Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.1% → 99.0%

Time: 11.9s

Alternatives: 12

Speedup: 0.7×

• 31.3% 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: 92.1% 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: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b + \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x + z \cdot \left(y + t\_1\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot y + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(t\_1 + \frac{x}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ b (/ t z)))))
   (if (<= z -4.5e+153)
     (+ x (* z (+ y t_1)))
     (if (<= z 2e+51)
       (+ (* z y) (+ x (* a (+ t (* z b)))))
       (* z (+ y (+ t_1 (/ x z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (b + (t / z));
	double tmp;
	if (z <= -4.5e+153) {
		tmp = x + (z * (y + t_1));
	} else if (z <= 2e+51) {
		tmp = (z * y) + (x + (a * (t + (z * b))));
	} else {
		tmp = z * (y + (t_1 + (x / 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 = a * (b + (t / z))
    if (z <= (-4.5d+153)) then
        tmp = x + (z * (y + t_1))
    else if (z <= 2d+51) then
        tmp = (z * y) + (x + (a * (t + (z * b))))
    else
        tmp = z * (y + (t_1 + (x / 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 = a * (b + (t / z));
	double tmp;
	if (z <= -4.5e+153) {
		tmp = x + (z * (y + t_1));
	} else if (z <= 2e+51) {
		tmp = (z * y) + (x + (a * (t + (z * b))));
	} else {
		tmp = z * (y + (t_1 + (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (b + (t / z))
	tmp = 0
	if z <= -4.5e+153:
		tmp = x + (z * (y + t_1))
	elif z <= 2e+51:
		tmp = (z * y) + (x + (a * (t + (z * b))))
	else:
		tmp = z * (y + (t_1 + (x / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(b + Float64(t / z)))
	tmp = 0.0
	if (z <= -4.5e+153)
		tmp = Float64(x + Float64(z * Float64(y + t_1)));
	elseif (z <= 2e+51)
		tmp = Float64(Float64(z * y) + Float64(x + Float64(a * Float64(t + Float64(z * b)))));
	else
		tmp = Float64(z * Float64(y + Float64(t_1 + Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (b + (t / z));
	tmp = 0.0;
	if (z <= -4.5e+153)
		tmp = x + (z * (y + t_1));
	elseif (z <= 2e+51)
		tmp = (z * y) + (x + (a * (t + (z * b))));
	else
		tmp = z * (y + (t_1 + (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+153], N[(x + N[(z * N[(y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+51], N[(N[(z * y), $MachinePrecision] + N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(t$95$1 + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5000000000000001e153

   1. Initial program 85.4%

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

      1. associate-+l+ 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 77.1%

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

   3. Simplified 77.1%

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

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

   8. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

      6. /-lowering-/.f64 100.0%

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

   10. Simplified 100.0%

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

   if -4.5000000000000001e153 < z < 2e51

   1. Initial program 97.1%

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

      1. associate-+l+ 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

   if 2e51 < z

   1. Initial program 75.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in z around inf

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot y + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 39.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-39}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 1.58 \cdot 10^{-260}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 1550000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+163}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.05e-39)
   (* a t)
   (if (<= a 1.58e-260)
     (* z y)
     (if (<= a 1550000.0) x (if (<= a 3.8e+163) (* a (* z b)) (* a t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.05e-39) {
		tmp = a * t;
	} else if (a <= 1.58e-260) {
		tmp = z * y;
	} else if (a <= 1550000.0) {
		tmp = x;
	} else if (a <= 3.8e+163) {
		tmp = a * (z * b);
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.05d-39)) then
        tmp = a * t
    else if (a <= 1.58d-260) then
        tmp = z * y
    else if (a <= 1550000.0d0) then
        tmp = x
    else if (a <= 3.8d+163) then
        tmp = a * (z * b)
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.05e-39) {
		tmp = a * t;
	} else if (a <= 1.58e-260) {
		tmp = z * y;
	} else if (a <= 1550000.0) {
		tmp = x;
	} else if (a <= 3.8e+163) {
		tmp = a * (z * b);
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.05e-39:
		tmp = a * t
	elif a <= 1.58e-260:
		tmp = z * y
	elif a <= 1550000.0:
		tmp = x
	elif a <= 3.8e+163:
		tmp = a * (z * b)
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.05e-39)
		tmp = Float64(a * t);
	elseif (a <= 1.58e-260)
		tmp = Float64(z * y);
	elseif (a <= 1550000.0)
		tmp = x;
	elseif (a <= 3.8e+163)
		tmp = Float64(a * Float64(z * b));
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.05e-39)
		tmp = a * t;
	elseif (a <= 1.58e-260)
		tmp = z * y;
	elseif (a <= 1550000.0)
		tmp = x;
	elseif (a <= 3.8e+163)
		tmp = a * (z * b);
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.05e-39], N[(a * t), $MachinePrecision], If[LessEqual[a, 1.58e-260], N[(z * y), $MachinePrecision], If[LessEqual[a, 1550000.0], x, If[LessEqual[a, 3.8e+163], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], N[(a * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.04999999999999997e-39 or 3.80000000000000008e163 < a

   1. Initial program 85.8%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 45.0%

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

   7. Simplified 45.0%

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

   if -1.04999999999999997e-39 < a < 1.58000000000000002e-260

   1. Initial program 97.2%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 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 56.9%

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

   7. Simplified 56.9%

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

   if 1.58000000000000002e-260 < a < 1.55e6

   1. Initial program 97.9%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 56.7%

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

   if 1.55e6 < a < 3.80000000000000008e163

   1. Initial program 86.2%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 42.0%

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

   7. Simplified 42.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 45.1%

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

   9. Applied egg-rr 45.1%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-39}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 1.58 \cdot 10^{-260}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 1550000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+163}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot y + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ y (* a (+ b (/ t z))))))))
   (if (<= z -1e+154)
     t_1
     (if (<= z 2e+51) (+ (* z y) (+ x (* a (+ t (* z b))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * (b + (t / z)))));
	double tmp;
	if (z <= -1e+154) {
		tmp = t_1;
	} else if (z <= 2e+51) {
		tmp = (z * y) + (x + (a * (t + (z * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y + (a * (b + (t / z)))))
    if (z <= (-1d+154)) then
        tmp = t_1
    else if (z <= 2d+51) then
        tmp = (z * y) + (x + (a * (t + (z * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * (b + (t / z)))));
	double tmp;
	if (z <= -1e+154) {
		tmp = t_1;
	} else if (z <= 2e+51) {
		tmp = (z * y) + (x + (a * (t + (z * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y + (a * (b + (t / z)))))
	tmp = 0
	if z <= -1e+154:
		tmp = t_1
	elif z <= 2e+51:
		tmp = (z * y) + (x + (a * (t + (z * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y + Float64(a * Float64(b + Float64(t / z))))))
	tmp = 0.0
	if (z <= -1e+154)
		tmp = t_1;
	elseif (z <= 2e+51)
		tmp = Float64(Float64(z * y) + Float64(x + Float64(a * Float64(t + Float64(z * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y + (a * (b + (t / z)))));
	tmp = 0.0;
	if (z <= -1e+154)
		tmp = t_1;
	elseif (z <= 2e+51)
		tmp = (z * y) + (x + (a * (t + (z * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+154], t$95$1, If[LessEqual[z, 2e+51], N[(N[(z * y), $MachinePrecision] + N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000004e154 or 2e51 < z

   1. Initial program 79.3%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in 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%

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

   8. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

      6. /-lowering-/.f64 100.0%

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

   10. Simplified 100.0%

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

   if -1.00000000000000004e154 < z < 2e51

   1. Initial program 97.1%

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

      1. associate-+l+ 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 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+154}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot y + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-156}:\\ \;\;\;\;b \cdot \left(z \cdot a\right) + \left(x + a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ y (* a (+ b (/ t z))))))))
   (if (<= z -3.2e-66)
     t_1
     (if (<= z 4.8e-156) (+ (* b (* z a)) (+ x (* a t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * (b + (t / z)))));
	double tmp;
	if (z <= -3.2e-66) {
		tmp = t_1;
	} else if (z <= 4.8e-156) {
		tmp = (b * (z * a)) + (x + (a * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y + (a * (b + (t / z)))))
    if (z <= (-3.2d-66)) then
        tmp = t_1
    else if (z <= 4.8d-156) then
        tmp = (b * (z * a)) + (x + (a * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * (b + (t / z)))));
	double tmp;
	if (z <= -3.2e-66) {
		tmp = t_1;
	} else if (z <= 4.8e-156) {
		tmp = (b * (z * a)) + (x + (a * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y + (a * (b + (t / z)))))
	tmp = 0
	if z <= -3.2e-66:
		tmp = t_1
	elif z <= 4.8e-156:
		tmp = (b * (z * a)) + (x + (a * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y + Float64(a * Float64(b + Float64(t / z))))))
	tmp = 0.0
	if (z <= -3.2e-66)
		tmp = t_1;
	elseif (z <= 4.8e-156)
		tmp = Float64(Float64(b * Float64(z * a)) + Float64(x + Float64(a * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y + (a * (b + (t / z)))));
	tmp = 0.0;
	if (z <= -3.2e-66)
		tmp = t_1;
	elseif (z <= 4.8e-156)
		tmp = (b * (z * a)) + (x + (a * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-66], t$95$1, If[LessEqual[z, 4.8e-156], N[(N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision] + N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999982e-66 or 4.8e-156 < z

   1. Initial program 87.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 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 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

      6. /-lowering-/.f64 97.6%

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

   10. Simplified 97.6%

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

   if -3.19999999999999982e-66 < z < 4.8e-156

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 91.6%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-156}:\\ \;\;\;\;b \cdot \left(z \cdot a\right) + \left(x + a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(z \cdot a\right) + \left(x + a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ y (* a b))))))
   (if (<= z -8.2e+39)
     t_1
     (if (<= z 2.85e-112) (+ (* b (* z a)) (+ x (* a t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -8.2e+39) {
		tmp = t_1;
	} else if (z <= 2.85e-112) {
		tmp = (b * (z * a)) + (x + (a * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y + (a * b)))
    if (z <= (-8.2d+39)) then
        tmp = t_1
    else if (z <= 2.85d-112) then
        tmp = (b * (z * a)) + (x + (a * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -8.2e+39) {
		tmp = t_1;
	} else if (z <= 2.85e-112) {
		tmp = (b * (z * a)) + (x + (a * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y + (a * b)))
	tmp = 0
	if z <= -8.2e+39:
		tmp = t_1
	elif z <= 2.85e-112:
		tmp = (b * (z * a)) + (x + (a * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y + Float64(a * b))))
	tmp = 0.0
	if (z <= -8.2e+39)
		tmp = t_1;
	elseif (z <= 2.85e-112)
		tmp = Float64(Float64(b * Float64(z * a)) + Float64(x + Float64(a * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y + (a * b)));
	tmp = 0.0;
	if (z <= -8.2e+39)
		tmp = t_1;
	elseif (z <= 2.85e-112)
		tmp = (b * (z * a)) + (x + (a * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+39], t$95$1, If[LessEqual[z, 2.85e-112], N[(N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision] + N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.20000000000000008e39 or 2.85000000000000008e-112 < z

   1. Initial program 84.0%

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

      1. associate-+l+ 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 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

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

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

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

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

      7. *-lowering-*.f64 88.7%

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

   7. Simplified 88.7%

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

   if -8.20000000000000008e39 < z < 2.85000000000000008e-112

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 89.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+39}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(z \cdot a\right) + \left(x + a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot y\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+257}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-111}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z y))))
   (if (<= z -6.8e+257)
     (* a (* z b))
     (if (<= z -2.6e+83) t_1 (if (<= z 1.45e-111) (+ x (* a t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * y);
	double tmp;
	if (z <= -6.8e+257) {
		tmp = a * (z * b);
	} else if (z <= -2.6e+83) {
		tmp = t_1;
	} else if (z <= 1.45e-111) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * y)
    if (z <= (-6.8d+257)) then
        tmp = a * (z * b)
    else if (z <= (-2.6d+83)) then
        tmp = t_1
    else if (z <= 1.45d-111) then
        tmp = x + (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * y);
	double tmp;
	if (z <= -6.8e+257) {
		tmp = a * (z * b);
	} else if (z <= -2.6e+83) {
		tmp = t_1;
	} else if (z <= 1.45e-111) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * y)
	tmp = 0
	if z <= -6.8e+257:
		tmp = a * (z * b)
	elif z <= -2.6e+83:
		tmp = t_1
	elif z <= 1.45e-111:
		tmp = x + (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * y))
	tmp = 0.0
	if (z <= -6.8e+257)
		tmp = Float64(a * Float64(z * b));
	elseif (z <= -2.6e+83)
		tmp = t_1;
	elseif (z <= 1.45e-111)
		tmp = Float64(x + Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * y);
	tmp = 0.0;
	if (z <= -6.8e+257)
		tmp = a * (z * b);
	elseif (z <= -2.6e+83)
		tmp = t_1;
	elseif (z <= 1.45e-111)
		tmp = x + (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+257], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e+83], t$95$1, If[LessEqual[z, 1.45e-111], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8000000000000005e257

   1. Initial program 83.2%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 91.7%

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

   3. Simplified 91.7%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   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 76.0%

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

   7. Simplified 76.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 83.7%

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

   9. Applied egg-rr 83.7%

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

   if -6.8000000000000005e257 < z < -2.6000000000000001e83 or 1.45000000000000001e-111 < z

   1. Initial program 84.9%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 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 x around inf

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

   7. Simplified 62.3%

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

   if -2.6000000000000001e83 < z < 1.45000000000000001e-111

   1. Initial program 97.7%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 77.9%

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

   7. Simplified 77.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+257}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+83}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-111}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-115}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ y (* a b))))))
   (if (<= z -2.15e-73) t_1 (if (<= z 3.65e-115) (+ x (* a t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -2.15e-73) {
		tmp = t_1;
	} else if (z <= 3.65e-115) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y + (a * b)))
    if (z <= (-2.15d-73)) then
        tmp = t_1
    else if (z <= 3.65d-115) then
        tmp = x + (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -2.15e-73) {
		tmp = t_1;
	} else if (z <= 3.65e-115) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y + (a * b)))
	tmp = 0
	if z <= -2.15e-73:
		tmp = t_1
	elif z <= 3.65e-115:
		tmp = x + (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y + Float64(a * b))))
	tmp = 0.0
	if (z <= -2.15e-73)
		tmp = t_1;
	elseif (z <= 3.65e-115)
		tmp = Float64(x + Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y + (a * b)));
	tmp = 0.0;
	if (z <= -2.15e-73)
		tmp = t_1;
	elseif (z <= 3.65e-115)
		tmp = x + (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e-73], t$95$1, If[LessEqual[z, 3.65e-115], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1499999999999999e-73 or 3.64999999999999982e-115 < z

   1. Initial program 86.7%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

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

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

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

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

      7. *-lowering-*.f64 87.0%

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

   7. Simplified 87.0%

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

   if -2.1499999999999999e-73 < z < 3.64999999999999982e-115

   1. Initial program 99.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 99.9%

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

   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 84.7%

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

   7. Simplified 84.7%

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

Alternative 8: 39.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-41}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-260}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.6e-41)
   (* a t)
   (if (<= a 2.95e-260) (* z y) (if (<= a 3.9e+29) x (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.6e-41) {
		tmp = a * t;
	} else if (a <= 2.95e-260) {
		tmp = z * y;
	} else if (a <= 3.9e+29) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.6d-41)) then
        tmp = a * t
    else if (a <= 2.95d-260) then
        tmp = z * y
    else if (a <= 3.9d+29) then
        tmp = x
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.6e-41) {
		tmp = a * t;
	} else if (a <= 2.95e-260) {
		tmp = z * y;
	} else if (a <= 3.9e+29) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.6e-41:
		tmp = a * t
	elif a <= 2.95e-260:
		tmp = z * y
	elif a <= 3.9e+29:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.6e-41)
		tmp = Float64(a * t);
	elseif (a <= 2.95e-260)
		tmp = Float64(z * y);
	elseif (a <= 3.9e+29)
		tmp = x;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.6e-41)
		tmp = a * t;
	elseif (a <= 2.95e-260)
		tmp = z * y;
	elseif (a <= 3.9e+29)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.6e-41], N[(a * t), $MachinePrecision], If[LessEqual[a, 2.95e-260], N[(z * y), $MachinePrecision], If[LessEqual[a, 3.9e+29], x, N[(a * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5999999999999999e-41 or 3.89999999999999968e29 < a

   1. Initial program 85.5%

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

      1. associate-+l+ 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 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 43.0%

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

   7. Simplified 43.0%

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

   if -2.5999999999999999e-41 < a < 2.95e-260

   1. Initial program 97.2%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 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 56.9%

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

   7. Simplified 56.9%

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

   if 2.95e-260 < a < 3.89999999999999968e29

   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 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 52.6%

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

Alternative 9: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 112000:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -1.85e-37) t_1 (if (<= a 112000.0) (+ x (* z y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.85e-37) {
		tmp = t_1;
	} else if (a <= 112000.0) {
		tmp = x + (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t + (z * b))
    if (a <= (-1.85d-37)) then
        tmp = t_1
    else if (a <= 112000.0d0) then
        tmp = x + (z * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.85e-37) {
		tmp = t_1;
	} else if (a <= 112000.0) {
		tmp = x + (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -1.85e-37:
		tmp = t_1
	elif a <= 112000.0:
		tmp = x + (z * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -1.85e-37)
		tmp = t_1;
	elseif (a <= 112000.0)
		tmp = Float64(x + Float64(z * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -1.85e-37)
		tmp = t_1;
	elseif (a <= 112000.0)
		tmp = x + (z * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e-37], t$95$1, If[LessEqual[a, 112000.0], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.85e-37 or 112000 < a

   1. Initial program 85.8%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in 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 76.7%

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

   7. Simplified 76.7%

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

   if -1.85e-37 < a < 112000

   1. Initial program 97.5%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 80.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 112000:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+153}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-108}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.6e+153)
   (* z (* a b))
   (if (<= z 6.1e-108) (+ x (* a t)) (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e+153) {
		tmp = z * (a * b);
	} else if (z <= 6.1e-108) {
		tmp = x + (a * t);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.6d+153)) then
        tmp = z * (a * b)
    else if (z <= 6.1d-108) then
        tmp = x + (a * t)
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e+153) {
		tmp = z * (a * b);
	} else if (z <= 6.1e-108) {
		tmp = x + (a * t);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.6e+153:
		tmp = z * (a * b)
	elif z <= 6.1e-108:
		tmp = x + (a * t)
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.6e+153)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= 6.1e-108)
		tmp = Float64(x + Float64(a * t));
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.6e+153)
		tmp = z * (a * b);
	elseif (z <= 6.1e-108)
		tmp = x + (a * t);
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.6e+153], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.1e-108], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6000000000000003e153

   1. Initial program 85.4%

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

      1. associate-+l+ 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 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in 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 54.0%

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

   7. Simplified 54.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot z\right)} \]
   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 56.9%

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

   9. Applied egg-rr 56.9%

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

   if -4.6000000000000003e153 < z < 6.10000000000000007e-108

   1. Initial program 96.5%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 75.2%

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

   7. Simplified 75.2%

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

   if 6.10000000000000007e-108 < z

   1. Initial program 84.9%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 89.5%

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

   3. Simplified 89.5%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   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 48.7%

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

   7. Simplified 48.7%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+153}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-108}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+42}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.5e+51) x (if (<= x 1.45e+42) (* a t) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.5e+51) {
		tmp = x;
	} else if (x <= 1.45e+42) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.5d+51)) then
        tmp = x
    else if (x <= 1.45d+42) then
        tmp = a * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.5e+51) {
		tmp = x;
	} else if (x <= 1.45e+42) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.5e+51:
		tmp = x
	elif x <= 1.45e+42:
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.5e+51)
		tmp = x;
	elseif (x <= 1.45e+42)
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.5e+51)
		tmp = x;
	elseif (x <= 1.45e+42)
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.5e+51], x, If[LessEqual[x, 1.45e+42], N[(a * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5e51 or 1.4499999999999999e42 < x

   1. Initial program 92.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 49.0%

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

   if -6.5e51 < x < 1.4499999999999999e42

   1. Initial program 90.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 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 t around inf

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

      1. *-lowering-*.f64 38.1%

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

   7. Simplified 38.1%

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

Alternative 12: 26.1% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 91.2%

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

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

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

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

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

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

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

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

   7. *-commutative N/A

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

   8. associate-*l* N/A

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

   9. distribute-lft-out N/A

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

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

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

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

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

   12. *-lowering-*.f64 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 24.5%

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

Developer Target 1: 97.1% 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 2024163 
(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)))