Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.3% → 97.9%

Time: 18.2s

Alternatives: 25

Speedup: 0.5×

• 36.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * 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 - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * 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 - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* b (- (+ y t) 2.0)))))
   (if (<= t_1 INFINITY) t_1 (* y (- b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a * Float64(1.0 - t))) + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 75.1%

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

4. Final simplification 99.2%

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

Alternative 2: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (+ y (+ t -2.0)) b (- x (fma (+ y -1.0) z (* a (+ t -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((y + (t + -2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(y + Float64(t + -2.0)), b, Float64(x - fma(Float64(y + -1.0), z, Float64(a * Float64(t + -1.0)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 96.9%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

   2. fma-define 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

   3. associate--l+ 98.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{y + \left(t - 2\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   4. sub-neg 98.0%

      \[\leadsto \mathsf{fma}\left(y + \color{blue}{\left(t + \left(-2\right)\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   5. metadata-eval 98.0%

      \[\leadsto \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   6. sub-neg 98.0%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)}\right) \]

   7. associate-+l- 98.0%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x - \left(\left(y - 1\right) \cdot z - \left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]

   8. fma-neg 98.0%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -\left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]

   9. sub-neg 98.0%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(\color{blue}{y + \left(-1\right)}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]

   10. metadata-eval 98.0%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + \color{blue}{-1}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]

   11. remove-double-neg 98.0%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t - 1\right) \cdot a}\right)\right) \]

   12. sub-neg 98.0%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot a\right)\right) \]

   13. metadata-eval 98.0%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + \color{blue}{-1}\right) \cdot a\right)\right) \]

3. Simplified 98.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a\right)\right)} \]
4. Add Preprocessing

5. Final simplification 98.0%

   \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right) \]
6. Add Preprocessing

Alternative 3: 54.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := x + \left(z + a\right)\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-212}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-272}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-266}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-195}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 880000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+110}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))) (t_3 (+ x (+ z a))))
   (if (<= y -5.4e+75)
     t_1
     (if (<= y -7.5e+40)
       (* a (- 1.0 t))
       (if (<= y -4.6e+16)
         t_1
         (if (<= y -3.1e-212)
           t_3
           (if (<= y -3.4e-272)
             (* b (- t 2.0))
             (if (<= y 9.6e-266)
               t_3
               (if (<= y 4e-195)
                 t_2
                 (if (<= y 880000000000.0)
                   t_3
                   (if (<= y 1.4e+57)
                     t_2
                     (if (<= y 7.5e+110) (- x (* y z)) t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double t_3 = x + (z + a);
	double tmp;
	if (y <= -5.4e+75) {
		tmp = t_1;
	} else if (y <= -7.5e+40) {
		tmp = a * (1.0 - t);
	} else if (y <= -4.6e+16) {
		tmp = t_1;
	} else if (y <= -3.1e-212) {
		tmp = t_3;
	} else if (y <= -3.4e-272) {
		tmp = b * (t - 2.0);
	} else if (y <= 9.6e-266) {
		tmp = t_3;
	} else if (y <= 4e-195) {
		tmp = t_2;
	} else if (y <= 880000000000.0) {
		tmp = t_3;
	} else if (y <= 1.4e+57) {
		tmp = t_2;
	} else if (y <= 7.5e+110) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    t_3 = x + (z + a)
    if (y <= (-5.4d+75)) then
        tmp = t_1
    else if (y <= (-7.5d+40)) then
        tmp = a * (1.0d0 - t)
    else if (y <= (-4.6d+16)) then
        tmp = t_1
    else if (y <= (-3.1d-212)) then
        tmp = t_3
    else if (y <= (-3.4d-272)) then
        tmp = b * (t - 2.0d0)
    else if (y <= 9.6d-266) then
        tmp = t_3
    else if (y <= 4d-195) then
        tmp = t_2
    else if (y <= 880000000000.0d0) then
        tmp = t_3
    else if (y <= 1.4d+57) then
        tmp = t_2
    else if (y <= 7.5d+110) then
        tmp = x - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double t_3 = x + (z + a);
	double tmp;
	if (y <= -5.4e+75) {
		tmp = t_1;
	} else if (y <= -7.5e+40) {
		tmp = a * (1.0 - t);
	} else if (y <= -4.6e+16) {
		tmp = t_1;
	} else if (y <= -3.1e-212) {
		tmp = t_3;
	} else if (y <= -3.4e-272) {
		tmp = b * (t - 2.0);
	} else if (y <= 9.6e-266) {
		tmp = t_3;
	} else if (y <= 4e-195) {
		tmp = t_2;
	} else if (y <= 880000000000.0) {
		tmp = t_3;
	} else if (y <= 1.4e+57) {
		tmp = t_2;
	} else if (y <= 7.5e+110) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	t_3 = x + (z + a)
	tmp = 0
	if y <= -5.4e+75:
		tmp = t_1
	elif y <= -7.5e+40:
		tmp = a * (1.0 - t)
	elif y <= -4.6e+16:
		tmp = t_1
	elif y <= -3.1e-212:
		tmp = t_3
	elif y <= -3.4e-272:
		tmp = b * (t - 2.0)
	elif y <= 9.6e-266:
		tmp = t_3
	elif y <= 4e-195:
		tmp = t_2
	elif y <= 880000000000.0:
		tmp = t_3
	elif y <= 1.4e+57:
		tmp = t_2
	elif y <= 7.5e+110:
		tmp = x - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(x + Float64(z + a))
	tmp = 0.0
	if (y <= -5.4e+75)
		tmp = t_1;
	elseif (y <= -7.5e+40)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= -4.6e+16)
		tmp = t_1;
	elseif (y <= -3.1e-212)
		tmp = t_3;
	elseif (y <= -3.4e-272)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 9.6e-266)
		tmp = t_3;
	elseif (y <= 4e-195)
		tmp = t_2;
	elseif (y <= 880000000000.0)
		tmp = t_3;
	elseif (y <= 1.4e+57)
		tmp = t_2;
	elseif (y <= 7.5e+110)
		tmp = Float64(x - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	t_3 = x + (z + a);
	tmp = 0.0;
	if (y <= -5.4e+75)
		tmp = t_1;
	elseif (y <= -7.5e+40)
		tmp = a * (1.0 - t);
	elseif (y <= -4.6e+16)
		tmp = t_1;
	elseif (y <= -3.1e-212)
		tmp = t_3;
	elseif (y <= -3.4e-272)
		tmp = b * (t - 2.0);
	elseif (y <= 9.6e-266)
		tmp = t_3;
	elseif (y <= 4e-195)
		tmp = t_2;
	elseif (y <= 880000000000.0)
		tmp = t_3;
	elseif (y <= 1.4e+57)
		tmp = t_2;
	elseif (y <= 7.5e+110)
		tmp = x - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+75], t$95$1, If[LessEqual[y, -7.5e+40], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e+16], t$95$1, If[LessEqual[y, -3.1e-212], t$95$3, If[LessEqual[y, -3.4e-272], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e-266], t$95$3, If[LessEqual[y, 4e-195], t$95$2, If[LessEqual[y, 880000000000.0], t$95$3, If[LessEqual[y, 1.4e+57], t$95$2, If[LessEqual[y, 7.5e+110], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.39999999999999996e75 or -7.4999999999999996e40 < y < -4.6e16 or 7.5e110 < y

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.7%

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

   if -5.39999999999999996e75 < y < -7.4999999999999996e40

   1. Initial program 93.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 63.7%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -4.6e16 < y < -3.10000000000000006e-212 or -3.4000000000000003e-272 < y < 9.5999999999999999e-266 or 4.0000000000000004e-195 < y < 8.8e11

   1. Initial program 99.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 79.2%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around 0 77.1%

      \[\leadsto x - \color{blue}{\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 77.1%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)} \]

      2. sub-neg 77.1%

         \[\leadsto x - \left(a \cdot \color{blue}{\left(t + \left(-1\right)\right)} + -1 \cdot z\right) \]

      3. metadata-eval 77.1%

         \[\leadsto x - \left(a \cdot \left(t + \color{blue}{-1}\right) + -1 \cdot z\right) \]

      4. mul-1-neg 77.1%

         \[\leadsto x - \left(a \cdot \left(t + -1\right) + \color{blue}{\left(-z\right)}\right) \]

      5. unsub-neg 77.1%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   6. Simplified 77.1%

      \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   7. Taylor expanded in t around 0 60.6%

      \[\leadsto x - \left(\color{blue}{-1 \cdot a} - z\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 60.6%

         \[\leadsto x - \left(\color{blue}{\left(-a\right)} - z\right) \]

   9. Simplified 60.6%

      \[\leadsto x - \left(\color{blue}{\left(-a\right)} - z\right) \]

   if -3.10000000000000006e-212 < y < -3.4000000000000003e-272

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 67.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in y around 0 67.8%

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]

   if 9.5999999999999999e-266 < y < 4.0000000000000004e-195 or 8.8e11 < y < 1.4e57

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.0%

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

   if 1.4e57 < y < 7.5e110

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 86.4%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around inf 73.4%

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

      1. *-commutative 73.4%

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

   6. Simplified 73.4%

      \[\leadsto x - \color{blue}{z \cdot y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-212}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-272}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-266}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 880000000000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+110}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ t_3 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{-9}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-273}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-307}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z a)))
        (t_2 (+ x (* a (- 1.0 t))))
        (t_3 (* b (- (+ y t) 2.0))))
   (if (<= b -6.5e-9)
     t_3
     (if (<= b -3.9e-273)
       t_2
       (if (<= b -1.9e-307)
         (- x (* y z))
         (if (<= b 2.7e-182)
           t_1
           (if (<= b 2.8e-98)
             t_2
             (if (<= b 3.2e-31)
               t_1
               (if (<= b 2.5e-15)
                 (* y (- b z))
                 (if (<= b 9.6e+54) t_2 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = x + (a * (1.0 - t));
	double t_3 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -6.5e-9) {
		tmp = t_3;
	} else if (b <= -3.9e-273) {
		tmp = t_2;
	} else if (b <= -1.9e-307) {
		tmp = x - (y * z);
	} else if (b <= 2.7e-182) {
		tmp = t_1;
	} else if (b <= 2.8e-98) {
		tmp = t_2;
	} else if (b <= 3.2e-31) {
		tmp = t_1;
	} else if (b <= 2.5e-15) {
		tmp = y * (b - z);
	} else if (b <= 9.6e+54) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z + a)
    t_2 = x + (a * (1.0d0 - t))
    t_3 = b * ((y + t) - 2.0d0)
    if (b <= (-6.5d-9)) then
        tmp = t_3
    else if (b <= (-3.9d-273)) then
        tmp = t_2
    else if (b <= (-1.9d-307)) then
        tmp = x - (y * z)
    else if (b <= 2.7d-182) then
        tmp = t_1
    else if (b <= 2.8d-98) then
        tmp = t_2
    else if (b <= 3.2d-31) then
        tmp = t_1
    else if (b <= 2.5d-15) then
        tmp = y * (b - z)
    else if (b <= 9.6d+54) then
        tmp = t_2
    else
        tmp = t_3
    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 + a);
	double t_2 = x + (a * (1.0 - t));
	double t_3 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -6.5e-9) {
		tmp = t_3;
	} else if (b <= -3.9e-273) {
		tmp = t_2;
	} else if (b <= -1.9e-307) {
		tmp = x - (y * z);
	} else if (b <= 2.7e-182) {
		tmp = t_1;
	} else if (b <= 2.8e-98) {
		tmp = t_2;
	} else if (b <= 3.2e-31) {
		tmp = t_1;
	} else if (b <= 2.5e-15) {
		tmp = y * (b - z);
	} else if (b <= 9.6e+54) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + a)
	t_2 = x + (a * (1.0 - t))
	t_3 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -6.5e-9:
		tmp = t_3
	elif b <= -3.9e-273:
		tmp = t_2
	elif b <= -1.9e-307:
		tmp = x - (y * z)
	elif b <= 2.7e-182:
		tmp = t_1
	elif b <= 2.8e-98:
		tmp = t_2
	elif b <= 3.2e-31:
		tmp = t_1
	elif b <= 2.5e-15:
		tmp = y * (b - z)
	elif b <= 9.6e+54:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + a))
	t_2 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_3 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -6.5e-9)
		tmp = t_3;
	elseif (b <= -3.9e-273)
		tmp = t_2;
	elseif (b <= -1.9e-307)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= 2.7e-182)
		tmp = t_1;
	elseif (b <= 2.8e-98)
		tmp = t_2;
	elseif (b <= 3.2e-31)
		tmp = t_1;
	elseif (b <= 2.5e-15)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 9.6e+54)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + a);
	t_2 = x + (a * (1.0 - t));
	t_3 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -6.5e-9)
		tmp = t_3;
	elseif (b <= -3.9e-273)
		tmp = t_2;
	elseif (b <= -1.9e-307)
		tmp = x - (y * z);
	elseif (b <= 2.7e-182)
		tmp = t_1;
	elseif (b <= 2.8e-98)
		tmp = t_2;
	elseif (b <= 3.2e-31)
		tmp = t_1;
	elseif (b <= 2.5e-15)
		tmp = y * (b - z);
	elseif (b <= 9.6e+54)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e-9], t$95$3, If[LessEqual[b, -3.9e-273], t$95$2, If[LessEqual[b, -1.9e-307], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e-182], t$95$1, If[LessEqual[b, 2.8e-98], t$95$2, If[LessEqual[b, 3.2e-31], t$95$1, If[LessEqual[b, 2.5e-15], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.6e+54], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.5000000000000003e-9 or 9.59999999999999993e54 < b

   1. Initial program 94.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 74.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -6.5000000000000003e-9 < b < -3.9000000000000004e-273 or 2.69999999999999999e-182 < b < 2.7999999999999999e-98 or 2.5e-15 < b < 9.59999999999999993e54

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 73.2%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in b around 0 64.7%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]

   if -3.9000000000000004e-273 < b < -1.89999999999999993e-307

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 100.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

   6. Simplified 81.0%

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

   if -1.89999999999999993e-307 < b < 2.69999999999999999e-182 or 2.7999999999999999e-98 < b < 3.20000000000000018e-31

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 90.1%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around 0 80.5%

      \[\leadsto x - \color{blue}{\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 80.5%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)} \]

      2. sub-neg 80.5%

         \[\leadsto x - \left(a \cdot \color{blue}{\left(t + \left(-1\right)\right)} + -1 \cdot z\right) \]

      3. metadata-eval 80.5%

         \[\leadsto x - \left(a \cdot \left(t + \color{blue}{-1}\right) + -1 \cdot z\right) \]

      4. mul-1-neg 80.5%

         \[\leadsto x - \left(a \cdot \left(t + -1\right) + \color{blue}{\left(-z\right)}\right) \]

      5. unsub-neg 80.5%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   6. Simplified 80.5%

      \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   7. Taylor expanded in t around 0 71.1%

      \[\leadsto x - \left(\color{blue}{-1 \cdot a} - z\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 71.1%

         \[\leadsto x - \left(\color{blue}{\left(-a\right)} - z\right) \]

   9. Simplified 71.1%

      \[\leadsto x - \left(\color{blue}{\left(-a\right)} - z\right) \]

   if 3.20000000000000018e-31 < b < 2.5e-15

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.6%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-273}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-307}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-182}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-98}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+54}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.22 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-161}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-274}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-31}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.22e-5)
     t_2
     (if (<= b -1.7e-161)
       (- x (* t a))
       (if (<= b -4.6e-274)
         (* a (- 1.0 t))
         (if (<= b -1.08e-306)
           t_1
           (if (<= b 3.3e-31)
             (+ x (+ z a))
             (if (<= b 1.15e-15)
               (* y (- b z))
               (if (<= b 3.8e+52) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.22e-5) {
		tmp = t_2;
	} else if (b <= -1.7e-161) {
		tmp = x - (t * a);
	} else if (b <= -4.6e-274) {
		tmp = a * (1.0 - t);
	} else if (b <= -1.08e-306) {
		tmp = t_1;
	} else if (b <= 3.3e-31) {
		tmp = x + (z + a);
	} else if (b <= 1.15e-15) {
		tmp = y * (b - z);
	} else if (b <= 3.8e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.22d-5)) then
        tmp = t_2
    else if (b <= (-1.7d-161)) then
        tmp = x - (t * a)
    else if (b <= (-4.6d-274)) then
        tmp = a * (1.0d0 - t)
    else if (b <= (-1.08d-306)) then
        tmp = t_1
    else if (b <= 3.3d-31) then
        tmp = x + (z + a)
    else if (b <= 1.15d-15) then
        tmp = y * (b - z)
    else if (b <= 3.8d+52) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.22e-5) {
		tmp = t_2;
	} else if (b <= -1.7e-161) {
		tmp = x - (t * a);
	} else if (b <= -4.6e-274) {
		tmp = a * (1.0 - t);
	} else if (b <= -1.08e-306) {
		tmp = t_1;
	} else if (b <= 3.3e-31) {
		tmp = x + (z + a);
	} else if (b <= 1.15e-15) {
		tmp = y * (b - z);
	} else if (b <= 3.8e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.22e-5:
		tmp = t_2
	elif b <= -1.7e-161:
		tmp = x - (t * a)
	elif b <= -4.6e-274:
		tmp = a * (1.0 - t)
	elif b <= -1.08e-306:
		tmp = t_1
	elif b <= 3.3e-31:
		tmp = x + (z + a)
	elif b <= 1.15e-15:
		tmp = y * (b - z)
	elif b <= 3.8e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.22e-5)
		tmp = t_2;
	elseif (b <= -1.7e-161)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= -4.6e-274)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= -1.08e-306)
		tmp = t_1;
	elseif (b <= 3.3e-31)
		tmp = Float64(x + Float64(z + a));
	elseif (b <= 1.15e-15)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 3.8e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.22e-5)
		tmp = t_2;
	elseif (b <= -1.7e-161)
		tmp = x - (t * a);
	elseif (b <= -4.6e-274)
		tmp = a * (1.0 - t);
	elseif (b <= -1.08e-306)
		tmp = t_1;
	elseif (b <= 3.3e-31)
		tmp = x + (z + a);
	elseif (b <= 1.15e-15)
		tmp = y * (b - z);
	elseif (b <= 3.8e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.22e-5], t$95$2, If[LessEqual[b, -1.7e-161], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.6e-274], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.08e-306], t$95$1, If[LessEqual[b, 3.3e-31], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-15], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+52], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.22000000000000001e-5 or 3.8e52 < b

   1. Initial program 94.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 74.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -1.22000000000000001e-5 < b < -1.69999999999999991e-161

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 91.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in t around inf 59.7%

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

   if -1.69999999999999991e-161 < b < -4.59999999999999992e-274

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 70.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -4.59999999999999992e-274 < b < -1.07999999999999994e-306 or 1.14999999999999995e-15 < b < 3.8e52

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 96.3%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around inf 71.6%

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

      1. *-commutative 71.6%

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

   6. Simplified 71.6%

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

   if -1.07999999999999994e-306 < b < 3.2999999999999999e-31

   1. Initial program 96.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 89.7%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around 0 74.7%

      \[\leadsto x - \color{blue}{\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 74.7%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)} \]

      2. sub-neg 74.7%

         \[\leadsto x - \left(a \cdot \color{blue}{\left(t + \left(-1\right)\right)} + -1 \cdot z\right) \]

      3. metadata-eval 74.7%

         \[\leadsto x - \left(a \cdot \left(t + \color{blue}{-1}\right) + -1 \cdot z\right) \]

      4. mul-1-neg 74.7%

         \[\leadsto x - \left(a \cdot \left(t + -1\right) + \color{blue}{\left(-z\right)}\right) \]

      5. unsub-neg 74.7%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   6. Simplified 74.7%

      \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   7. Taylor expanded in t around 0 60.6%

      \[\leadsto x - \left(\color{blue}{-1 \cdot a} - z\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 60.6%

         \[\leadsto x - \left(\color{blue}{\left(-a\right)} - z\right) \]

   9. Simplified 60.6%

      \[\leadsto x - \left(\color{blue}{\left(-a\right)} - z\right) \]

   if 3.2999999999999999e-31 < b < 1.14999999999999995e-15

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.6%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{-5}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-161}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-274}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-306}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-31}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := x - y \cdot z\\ \mathbf{if}\;t \leq -5500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-100}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-169}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-228}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 100000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+179} \lor \neg \left(t \leq 5 \cdot 10^{+205}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (- x (* y z))))
   (if (<= t -5500000000.0)
     t_1
     (if (<= t -3.5e-100)
       (- x (* t a))
       (if (<= t -3.1e-169)
         (* z (- 1.0 y))
         (if (<= t 4.8e-228)
           t_2
           (if (<= t 100000.0)
             (* y (- b z))
             (if (or (<= t 1.85e+179) (not (<= t 5e+205))) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = x - (y * z);
	double tmp;
	if (t <= -5500000000.0) {
		tmp = t_1;
	} else if (t <= -3.5e-100) {
		tmp = x - (t * a);
	} else if (t <= -3.1e-169) {
		tmp = z * (1.0 - y);
	} else if (t <= 4.8e-228) {
		tmp = t_2;
	} else if (t <= 100000.0) {
		tmp = y * (b - z);
	} else if ((t <= 1.85e+179) || !(t <= 5e+205)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = x - (y * z)
    if (t <= (-5500000000.0d0)) then
        tmp = t_1
    else if (t <= (-3.5d-100)) then
        tmp = x - (t * a)
    else if (t <= (-3.1d-169)) then
        tmp = z * (1.0d0 - y)
    else if (t <= 4.8d-228) then
        tmp = t_2
    else if (t <= 100000.0d0) then
        tmp = y * (b - z)
    else if ((t <= 1.85d+179) .or. (.not. (t <= 5d+205))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = x - (y * z);
	double tmp;
	if (t <= -5500000000.0) {
		tmp = t_1;
	} else if (t <= -3.5e-100) {
		tmp = x - (t * a);
	} else if (t <= -3.1e-169) {
		tmp = z * (1.0 - y);
	} else if (t <= 4.8e-228) {
		tmp = t_2;
	} else if (t <= 100000.0) {
		tmp = y * (b - z);
	} else if ((t <= 1.85e+179) || !(t <= 5e+205)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = x - (y * z)
	tmp = 0
	if t <= -5500000000.0:
		tmp = t_1
	elif t <= -3.5e-100:
		tmp = x - (t * a)
	elif t <= -3.1e-169:
		tmp = z * (1.0 - y)
	elif t <= 4.8e-228:
		tmp = t_2
	elif t <= 100000.0:
		tmp = y * (b - z)
	elif (t <= 1.85e+179) or not (t <= 5e+205):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (t <= -5500000000.0)
		tmp = t_1;
	elseif (t <= -3.5e-100)
		tmp = Float64(x - Float64(t * a));
	elseif (t <= -3.1e-169)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 4.8e-228)
		tmp = t_2;
	elseif (t <= 100000.0)
		tmp = Float64(y * Float64(b - z));
	elseif ((t <= 1.85e+179) || !(t <= 5e+205))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = x - (y * z);
	tmp = 0.0;
	if (t <= -5500000000.0)
		tmp = t_1;
	elseif (t <= -3.5e-100)
		tmp = x - (t * a);
	elseif (t <= -3.1e-169)
		tmp = z * (1.0 - y);
	elseif (t <= 4.8e-228)
		tmp = t_2;
	elseif (t <= 100000.0)
		tmp = y * (b - z);
	elseif ((t <= 1.85e+179) || ~((t <= 5e+205)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5500000000.0], t$95$1, If[LessEqual[t, -3.5e-100], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.1e-169], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-228], t$95$2, If[LessEqual[t, 100000.0], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.85e+179], N[Not[LessEqual[t, 5e+205]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.5e9 or 1e5 < t < 1.85e179 or 5.0000000000000002e205 < t

   1. Initial program 95.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.5%

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

   if -5.5e9 < t < -3.5000000000000001e-100

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 78.2%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in t around inf 39.4%

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

   if -3.5000000000000001e-100 < t < -3.1000000000000002e-169

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 68.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   if -3.1000000000000002e-169 < t < 4.80000000000000004e-228 or 1.85e179 < t < 5.0000000000000002e205

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 75.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around inf 51.7%

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

      1. *-commutative 51.7%

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

   6. Simplified 51.7%

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

   if 4.80000000000000004e-228 < t < 1e5

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 47.0%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5500000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-100}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-169}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-228}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 100000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+179} \lor \neg \left(t \leq 5 \cdot 10^{+205}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-294}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.45e+143)
     t_2
     (if (<= b -1.45e-272)
       t_1
       (if (<= b -3.5e-294)
         (+ x (* z (- 1.0 y)))
         (if (<= b 7e-31)
           t_1
           (if (<= b 1.72e-15)
             (* y (- b z))
             (if (<= b 3.5e+49) t_1 (+ x t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.45e+143) {
		tmp = t_2;
	} else if (b <= -1.45e-272) {
		tmp = t_1;
	} else if (b <= -3.5e-294) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 7e-31) {
		tmp = t_1;
	} else if (b <= 1.72e-15) {
		tmp = y * (b - z);
	} else if (b <= 3.5e+49) {
		tmp = t_1;
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z + (a * (1.0d0 - t)))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.45d+143)) then
        tmp = t_2
    else if (b <= (-1.45d-272)) then
        tmp = t_1
    else if (b <= (-3.5d-294)) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 7d-31) then
        tmp = t_1
    else if (b <= 1.72d-15) then
        tmp = y * (b - z)
    else if (b <= 3.5d+49) then
        tmp = t_1
    else
        tmp = x + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.45e+143) {
		tmp = t_2;
	} else if (b <= -1.45e-272) {
		tmp = t_1;
	} else if (b <= -3.5e-294) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 7e-31) {
		tmp = t_1;
	} else if (b <= 1.72e-15) {
		tmp = y * (b - z);
	} else if (b <= 3.5e+49) {
		tmp = t_1;
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.45e+143:
		tmp = t_2
	elif b <= -1.45e-272:
		tmp = t_1
	elif b <= -3.5e-294:
		tmp = x + (z * (1.0 - y))
	elif b <= 7e-31:
		tmp = t_1
	elif b <= 1.72e-15:
		tmp = y * (b - z)
	elif b <= 3.5e+49:
		tmp = t_1
	else:
		tmp = x + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.45e+143)
		tmp = t_2;
	elseif (b <= -1.45e-272)
		tmp = t_1;
	elseif (b <= -3.5e-294)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 7e-31)
		tmp = t_1;
	elseif (b <= 1.72e-15)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 3.5e+49)
		tmp = t_1;
	else
		tmp = Float64(x + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a * (1.0 - t)));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.45e+143)
		tmp = t_2;
	elseif (b <= -1.45e-272)
		tmp = t_1;
	elseif (b <= -3.5e-294)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 7e-31)
		tmp = t_1;
	elseif (b <= 1.72e-15)
		tmp = y * (b - z);
	elseif (b <= 3.5e+49)
		tmp = t_1;
	else
		tmp = x + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+143], t$95$2, If[LessEqual[b, -1.45e-272], t$95$1, If[LessEqual[b, -3.5e-294], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-31], t$95$1, If[LessEqual[b, 1.72e-15], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+49], t$95$1, N[(x + t$95$2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.4499999999999999e143

   1. Initial program 94.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 93.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -1.4499999999999999e143 < b < -1.44999999999999997e-272 or -3.50000000000000032e-294 < b < 6.99999999999999971e-31 or 1.7199999999999999e-15 < b < 3.49999999999999975e49

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 86.5%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around 0 71.9%

      \[\leadsto x - \color{blue}{\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 71.9%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)} \]

      2. sub-neg 71.9%

         \[\leadsto x - \left(a \cdot \color{blue}{\left(t + \left(-1\right)\right)} + -1 \cdot z\right) \]

      3. metadata-eval 71.9%

         \[\leadsto x - \left(a \cdot \left(t + \color{blue}{-1}\right) + -1 \cdot z\right) \]

      4. mul-1-neg 71.9%

         \[\leadsto x - \left(a \cdot \left(t + -1\right) + \color{blue}{\left(-z\right)}\right) \]

      5. unsub-neg 71.9%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   6. Simplified 71.9%

      \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   if -1.44999999999999997e-272 < b < -3.50000000000000032e-294

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 100.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in a around 0 91.1%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

   if 6.99999999999999971e-31 < b < 1.7199999999999999e-15

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.6%

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

   if 3.49999999999999975e49 < b

   1. Initial program 95.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.3%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in a around 0 85.0%

      \[\leadsto \color{blue}{x + b \cdot \left(\left(t + y\right) - 2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-272}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-294}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-31}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-292}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-14}:\\ \;\;\;\;t\_2 - y \cdot z\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.45e+143)
     t_2
     (if (<= b -8.8e-275)
       t_1
       (if (<= b -1.9e-292)
         (+ x (* z (- 1.0 y)))
         (if (<= b 3e-31)
           t_1
           (if (<= b 3.1e-14)
             (- t_2 (* y z))
             (if (<= b 2.6e+49) t_1 (+ x t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.45e+143) {
		tmp = t_2;
	} else if (b <= -8.8e-275) {
		tmp = t_1;
	} else if (b <= -1.9e-292) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 3e-31) {
		tmp = t_1;
	} else if (b <= 3.1e-14) {
		tmp = t_2 - (y * z);
	} else if (b <= 2.6e+49) {
		tmp = t_1;
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z + (a * (1.0d0 - t)))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.45d+143)) then
        tmp = t_2
    else if (b <= (-8.8d-275)) then
        tmp = t_1
    else if (b <= (-1.9d-292)) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 3d-31) then
        tmp = t_1
    else if (b <= 3.1d-14) then
        tmp = t_2 - (y * z)
    else if (b <= 2.6d+49) then
        tmp = t_1
    else
        tmp = x + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.45e+143) {
		tmp = t_2;
	} else if (b <= -8.8e-275) {
		tmp = t_1;
	} else if (b <= -1.9e-292) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 3e-31) {
		tmp = t_1;
	} else if (b <= 3.1e-14) {
		tmp = t_2 - (y * z);
	} else if (b <= 2.6e+49) {
		tmp = t_1;
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.45e+143:
		tmp = t_2
	elif b <= -8.8e-275:
		tmp = t_1
	elif b <= -1.9e-292:
		tmp = x + (z * (1.0 - y))
	elif b <= 3e-31:
		tmp = t_1
	elif b <= 3.1e-14:
		tmp = t_2 - (y * z)
	elif b <= 2.6e+49:
		tmp = t_1
	else:
		tmp = x + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.45e+143)
		tmp = t_2;
	elseif (b <= -8.8e-275)
		tmp = t_1;
	elseif (b <= -1.9e-292)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 3e-31)
		tmp = t_1;
	elseif (b <= 3.1e-14)
		tmp = Float64(t_2 - Float64(y * z));
	elseif (b <= 2.6e+49)
		tmp = t_1;
	else
		tmp = Float64(x + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a * (1.0 - t)));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.45e+143)
		tmp = t_2;
	elseif (b <= -8.8e-275)
		tmp = t_1;
	elseif (b <= -1.9e-292)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 3e-31)
		tmp = t_1;
	elseif (b <= 3.1e-14)
		tmp = t_2 - (y * z);
	elseif (b <= 2.6e+49)
		tmp = t_1;
	else
		tmp = x + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+143], t$95$2, If[LessEqual[b, -8.8e-275], t$95$1, If[LessEqual[b, -1.9e-292], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-31], t$95$1, If[LessEqual[b, 3.1e-14], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+49], t$95$1, N[(x + t$95$2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.4499999999999999e143

   1. Initial program 94.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 93.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -1.4499999999999999e143 < b < -8.79999999999999955e-275 or -1.9000000000000001e-292 < b < 2.99999999999999981e-31 or 3.10000000000000004e-14 < b < 2.59999999999999989e49

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 86.5%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around 0 71.9%

      \[\leadsto x - \color{blue}{\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 71.9%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)} \]

      2. sub-neg 71.9%

         \[\leadsto x - \left(a \cdot \color{blue}{\left(t + \left(-1\right)\right)} + -1 \cdot z\right) \]

      3. metadata-eval 71.9%

         \[\leadsto x - \left(a \cdot \left(t + \color{blue}{-1}\right) + -1 \cdot z\right) \]

      4. mul-1-neg 71.9%

         \[\leadsto x - \left(a \cdot \left(t + -1\right) + \color{blue}{\left(-z\right)}\right) \]

      5. unsub-neg 71.9%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   6. Simplified 71.9%

      \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   if -8.79999999999999955e-275 < b < -1.9000000000000001e-292

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 100.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in a around 0 91.1%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

   if 2.99999999999999981e-31 < b < 3.10000000000000004e-14

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \color{blue}{\left(-y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. *-commutative 100.0%

         \[\leadsto \left(-\color{blue}{z \cdot y}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{z \cdot \left(-y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(-y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if 2.59999999999999989e49 < b

   1. Initial program 95.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.3%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in a around 0 85.0%

      \[\leadsto \color{blue}{x + b \cdot \left(\left(t + y\right) - 2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-275}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-292}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-31}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+49}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-15}:\\ \;\;\;\;t\_2 - y \cdot z\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y)))))
        (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -4.6e+143)
     t_2
     (if (<= b 7e-31)
       t_1
       (if (<= b 6e-15) (- t_2 (* y z)) (if (<= b 6.2e+49) t_1 (+ x t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.6e+143) {
		tmp = t_2;
	} else if (b <= 7e-31) {
		tmp = t_1;
	} else if (b <= 6e-15) {
		tmp = t_2 - (y * z);
	} else if (b <= 6.2e+49) {
		tmp = t_1;
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-4.6d+143)) then
        tmp = t_2
    else if (b <= 7d-31) then
        tmp = t_1
    else if (b <= 6d-15) then
        tmp = t_2 - (y * z)
    else if (b <= 6.2d+49) then
        tmp = t_1
    else
        tmp = x + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.6e+143) {
		tmp = t_2;
	} else if (b <= 7e-31) {
		tmp = t_1;
	} else if (b <= 6e-15) {
		tmp = t_2 - (y * z);
	} else if (b <= 6.2e+49) {
		tmp = t_1;
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -4.6e+143:
		tmp = t_2
	elif b <= 7e-31:
		tmp = t_1
	elif b <= 6e-15:
		tmp = t_2 - (y * z)
	elif b <= 6.2e+49:
		tmp = t_1
	else:
		tmp = x + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -4.6e+143)
		tmp = t_2;
	elseif (b <= 7e-31)
		tmp = t_1;
	elseif (b <= 6e-15)
		tmp = Float64(t_2 - Float64(y * z));
	elseif (b <= 6.2e+49)
		tmp = t_1;
	else
		tmp = Float64(x + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -4.6e+143)
		tmp = t_2;
	elseif (b <= 7e-31)
		tmp = t_1;
	elseif (b <= 6e-15)
		tmp = t_2 - (y * z);
	elseif (b <= 6.2e+49)
		tmp = t_1;
	else
		tmp = x + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.6e+143], t$95$2, If[LessEqual[b, 7e-31], t$95$1, If[LessEqual[b, 6e-15], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+49], t$95$1, N[(x + t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.5999999999999999e143

   1. Initial program 94.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 93.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -4.5999999999999999e143 < b < 6.99999999999999971e-31 or 6e-15 < b < 6.19999999999999985e49

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 87.4%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   if 6.99999999999999971e-31 < b < 6e-15

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \color{blue}{\left(-y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. *-commutative 100.0%

         \[\leadsto \left(-\color{blue}{z \cdot y}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{z \cdot \left(-y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(-y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if 6.19999999999999985e49 < b

   1. Initial program 95.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.3%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in a around 0 85.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-31}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-64}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))) (t_2 (+ x (* z (- 1.0 y)))))
   (if (<= b -4.2e-9)
     t_1
     (if (<= b -3e-64)
       (- x (* t a))
       (if (<= b -7.2e-162)
         t_2
         (if (<= b -1.15e-274)
           (+ x (* a (- 1.0 t)))
           (if (<= b 5.6e+56) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -4.2e-9) {
		tmp = t_1;
	} else if (b <= -3e-64) {
		tmp = x - (t * a);
	} else if (b <= -7.2e-162) {
		tmp = t_2;
	} else if (b <= -1.15e-274) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 5.6e+56) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    t_2 = x + (z * (1.0d0 - y))
    if (b <= (-4.2d-9)) then
        tmp = t_1
    else if (b <= (-3d-64)) then
        tmp = x - (t * a)
    else if (b <= (-7.2d-162)) then
        tmp = t_2
    else if (b <= (-1.15d-274)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 5.6d+56) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -4.2e-9) {
		tmp = t_1;
	} else if (b <= -3e-64) {
		tmp = x - (t * a);
	} else if (b <= -7.2e-162) {
		tmp = t_2;
	} else if (b <= -1.15e-274) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 5.6e+56) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	t_2 = x + (z * (1.0 - y))
	tmp = 0
	if b <= -4.2e-9:
		tmp = t_1
	elif b <= -3e-64:
		tmp = x - (t * a)
	elif b <= -7.2e-162:
		tmp = t_2
	elif b <= -1.15e-274:
		tmp = x + (a * (1.0 - t))
	elif b <= 5.6e+56:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_2 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -4.2e-9)
		tmp = t_1;
	elseif (b <= -3e-64)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= -7.2e-162)
		tmp = t_2;
	elseif (b <= -1.15e-274)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 5.6e+56)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	t_2 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -4.2e-9)
		tmp = t_1;
	elseif (b <= -3e-64)
		tmp = x - (t * a);
	elseif (b <= -7.2e-162)
		tmp = t_2;
	elseif (b <= -1.15e-274)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 5.6e+56)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e-9], t$95$1, If[LessEqual[b, -3e-64], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.2e-162], t$95$2, If[LessEqual[b, -1.15e-274], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+56], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.20000000000000039e-9 or 5.60000000000000017e56 < b

   1. Initial program 94.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 74.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -4.20000000000000039e-9 < b < -3.0000000000000001e-64

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 98.4%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in t around inf 88.5%

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

   if -3.0000000000000001e-64 < b < -7.1999999999999996e-162 or -1.14999999999999998e-274 < b < 5.60000000000000017e56

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 87.6%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in a around 0 68.0%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

   if -7.1999999999999996e-162 < b < -1.14999999999999998e-274

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 80.0%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in b around 0 75.4%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-64}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-162}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+56}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -85000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 100000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -85000.0)
     t_1
     (if (<= t -3.1e-100)
       x
       (if (<= t -1.15e-191)
         (* z (- 1.0 y))
         (if (<= t -3.9e-213)
           (* b (- y 2.0))
           (if (<= t 100000.0) (* y (- b z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -85000.0) {
		tmp = t_1;
	} else if (t <= -3.1e-100) {
		tmp = x;
	} else if (t <= -1.15e-191) {
		tmp = z * (1.0 - y);
	} else if (t <= -3.9e-213) {
		tmp = b * (y - 2.0);
	} else if (t <= 100000.0) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-85000.0d0)) then
        tmp = t_1
    else if (t <= (-3.1d-100)) then
        tmp = x
    else if (t <= (-1.15d-191)) then
        tmp = z * (1.0d0 - y)
    else if (t <= (-3.9d-213)) then
        tmp = b * (y - 2.0d0)
    else if (t <= 100000.0d0) then
        tmp = y * (b - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -85000.0) {
		tmp = t_1;
	} else if (t <= -3.1e-100) {
		tmp = x;
	} else if (t <= -1.15e-191) {
		tmp = z * (1.0 - y);
	} else if (t <= -3.9e-213) {
		tmp = b * (y - 2.0);
	} else if (t <= 100000.0) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -85000.0:
		tmp = t_1
	elif t <= -3.1e-100:
		tmp = x
	elif t <= -1.15e-191:
		tmp = z * (1.0 - y)
	elif t <= -3.9e-213:
		tmp = b * (y - 2.0)
	elif t <= 100000.0:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -85000.0)
		tmp = t_1;
	elseif (t <= -3.1e-100)
		tmp = x;
	elseif (t <= -1.15e-191)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= -3.9e-213)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 100000.0)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -85000.0)
		tmp = t_1;
	elseif (t <= -3.1e-100)
		tmp = x;
	elseif (t <= -1.15e-191)
		tmp = z * (1.0 - y);
	elseif (t <= -3.9e-213)
		tmp = b * (y - 2.0);
	elseif (t <= 100000.0)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -85000.0], t$95$1, If[LessEqual[t, -3.1e-100], x, If[LessEqual[t, -1.15e-191], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e-213], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 100000.0], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -85000 or 1e5 < t

   1. Initial program 95.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.9%

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

   if -85000 < t < -3.0999999999999999e-100

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 38.3%

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

   if -3.0999999999999999e-100 < t < -1.15000000000000005e-191

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   if -1.15000000000000005e-191 < t < -3.89999999999999989e-213

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 72.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in t around 0 72.3%

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right)} \]

   if -3.89999999999999989e-213 < t < 1e5

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 42.1%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -85000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 100000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -120000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-100}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 9000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -120000000000.0)
     t_1
     (if (<= t -3.5e-100)
       (- x (* t a))
       (if (<= t -7.4e-193)
         (* z (- 1.0 y))
         (if (<= t -1.6e-213)
           (* b (- y 2.0))
           (if (<= t 9000.0) (* y (- b z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -120000000000.0) {
		tmp = t_1;
	} else if (t <= -3.5e-100) {
		tmp = x - (t * a);
	} else if (t <= -7.4e-193) {
		tmp = z * (1.0 - y);
	} else if (t <= -1.6e-213) {
		tmp = b * (y - 2.0);
	} else if (t <= 9000.0) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-120000000000.0d0)) then
        tmp = t_1
    else if (t <= (-3.5d-100)) then
        tmp = x - (t * a)
    else if (t <= (-7.4d-193)) then
        tmp = z * (1.0d0 - y)
    else if (t <= (-1.6d-213)) then
        tmp = b * (y - 2.0d0)
    else if (t <= 9000.0d0) then
        tmp = y * (b - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -120000000000.0) {
		tmp = t_1;
	} else if (t <= -3.5e-100) {
		tmp = x - (t * a);
	} else if (t <= -7.4e-193) {
		tmp = z * (1.0 - y);
	} else if (t <= -1.6e-213) {
		tmp = b * (y - 2.0);
	} else if (t <= 9000.0) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -120000000000.0:
		tmp = t_1
	elif t <= -3.5e-100:
		tmp = x - (t * a)
	elif t <= -7.4e-193:
		tmp = z * (1.0 - y)
	elif t <= -1.6e-213:
		tmp = b * (y - 2.0)
	elif t <= 9000.0:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -120000000000.0)
		tmp = t_1;
	elseif (t <= -3.5e-100)
		tmp = Float64(x - Float64(t * a));
	elseif (t <= -7.4e-193)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= -1.6e-213)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 9000.0)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -120000000000.0)
		tmp = t_1;
	elseif (t <= -3.5e-100)
		tmp = x - (t * a);
	elseif (t <= -7.4e-193)
		tmp = z * (1.0 - y);
	elseif (t <= -1.6e-213)
		tmp = b * (y - 2.0);
	elseif (t <= 9000.0)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -120000000000.0], t$95$1, If[LessEqual[t, -3.5e-100], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.4e-193], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.6e-213], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9000.0], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.2e11 or 9e3 < t

   1. Initial program 95.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.9%

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

   if -1.2e11 < t < -3.5000000000000001e-100

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 78.2%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in t around inf 39.4%

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

   if -3.5000000000000001e-100 < t < -7.4000000000000004e-193

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   if -7.4000000000000004e-193 < t < -1.59999999999999986e-213

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 72.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in t around 0 72.3%

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right)} \]

   if -1.59999999999999986e-213 < t < 9e3

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 42.1%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -120000000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-100}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 9000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+254}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+87}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.82 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.2e+254)
   (* y b)
   (if (<= b -5e+87)
     (* t b)
     (if (<= b -8e-266)
       (* a (- t))
       (if (<= b 1.25e-135) x (if (<= b 1.82e+93) (* y (- z)) (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e+254) {
		tmp = y * b;
	} else if (b <= -5e+87) {
		tmp = t * b;
	} else if (b <= -8e-266) {
		tmp = a * -t;
	} else if (b <= 1.25e-135) {
		tmp = x;
	} else if (b <= 1.82e+93) {
		tmp = y * -z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.2d+254)) then
        tmp = y * b
    else if (b <= (-5d+87)) then
        tmp = t * b
    else if (b <= (-8d-266)) then
        tmp = a * -t
    else if (b <= 1.25d-135) then
        tmp = x
    else if (b <= 1.82d+93) then
        tmp = y * -z
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e+254) {
		tmp = y * b;
	} else if (b <= -5e+87) {
		tmp = t * b;
	} else if (b <= -8e-266) {
		tmp = a * -t;
	} else if (b <= 1.25e-135) {
		tmp = x;
	} else if (b <= 1.82e+93) {
		tmp = y * -z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.2e+254:
		tmp = y * b
	elif b <= -5e+87:
		tmp = t * b
	elif b <= -8e-266:
		tmp = a * -t
	elif b <= 1.25e-135:
		tmp = x
	elif b <= 1.82e+93:
		tmp = y * -z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.2e+254)
		tmp = Float64(y * b);
	elseif (b <= -5e+87)
		tmp = Float64(t * b);
	elseif (b <= -8e-266)
		tmp = Float64(a * Float64(-t));
	elseif (b <= 1.25e-135)
		tmp = x;
	elseif (b <= 1.82e+93)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.2e+254)
		tmp = y * b;
	elseif (b <= -5e+87)
		tmp = t * b;
	elseif (b <= -8e-266)
		tmp = a * -t;
	elseif (b <= 1.25e-135)
		tmp = x;
	elseif (b <= 1.82e+93)
		tmp = y * -z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.2e+254], N[(y * b), $MachinePrecision], If[LessEqual[b, -5e+87], N[(t * b), $MachinePrecision], If[LessEqual[b, -8e-266], N[(a * (-t)), $MachinePrecision], If[LessEqual[b, 1.25e-135], x, If[LessEqual[b, 1.82e+93], N[(y * (-z)), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.2000000000000002e254 or 1.82000000000000009e93 < b

   1. Initial program 91.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.9%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in y around inf 50.3%

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

   if -5.2000000000000002e254 < b < -4.9999999999999998e87

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 74.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in t around inf 43.6%

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

   if -4.9999999999999998e87 < b < -7.9999999999999999e-266

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 38.7%

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

   4. Taylor expanded in b around 0 32.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 32.8%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} \]

      2. *-commutative 32.8%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot a\right)} \]

      3. neg-mul-1 32.8%

         \[\leadsto t \cdot \color{blue}{\left(-a\right)} \]

   6. Simplified 32.8%

      \[\leadsto \color{blue}{t \cdot \left(-a\right)} \]

   if -7.9999999999999999e-266 < b < 1.25000000000000005e-135

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 33.0%

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

   if 1.25000000000000005e-135 < b < 1.82000000000000009e93

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 40.6%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   4. Taylor expanded in y around inf 30.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 30.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. mul-1-neg 30.1%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot z \]

   6. Simplified 30.1%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+254}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+87}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.82 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -45000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-152}:\\ \;\;\;\;x + \left(z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-273}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+40}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -45000.0)
     t_1
     (if (<= b -5.2e-152)
       (+ x (- z (* t a)))
       (if (<= b -5.2e-273)
         (+ x (* a (- 1.0 t)))
         (if (<= b 7.5e+40) (+ x (* z (- 1.0 y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -45000.0) {
		tmp = t_1;
	} else if (b <= -5.2e-152) {
		tmp = x + (z - (t * a));
	} else if (b <= -5.2e-273) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 7.5e+40) {
		tmp = x + (z * (1.0 - 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 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-45000.0d0)) then
        tmp = t_1
    else if (b <= (-5.2d-152)) then
        tmp = x + (z - (t * a))
    else if (b <= (-5.2d-273)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 7.5d+40) then
        tmp = x + (z * (1.0d0 - 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 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -45000.0) {
		tmp = t_1;
	} else if (b <= -5.2e-152) {
		tmp = x + (z - (t * a));
	} else if (b <= -5.2e-273) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 7.5e+40) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -45000.0:
		tmp = t_1
	elif b <= -5.2e-152:
		tmp = x + (z - (t * a))
	elif b <= -5.2e-273:
		tmp = x + (a * (1.0 - t))
	elif b <= 7.5e+40:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -45000.0)
		tmp = t_1;
	elseif (b <= -5.2e-152)
		tmp = Float64(x + Float64(z - Float64(t * a)));
	elseif (b <= -5.2e-273)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 7.5e+40)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -45000.0)
		tmp = t_1;
	elseif (b <= -5.2e-152)
		tmp = x + (z - (t * a));
	elseif (b <= -5.2e-273)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 7.5e+40)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -45000.0], t$95$1, If[LessEqual[b, -5.2e-152], N[(x + N[(z - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.2e-273], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+40], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -45000 or 7.4999999999999996e40 < b

   1. Initial program 94.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.3%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in a around 0 77.2%

      \[\leadsto \color{blue}{x + b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -45000 < b < -5.20000000000000026e-152

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 90.8%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around 0 76.7%

      \[\leadsto x - \color{blue}{\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 76.7%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)} \]

      2. sub-neg 76.7%

         \[\leadsto x - \left(a \cdot \color{blue}{\left(t + \left(-1\right)\right)} + -1 \cdot z\right) \]

      3. metadata-eval 76.7%

         \[\leadsto x - \left(a \cdot \left(t + \color{blue}{-1}\right) + -1 \cdot z\right) \]

      4. mul-1-neg 76.7%

         \[\leadsto x - \left(a \cdot \left(t + -1\right) + \color{blue}{\left(-z\right)}\right) \]

      5. unsub-neg 76.7%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   6. Simplified 76.7%

      \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   7. Taylor expanded in t around inf 76.7%

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

   if -5.20000000000000026e-152 < b < -5.19999999999999967e-273

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 77.9%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in b around 0 73.7%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]

   if -5.19999999999999967e-273 < b < 7.4999999999999996e40

   1. Initial program 97.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 88.1%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in a around 0 67.8%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -45000:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-152}:\\ \;\;\;\;x + \left(z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-273}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+40}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -20500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-152}:\\ \;\;\;\;x + \left(z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-273}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{+54}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -20500.0)
     t_1
     (if (<= b -3.6e-152)
       (+ x (- z (* t a)))
       (if (<= b -1.22e-273)
         (+ x (* a (- 1.0 t)))
         (if (<= b 1.38e+54) (+ x (* z (- 1.0 y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -20500.0) {
		tmp = t_1;
	} else if (b <= -3.6e-152) {
		tmp = x + (z - (t * a));
	} else if (b <= -1.22e-273) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 1.38e+54) {
		tmp = x + (z * (1.0 - 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 = b * ((y + t) - 2.0d0)
    if (b <= (-20500.0d0)) then
        tmp = t_1
    else if (b <= (-3.6d-152)) then
        tmp = x + (z - (t * a))
    else if (b <= (-1.22d-273)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 1.38d+54) then
        tmp = x + (z * (1.0d0 - 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 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -20500.0) {
		tmp = t_1;
	} else if (b <= -3.6e-152) {
		tmp = x + (z - (t * a));
	} else if (b <= -1.22e-273) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 1.38e+54) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -20500.0:
		tmp = t_1
	elif b <= -3.6e-152:
		tmp = x + (z - (t * a))
	elif b <= -1.22e-273:
		tmp = x + (a * (1.0 - t))
	elif b <= 1.38e+54:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -20500.0)
		tmp = t_1;
	elseif (b <= -3.6e-152)
		tmp = Float64(x + Float64(z - Float64(t * a)));
	elseif (b <= -1.22e-273)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 1.38e+54)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -20500.0)
		tmp = t_1;
	elseif (b <= -3.6e-152)
		tmp = x + (z - (t * a));
	elseif (b <= -1.22e-273)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 1.38e+54)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -20500.0], t$95$1, If[LessEqual[b, -3.6e-152], N[(x + N[(z - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.22e-273], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.38e+54], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -20500 or 1.38e54 < b

   1. Initial program 94.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 75.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -20500 < b < -3.6e-152

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 90.8%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around 0 76.7%

      \[\leadsto x - \color{blue}{\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 76.7%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)} \]

      2. sub-neg 76.7%

         \[\leadsto x - \left(a \cdot \color{blue}{\left(t + \left(-1\right)\right)} + -1 \cdot z\right) \]

      3. metadata-eval 76.7%

         \[\leadsto x - \left(a \cdot \left(t + \color{blue}{-1}\right) + -1 \cdot z\right) \]

      4. mul-1-neg 76.7%

         \[\leadsto x - \left(a \cdot \left(t + -1\right) + \color{blue}{\left(-z\right)}\right) \]

      5. unsub-neg 76.7%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   6. Simplified 76.7%

      \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   7. Taylor expanded in t around inf 76.7%

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

   if -3.6e-152 < b < -1.21999999999999991e-273

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 77.9%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in b around 0 73.7%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]

   if -1.21999999999999991e-273 < b < 1.38e54

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 87.5%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in a around 0 67.0%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -20500:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-152}:\\ \;\;\;\;x + \left(z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-273}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{+54}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* y (- z))))
   (if (<= z -1.4e+119)
     t_2
     (if (<= z -8.2e-116)
       t_1
       (if (<= z -4.4e-189) x (if (<= z 6.5e+186) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = y * -z;
	double tmp;
	if (z <= -1.4e+119) {
		tmp = t_2;
	} else if (z <= -8.2e-116) {
		tmp = t_1;
	} else if (z <= -4.4e-189) {
		tmp = x;
	} else if (z <= 6.5e+186) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = y * -z
    if (z <= (-1.4d+119)) then
        tmp = t_2
    else if (z <= (-8.2d-116)) then
        tmp = t_1
    else if (z <= (-4.4d-189)) then
        tmp = x
    else if (z <= 6.5d+186) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = y * -z;
	double tmp;
	if (z <= -1.4e+119) {
		tmp = t_2;
	} else if (z <= -8.2e-116) {
		tmp = t_1;
	} else if (z <= -4.4e-189) {
		tmp = x;
	} else if (z <= 6.5e+186) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = y * -z
	tmp = 0
	if z <= -1.4e+119:
		tmp = t_2
	elif z <= -8.2e-116:
		tmp = t_1
	elif z <= -4.4e-189:
		tmp = x
	elif z <= 6.5e+186:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -1.4e+119)
		tmp = t_2;
	elseif (z <= -8.2e-116)
		tmp = t_1;
	elseif (z <= -4.4e-189)
		tmp = x;
	elseif (z <= 6.5e+186)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = y * -z;
	tmp = 0.0;
	if (z <= -1.4e+119)
		tmp = t_2;
	elseif (z <= -8.2e-116)
		tmp = t_1;
	elseif (z <= -4.4e-189)
		tmp = x;
	elseif (z <= 6.5e+186)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.4e+119], t$95$2, If[LessEqual[z, -8.2e-116], t$95$1, If[LessEqual[z, -4.4e-189], x, If[LessEqual[z, 6.5e+186], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000007e119 or 6.4999999999999997e186 < z

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   4. Taylor expanded in y around inf 48.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 48.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. mul-1-neg 48.0%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot z \]

   6. Simplified 48.0%

      \[\leadsto \color{blue}{\left(-y\right) \cdot z} \]

   if -1.40000000000000007e119 < z < -8.1999999999999998e-116 or -4.40000000000000038e-189 < z < 6.4999999999999997e186

   1. Initial program 97.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 35.7%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -8.1999999999999998e-116 < z < -4.40000000000000038e-189

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 55.3%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+186}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -14600000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 130:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -14600000.0)
     t_1
     (if (<= t -1e-118)
       x
       (if (<= t -9.5e-171)
         (* y (- z))
         (if (<= t 130.0) (* b (- y 2.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -14600000.0) {
		tmp = t_1;
	} else if (t <= -1e-118) {
		tmp = x;
	} else if (t <= -9.5e-171) {
		tmp = y * -z;
	} else if (t <= 130.0) {
		tmp = b * (y - 2.0);
	} 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 = t * (b - a)
    if (t <= (-14600000.0d0)) then
        tmp = t_1
    else if (t <= (-1d-118)) then
        tmp = x
    else if (t <= (-9.5d-171)) then
        tmp = y * -z
    else if (t <= 130.0d0) then
        tmp = b * (y - 2.0d0)
    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 = t * (b - a);
	double tmp;
	if (t <= -14600000.0) {
		tmp = t_1;
	} else if (t <= -1e-118) {
		tmp = x;
	} else if (t <= -9.5e-171) {
		tmp = y * -z;
	} else if (t <= 130.0) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -14600000.0:
		tmp = t_1
	elif t <= -1e-118:
		tmp = x
	elif t <= -9.5e-171:
		tmp = y * -z
	elif t <= 130.0:
		tmp = b * (y - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -14600000.0)
		tmp = t_1;
	elseif (t <= -1e-118)
		tmp = x;
	elseif (t <= -9.5e-171)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 130.0)
		tmp = Float64(b * Float64(y - 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -14600000.0)
		tmp = t_1;
	elseif (t <= -1e-118)
		tmp = x;
	elseif (t <= -9.5e-171)
		tmp = y * -z;
	elseif (t <= 130.0)
		tmp = b * (y - 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -14600000.0], t$95$1, If[LessEqual[t, -1e-118], x, If[LessEqual[t, -9.5e-171], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 130.0], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.46e7 or 130 < t

   1. Initial program 95.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.9%

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

   if -1.46e7 < t < -9.99999999999999985e-119

   1. Initial program 96.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 35.3%

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

   if -9.99999999999999985e-119 < t < -9.4999999999999994e-171

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 65.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   4. Taylor expanded in y around inf 54.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 54.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. mul-1-neg 54.1%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot z \]

   6. Simplified 54.1%

      \[\leadsto \color{blue}{\left(-y\right) \cdot z} \]

   if -9.4999999999999994e-171 < t < 130

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 36.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in t around 0 36.1%

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -14600000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 130:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+67} \lor \neg \left(z \leq 2.2 \cdot 10^{+175}\right):\\ \;\;\;\;x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= z -2.7e+67) (not (<= z 2.2e+175)))
     (+ x (+ t_1 (* z (- 1.0 y))))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((z <= -2.7e+67) || !(z <= 2.2e+175)) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + 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 * (1.0d0 - t)
    if ((z <= (-2.7d+67)) .or. (.not. (z <= 2.2d+175))) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + 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 * (1.0 - t);
	double tmp;
	if ((z <= -2.7e+67) || !(z <= 2.2e+175)) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (z <= -2.7e+67) or not (z <= 2.2e+175):
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((z <= -2.7e+67) || !(z <= 2.2e+175))
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((z <= -2.7e+67) || ~((z <= 2.2e+175)))
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -2.7e+67], N[Not[LessEqual[z, 2.2e+175]], $MachinePrecision]], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e67 or 2.1999999999999999e175 < z

   1. Initial program 96.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 83.3%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   if -2.6999999999999999e67 < z < 2.1999999999999999e175

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 90.9%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+67} \lor \neg \left(z \leq 2.2 \cdot 10^{+175}\right):\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+254}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{+171}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-12} \lor \neg \left(b \leq 7 \cdot 10^{+70}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.2e+254)
   (* y b)
   (if (<= b -5.4e+171)
     (* t b)
     (if (or (<= b -3.45e-12) (not (<= b 7e+70))) (* y b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e+254) {
		tmp = y * b;
	} else if (b <= -5.4e+171) {
		tmp = t * b;
	} else if ((b <= -3.45e-12) || !(b <= 7e+70)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.2d+254)) then
        tmp = y * b
    else if (b <= (-5.4d+171)) then
        tmp = t * b
    else if ((b <= (-3.45d-12)) .or. (.not. (b <= 7d+70))) then
        tmp = y * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e+254) {
		tmp = y * b;
	} else if (b <= -5.4e+171) {
		tmp = t * b;
	} else if ((b <= -3.45e-12) || !(b <= 7e+70)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.2e+254:
		tmp = y * b
	elif b <= -5.4e+171:
		tmp = t * b
	elif (b <= -3.45e-12) or not (b <= 7e+70):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.2e+254)
		tmp = Float64(y * b);
	elseif (b <= -5.4e+171)
		tmp = Float64(t * b);
	elseif ((b <= -3.45e-12) || !(b <= 7e+70))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.2e+254)
		tmp = y * b;
	elseif (b <= -5.4e+171)
		tmp = t * b;
	elseif ((b <= -3.45e-12) || ~((b <= 7e+70)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.2e+254], N[(y * b), $MachinePrecision], If[LessEqual[b, -5.4e+171], N[(t * b), $MachinePrecision], If[Or[LessEqual[b, -3.45e-12], N[Not[LessEqual[b, 7e+70]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.2000000000000002e254 or -5.3999999999999996e171 < b < -3.45e-12 or 7.00000000000000005e70 < b

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 83.2%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in y around inf 40.3%

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

   if -5.2000000000000002e254 < b < -5.3999999999999996e171

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 86.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in t around inf 60.6%

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

   if -3.45e-12 < b < 7.00000000000000005e70

   1. Initial program 98.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 25.8%

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

4. Final simplification 33.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+254}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{+171}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-12} \lor \neg \left(b \leq 7 \cdot 10^{+70}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 26.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+254}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+85}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.9e+254)
   (* y b)
   (if (<= b -4.6e+85)
     (* t b)
     (if (<= b -6.5e-266) (* a (- t)) (if (<= b 3.2e+70) x (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+254) {
		tmp = y * b;
	} else if (b <= -4.6e+85) {
		tmp = t * b;
	} else if (b <= -6.5e-266) {
		tmp = a * -t;
	} else if (b <= 3.2e+70) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.9d+254)) then
        tmp = y * b
    else if (b <= (-4.6d+85)) then
        tmp = t * b
    else if (b <= (-6.5d-266)) then
        tmp = a * -t
    else if (b <= 3.2d+70) then
        tmp = x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+254) {
		tmp = y * b;
	} else if (b <= -4.6e+85) {
		tmp = t * b;
	} else if (b <= -6.5e-266) {
		tmp = a * -t;
	} else if (b <= 3.2e+70) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.9e+254:
		tmp = y * b
	elif b <= -4.6e+85:
		tmp = t * b
	elif b <= -6.5e-266:
		tmp = a * -t
	elif b <= 3.2e+70:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.9e+254)
		tmp = Float64(y * b);
	elseif (b <= -4.6e+85)
		tmp = Float64(t * b);
	elseif (b <= -6.5e-266)
		tmp = Float64(a * Float64(-t));
	elseif (b <= 3.2e+70)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.9e+254)
		tmp = y * b;
	elseif (b <= -4.6e+85)
		tmp = t * b;
	elseif (b <= -6.5e-266)
		tmp = a * -t;
	elseif (b <= 3.2e+70)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.9e+254], N[(y * b), $MachinePrecision], If[LessEqual[b, -4.6e+85], N[(t * b), $MachinePrecision], If[LessEqual[b, -6.5e-266], N[(a * (-t)), $MachinePrecision], If[LessEqual[b, 3.2e+70], x, N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.8999999999999999e254 or 3.2000000000000002e70 < b

   1. Initial program 93.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.4%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in y around inf 44.6%

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

   if -2.8999999999999999e254 < b < -4.5999999999999998e85

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 74.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in t around inf 43.6%

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

   if -4.5999999999999998e85 < b < -6.50000000000000024e-266

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 38.7%

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

   4. Taylor expanded in b around 0 32.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 32.8%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} \]

      2. *-commutative 32.8%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot a\right)} \]

      3. neg-mul-1 32.8%

         \[\leadsto t \cdot \color{blue}{\left(-a\right)} \]

   6. Simplified 32.8%

      \[\leadsto \color{blue}{t \cdot \left(-a\right)} \]

   if -6.50000000000000024e-266 < b < 3.2000000000000002e70

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 28.1%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+254}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+85}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3400000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-123}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 29500:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3400000.0)
     t_1
     (if (<= t -3e-123) x (if (<= t 29500.0) (* y (- b z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3400000.0) {
		tmp = t_1;
	} else if (t <= -3e-123) {
		tmp = x;
	} else if (t <= 29500.0) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-3400000.0d0)) then
        tmp = t_1
    else if (t <= (-3d-123)) then
        tmp = x
    else if (t <= 29500.0d0) then
        tmp = y * (b - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3400000.0) {
		tmp = t_1;
	} else if (t <= -3e-123) {
		tmp = x;
	} else if (t <= 29500.0) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -3400000.0:
		tmp = t_1
	elif t <= -3e-123:
		tmp = x
	elif t <= 29500.0:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3400000.0)
		tmp = t_1;
	elseif (t <= -3e-123)
		tmp = x;
	elseif (t <= 29500.0)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -3400000.0)
		tmp = t_1;
	elseif (t <= -3e-123)
		tmp = x;
	elseif (t <= 29500.0)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3400000.0], t$95$1, If[LessEqual[t, -3e-123], x, If[LessEqual[t, 29500.0], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4e6 or 29500 < t

   1. Initial program 95.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.9%

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

   if -3.4e6 < t < -2.99999999999999984e-123

   1. Initial program 96.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 34.2%

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

   if -2.99999999999999984e-123 < t < 29500

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 42.4%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3400000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-123}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 29500:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-33} \lor \neg \left(a \leq 6.4 \cdot 10^{-28}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.8e-33) (not (<= a 6.4e-28)))
   (* a (- 1.0 t))
   (* b (- t 2.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.8e-33) || !(a <= 6.4e-28)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-4.8d-33)) .or. (.not. (a <= 6.4d-28))) then
        tmp = a * (1.0d0 - t)
    else
        tmp = b * (t - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.8e-33) || !(a <= 6.4e-28)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.8e-33) or not (a <= 6.4e-28):
		tmp = a * (1.0 - t)
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4.8e-33) || !(a <= 6.4e-28))
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4.8e-33) || ~((a <= 6.4e-28)))
		tmp = a * (1.0 - t);
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.8e-33], N[Not[LessEqual[a, 6.4e-28]], $MachinePrecision]], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8e-33 or 6.39999999999999964e-28 < a

   1. Initial program 94.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 47.8%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -4.8e-33 < a < 6.39999999999999964e-28

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in y around 0 34.1%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-33} \lor \neg \left(a \leq 6.4 \cdot 10^{-28}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 26.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -22000000000000 \lor \neg \left(b \leq 2.3 \cdot 10^{+71}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -22000000000000.0) (not (<= b 2.3e+71))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -22000000000000.0) || !(b <= 2.3e+71)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-22000000000000.0d0)) .or. (.not. (b <= 2.3d+71))) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -22000000000000.0) || !(b <= 2.3e+71)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -22000000000000.0) or not (b <= 2.3e+71):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -22000000000000.0) || !(b <= 2.3e+71))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -22000000000000.0) || ~((b <= 2.3e+71)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -22000000000000.0], N[Not[LessEqual[b, 2.3e+71]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -2.2e13 or 2.3000000000000002e71 < b

   1. Initial program 94.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 75.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in t around inf 35.4%

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

   if -2.2e13 < b < 2.3000000000000002e71

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 25.5%

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

4. Final simplification 29.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -22000000000000 \lor \neg \left(b \leq 2.3 \cdot 10^{+71}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 20.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.8e+24) z (if (<= z 3.9e+87) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.8e+24) {
		tmp = z;
	} else if (z <= 3.9e+87) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.8d+24)) then
        tmp = z
    else if (z <= 3.9d+87) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.8e+24) {
		tmp = z;
	} else if (z <= 3.9e+87) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.8e+24:
		tmp = z
	elif z <= 3.9e+87:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.8e+24)
		tmp = z;
	elseif (z <= 3.9e+87)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.8e+24)
		tmp = z;
	elseif (z <= 3.9e+87)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.8e+24], z, If[LessEqual[z, 3.9e+87], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999992e24 or 3.9000000000000002e87 < z

   1. Initial program 94.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 61.3%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   4. Taylor expanded in y around 0 25.9%

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

   if -1.79999999999999992e24 < z < 3.9000000000000002e87

   1. Initial program 98.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 23.8%

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

4. Final simplification 24.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 15.6% accurate, 21.0× 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 96.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in x around inf 16.8%

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

4. Final simplification 16.8%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))