x, If[LessEqual[x, 7.2e-42], N[(t * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.10000000000000005e-80 or 7.2000000000000004e-42 < x

   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* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 49.9%

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

   if -1.10000000000000005e-80 < x < 7.2000000000000004e-42

   1. Initial program 94.6%

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

      1. associate-+l+ 94.6%

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

      2. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 42.1%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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 95.8%

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

   1. associate-+l+ 95.8%

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

   2. associate-*l* 96.1%

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

3. Simplified 96.1%

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

5. Taylor expanded in x around inf 31.9%

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

6. Final simplification 31.9%

   \[\leadsto x \]
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 2024082 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (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)))