Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.3% → 99.9%

Time: 8.5s

Alternatives: 13

Speedup: 0.8×

• 32.0% 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: 92.3% 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: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0005:\\ \;\;\;\;\left(x + a \cdot \left(t + z \cdot b\right)\right) + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))))
   (if (<= z -2e+27)
     t_1
     (if (<= z 0.0005) (+ (+ x (* a (+ t (* z b)))) (* y z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + ((x / z) + (a * (b + (t / z)))));
	double tmp;
	if (z <= -2e+27) {
		tmp = t_1;
	} else if (z <= 0.0005) {
		tmp = (x + (a * (t + (z * b)))) + (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 = z * (y + ((x / z) + (a * (b + (t / z)))))
    if (z <= (-2d+27)) then
        tmp = t_1
    else if (z <= 0.0005d0) then
        tmp = (x + (a * (t + (z * b)))) + (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 = z * (y + ((x / z) + (a * (b + (t / z)))));
	double tmp;
	if (z <= -2e+27) {
		tmp = t_1;
	} else if (z <= 0.0005) {
		tmp = (x + (a * (t + (z * b)))) + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + ((x / z) + (a * (b + (t / z)))))
	tmp = 0
	if z <= -2e+27:
		tmp = t_1
	elif z <= 0.0005:
		tmp = (x + (a * (t + (z * b)))) + (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))))
	tmp = 0.0
	if (z <= -2e+27)
		tmp = t_1;
	elseif (z <= 0.0005)
		tmp = Float64(Float64(x + Float64(a * Float64(t + Float64(z * b)))) + Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y + ((x / z) + (a * (b + (t / z)))));
	tmp = 0.0;
	if (z <= -2e+27)
		tmp = t_1;
	elseif (z <= 0.0005)
		tmp = (x + (a * (t + (z * b)))) + (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+27], t$95$1, If[LessEqual[z, 0.0005], N[(N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2e27 or 5.0000000000000001e-4 < z

   1. Initial program 83.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

      8. associate-/l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. /-lowering-/.f64 99.9%

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

   7. Simplified 99.9%

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

   if -2e27 < z < 5.0000000000000001e-4

   1. Initial program 98.6%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{elif}\;z \leq 0.0005:\\ \;\;\;\;\left(x + a \cdot \left(t + z \cdot b\right)\right) + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 1e+308) t_1 (* z (+ y (+ (/ x z) (* a (+ b (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= 1e+308) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
    if (t_1 <= 1d+308) then
        tmp = t_1
    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 t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= 1e+308) {
		tmp = t_1;
	} else {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
	tmp = 0
	if t_1 <= 1e+308:
		tmp = t_1
	else:
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= 1e+308)
		tmp = t_1;
	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)
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	tmp = 0.0;
	if (t_1 <= 1e+308)
		tmp = t_1;
	else
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+308], t$95$1, 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 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 1e308

   1. Initial program 98.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   if 1e308 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 66.7%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

      8. associate-/l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. /-lowering-/.f64 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq 10^{+308}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.26e+61)
   (+ x (* y z))
   (if (<= x 4.5e+113) (+ (* z (+ y (* a b))) (* t a)) (+ x (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.26e+61) {
		tmp = x + (y * z);
	} else if (x <= 4.5e+113) {
		tmp = (z * (y + (a * b))) + (t * a);
	} else {
		tmp = x + (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 (x <= (-1.26d+61)) then
        tmp = x + (y * z)
    else if (x <= 4.5d+113) then
        tmp = (z * (y + (a * b))) + (t * a)
    else
        tmp = x + (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 (x <= -1.26e+61) {
		tmp = x + (y * z);
	} else if (x <= 4.5e+113) {
		tmp = (z * (y + (a * b))) + (t * a);
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.26e+61:
		tmp = x + (y * z)
	elif x <= 4.5e+113:
		tmp = (z * (y + (a * b))) + (t * a)
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.26e+61)
		tmp = Float64(x + Float64(y * z));
	elseif (x <= 4.5e+113)
		tmp = Float64(Float64(z * Float64(y + Float64(a * b))) + Float64(t * a));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.26e+61)
		tmp = x + (y * z);
	elseif (x <= 4.5e+113)
		tmp = (z * (y + (a * b))) + (t * a);
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.26e+61], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+113], N[(N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2600000000000001e61

   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+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 75.8%

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

   if -1.2600000000000001e61 < x < 4.5000000000000001e113

   1. Initial program 90.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

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

      2. associate-+r+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-in N/A

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

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

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

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

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

      10. *-lowering-*.f64 87.7%

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

   7. Simplified 87.7%

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

   if 4.5000000000000001e113 < x

   1. Initial program 94.2%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+172}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 105000:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.8e+172)
   (* y z)
   (if (<= z -9.6e-33)
     (* z (* a b))
     (if (<= z 105000.0) (+ x (* t a)) (* (* z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.8e+172) {
		tmp = y * z;
	} else if (z <= -9.6e-33) {
		tmp = z * (a * b);
	} else if (z <= 105000.0) {
		tmp = x + (t * a);
	} else {
		tmp = (z * a) * 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 (z <= (-2.8d+172)) then
        tmp = y * z
    else if (z <= (-9.6d-33)) then
        tmp = z * (a * b)
    else if (z <= 105000.0d0) then
        tmp = x + (t * a)
    else
        tmp = (z * a) * 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 (z <= -2.8e+172) {
		tmp = y * z;
	} else if (z <= -9.6e-33) {
		tmp = z * (a * b);
	} else if (z <= 105000.0) {
		tmp = x + (t * a);
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.8e+172:
		tmp = y * z
	elif z <= -9.6e-33:
		tmp = z * (a * b)
	elif z <= 105000.0:
		tmp = x + (t * a)
	else:
		tmp = (z * a) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.8e+172)
		tmp = Float64(y * z);
	elseif (z <= -9.6e-33)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= 105000.0)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = Float64(Float64(z * a) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.8e+172)
		tmp = y * z;
	elseif (z <= -9.6e-33)
		tmp = z * (a * b);
	elseif (z <= 105000.0)
		tmp = x + (t * a);
	else
		tmp = (z * a) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.8e+172], N[(y * z), $MachinePrecision], If[LessEqual[z, -9.6e-33], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 105000.0], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8e172

   1. Initial program 88.6%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 58.9%

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

   7. Simplified 58.9%

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

   if -2.8e172 < z < -9.6e-33

   1. Initial program 83.6%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 46.2%

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

   7. Simplified 46.2%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 51.1%

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

   9. Applied egg-rr 51.1%

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

   if -9.6e-33 < z < 105000

   1. Initial program 98.5%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 71.1%

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

   7. Simplified 71.1%

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

   if 105000 < z

   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+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 55.3%

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

   7. Simplified 55.3%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+172}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 105000:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6200:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq 3.35 \cdot 10^{-267}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+27}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6200.0)
   (* (* z a) b)
   (if (<= b 3.35e-267) x (if (<= b 6e+27) (* y z) (* z (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6200.0) {
		tmp = (z * a) * b;
	} else if (b <= 3.35e-267) {
		tmp = x;
	} else if (b <= 6e+27) {
		tmp = y * z;
	} else {
		tmp = z * (a * 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 <= (-6200.0d0)) then
        tmp = (z * a) * b
    else if (b <= 3.35d-267) then
        tmp = x
    else if (b <= 6d+27) then
        tmp = y * z
    else
        tmp = z * (a * 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 <= -6200.0) {
		tmp = (z * a) * b;
	} else if (b <= 3.35e-267) {
		tmp = x;
	} else if (b <= 6e+27) {
		tmp = y * z;
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6200.0:
		tmp = (z * a) * b
	elif b <= 3.35e-267:
		tmp = x
	elif b <= 6e+27:
		tmp = y * z
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6200.0)
		tmp = Float64(Float64(z * a) * b);
	elseif (b <= 3.35e-267)
		tmp = x;
	elseif (b <= 6e+27)
		tmp = Float64(y * z);
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6200.0)
		tmp = (z * a) * b;
	elseif (b <= 3.35e-267)
		tmp = x;
	elseif (b <= 6e+27)
		tmp = y * z;
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6200.0], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 3.35e-267], x, If[LessEqual[b, 6e+27], N[(y * z), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6200

   1. Initial program 90.2%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 49.3%

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

   7. Simplified 49.3%

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

   if -6200 < b < 3.3500000000000001e-267

   1. Initial program 98.6%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 43.5%

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

   if 3.3500000000000001e-267 < b < 5.99999999999999953e27

   1. Initial program 88.4%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 47.3%

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

   7. Simplified 47.3%

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

   if 5.99999999999999953e27 < b

   1. Initial program 90.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 64.1%

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

   7. Simplified 64.1%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 67.3%

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

   9. Applied egg-rr 67.3%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6200:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq 3.35 \cdot 10^{-267}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+27}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;b \leq -15500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-267}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+25}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= b -15500.0)
     t_1
     (if (<= b 4.5e-267) x (if (<= b 1.8e+25) (* y z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (b <= -15500.0) {
		tmp = t_1;
	} else if (b <= 4.5e-267) {
		tmp = x;
	} else if (b <= 1.8e+25) {
		tmp = 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 = (z * a) * b
    if (b <= (-15500.0d0)) then
        tmp = t_1
    else if (b <= 4.5d-267) then
        tmp = x
    else if (b <= 1.8d+25) then
        tmp = 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 = (z * a) * b;
	double tmp;
	if (b <= -15500.0) {
		tmp = t_1;
	} else if (b <= 4.5e-267) {
		tmp = x;
	} else if (b <= 1.8e+25) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) * b
	tmp = 0
	if b <= -15500.0:
		tmp = t_1
	elif b <= 4.5e-267:
		tmp = x
	elif b <= 1.8e+25:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (b <= -15500.0)
		tmp = t_1;
	elseif (b <= 4.5e-267)
		tmp = x;
	elseif (b <= 1.8e+25)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * a) * b;
	tmp = 0.0;
	if (b <= -15500.0)
		tmp = t_1;
	elseif (b <= 4.5e-267)
		tmp = x;
	elseif (b <= 1.8e+25)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -15500.0], t$95$1, If[LessEqual[b, 4.5e-267], x, If[LessEqual[b, 1.8e+25], N[(y * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -15500 or 1.80000000000000008e25 < b

   1. Initial program 90.1%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 56.2%

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

   7. Simplified 56.2%

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

   if -15500 < b < 4.4999999999999999e-267

   1. Initial program 98.6%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 43.5%

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

   if 4.4999999999999999e-267 < b < 1.80000000000000008e25

   1. Initial program 88.4%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 47.3%

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

   7. Simplified 47.3%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -15500:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-267}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+25}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+184}:\\ \;\;\;\;\left(x + a \cdot \left(t + z \cdot b\right)\right) + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 5e+184) (+ (+ x (* a (+ t (* z b)))) (* y z)) (* z (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 5e+184) {
		tmp = (x + (a * (t + (z * b)))) + (y * z);
	} else {
		tmp = z * (y + (a * 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 (z <= 5d+184) then
        tmp = (x + (a * (t + (z * b)))) + (y * z)
    else
        tmp = z * (y + (a * 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 (z <= 5e+184) {
		tmp = (x + (a * (t + (z * b)))) + (y * z);
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 5e+184:
		tmp = (x + (a * (t + (z * b)))) + (y * z)
	else:
		tmp = z * (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 5e+184)
		tmp = Float64(Float64(x + Float64(a * Float64(t + Float64(z * b)))) + Float64(y * z));
	else
		tmp = Float64(z * Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 5e+184)
		tmp = (x + (a * (t + (z * b)))) + (y * z);
	else
		tmp = z * (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 5e+184], N[(N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.9999999999999999e184

   1. Initial program 93.4%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.1%

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

   3. Simplified 95.1%

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

   if 4.9999999999999999e184 < z

   1. Initial program 79.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+184}:\\ \;\;\;\;\left(x + a \cdot \left(t + z \cdot b\right)\right) + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -1.86 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-34}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -1.86e-34) t_1 (if (<= z 8.2e-34) (+ x (* t a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -1.86e-34) {
		tmp = t_1;
	} else if (z <= 8.2e-34) {
		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 = z * (y + (a * b))
    if (z <= (-1.86d-34)) then
        tmp = t_1
    else if (z <= 8.2d-34) 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 = z * (y + (a * b));
	double tmp;
	if (z <= -1.86e-34) {
		tmp = t_1;
	} else if (z <= 8.2e-34) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (a * b))
	tmp = 0
	if z <= -1.86e-34:
		tmp = t_1
	elif z <= 8.2e-34:
		tmp = x + (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -1.86e-34)
		tmp = t_1;
	elseif (z <= 8.2e-34)
		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 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -1.86e-34)
		tmp = t_1;
	elseif (z <= 8.2e-34)
		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[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.86e-34], t$95$1, If[LessEqual[z, 8.2e-34], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.86e-34 or 8.2000000000000007e-34 < z

   1. Initial program 85.6%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 82.4%

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

   7. Simplified 82.4%

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

   if -1.86e-34 < z < 8.2000000000000007e-34

   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+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.86 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-34}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -5.1e+29) t_1 (if (<= a 1.85e-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 <= -5.1e+29) {
		tmp = t_1;
	} else if (a <= 1.85e-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 <= (-5.1d+29)) then
        tmp = t_1
    else if (a <= 1.85d-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 <= -5.1e+29) {
		tmp = t_1;
	} else if (a <= 1.85e-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 <= -5.1e+29:
		tmp = t_1
	elif a <= 1.85e-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 <= -5.1e+29)
		tmp = t_1;
	elseif (a <= 1.85e-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 <= -5.1e+29)
		tmp = t_1;
	elseif (a <= 1.85e-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, -5.1e+29], t$95$1, If[LessEqual[a, 1.85e-64], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.1000000000000001e29 or 1.84999999999999999e-64 < a

   1. Initial program 85.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around inf

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

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

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

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

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

      3. *-lowering-*.f64 78.2%

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

   7. Simplified 78.2%

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

   if -5.1000000000000001e29 < a < 1.84999999999999999e-64

   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+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 75.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+117}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6e+117)
   (* (* z a) b)
   (if (<= b 1.55e+28) (+ x (* y z)) (* z (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6e+117) {
		tmp = (z * a) * b;
	} else if (b <= 1.55e+28) {
		tmp = x + (y * z);
	} else {
		tmp = z * (a * 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 <= (-6d+117)) then
        tmp = (z * a) * b
    else if (b <= 1.55d+28) then
        tmp = x + (y * z)
    else
        tmp = z * (a * 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 <= -6e+117) {
		tmp = (z * a) * b;
	} else if (b <= 1.55e+28) {
		tmp = x + (y * z);
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6e+117:
		tmp = (z * a) * b
	elif b <= 1.55e+28:
		tmp = x + (y * z)
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6e+117)
		tmp = Float64(Float64(z * a) * b);
	elseif (b <= 1.55e+28)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6e+117)
		tmp = (z * a) * b;
	elseif (b <= 1.55e+28)
		tmp = x + (y * z);
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6e+117], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 1.55e+28], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6e117

   1. Initial program 88.2%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 60.9%

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

   7. Simplified 60.9%

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

   if -6e117 < b < 1.55e28

   1. Initial program 93.6%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 66.7%

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

   if 1.55e28 < b

   1. Initial program 90.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 64.1%

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

   7. Simplified 64.1%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 67.3%

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

   9. Applied egg-rr 67.3%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+117}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+33}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.8e-14) x (if (<= x 4.5e+33) (* y z) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.8e-14) {
		tmp = x;
	} else if (x <= 4.5e+33) {
		tmp = y * z;
	} 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 <= (-3.8d-14)) then
        tmp = x
    else if (x <= 4.5d+33) then
        tmp = y * z
    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 <= -3.8e-14) {
		tmp = x;
	} else if (x <= 4.5e+33) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.8e-14:
		tmp = x
	elif x <= 4.5e+33:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.8e-14)
		tmp = x;
	elseif (x <= 4.5e+33)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.8e-14)
		tmp = x;
	elseif (x <= 4.5e+33)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.8e-14], x, If[LessEqual[x, 4.5e+33], N[(y * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8000000000000002e-14 or 4.5e33 < x

   1. Initial program 92.5%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 49.1%

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

   if -3.8000000000000002e-14 < x < 4.5e33

   1. Initial program 91.3%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 37.5%

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

   7. Simplified 37.5%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+33}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+57}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.4e+57) (* t a) (if (<= a 1.5e-5) x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.4e+57) {
		tmp = t * a;
	} else if (a <= 1.5e-5) {
		tmp = x;
	} else {
		tmp = 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 (a <= (-3.4d+57)) then
        tmp = t * a
    else if (a <= 1.5d-5) then
        tmp = x
    else
        tmp = 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 (a <= -3.4e+57) {
		tmp = t * a;
	} else if (a <= 1.5e-5) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.4e+57:
		tmp = t * a
	elif a <= 1.5e-5:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.4e+57)
		tmp = Float64(t * a);
	elseif (a <= 1.5e-5)
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.4e+57)
		tmp = t * a;
	elseif (a <= 1.5e-5)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.4e+57], N[(t * a), $MachinePrecision], If[LessEqual[a, 1.5e-5], x, N[(t * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.39999999999999992e57 or 1.50000000000000004e-5 < a

   1. Initial program 83.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 39.7%

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

   7. Simplified 39.7%

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

   if -3.39999999999999992e57 < a < 1.50000000000000004e-5

   1. Initial program 98.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 35.6%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+57}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.8% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 91.8%

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

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

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

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

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

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

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

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

   7. *-commutative N/A

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

   8. associate-*l* N/A

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

   9. distribute-lft-out N/A

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

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

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

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

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

   12. *-lowering-*.f64 92.3%

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

3. Simplified 92.3%

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

5. Taylor expanded in x around inf

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

7. Simplified 25.7%

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

Developer Target 1: 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 2024155 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

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