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

Percentage Accurate: 95.1% → 97.9%

Time: 12.2s

Alternatives: 18

Speedup: 0.5×

• 36.2% 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: 95.1% 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

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* (- (+ y t) 2.0) b))))
   (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))) + (((y + t) - 2.0) * b);
	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))) + (((y + t) - 2.0) * b);
	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))) + (((y + t) - 2.0) * b)
	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(Float64(Float64(y + t) - 2.0) * b))
	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))) + (((y + t) - 2.0) * b);
	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[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $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 71.7%

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

4. Final simplification 98.5%

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

Alternative 2: 56.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := x + \left(z + b \cdot -2\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{-100}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-140}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-70}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (* y (- b z)))
        (t_3 (+ x (+ z (* b -2.0)))))
   (if (<= y -4.5e+80)
     t_2
     (if (<= y -2.8e-20)
       t_1
       (if (<= y -3.65e-100)
         t_3
         (if (<= y -8.5e-121)
           (* t (- b a))
           (if (<= y -8.2e-140)
             t_3
             (if (<= y 6e-152)
               t_1
               (if (<= y 1.95e-70) t_3 (if (<= y 3.5e+24) t_1 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));
	double t_2 = y * (b - z);
	double t_3 = x + (z + (b * -2.0));
	double tmp;
	if (y <= -4.5e+80) {
		tmp = t_2;
	} else if (y <= -2.8e-20) {
		tmp = t_1;
	} else if (y <= -3.65e-100) {
		tmp = t_3;
	} else if (y <= -8.5e-121) {
		tmp = t * (b - a);
	} else if (y <= -8.2e-140) {
		tmp = t_3;
	} else if (y <= 6e-152) {
		tmp = t_1;
	} else if (y <= 1.95e-70) {
		tmp = t_3;
	} else if (y <= 3.5e+24) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = y * (b - z)
    t_3 = x + (z + (b * (-2.0d0)))
    if (y <= (-4.5d+80)) then
        tmp = t_2
    else if (y <= (-2.8d-20)) then
        tmp = t_1
    else if (y <= (-3.65d-100)) then
        tmp = t_3
    else if (y <= (-8.5d-121)) then
        tmp = t * (b - a)
    else if (y <= (-8.2d-140)) then
        tmp = t_3
    else if (y <= 6d-152) then
        tmp = t_1
    else if (y <= 1.95d-70) then
        tmp = t_3
    else if (y <= 3.5d+24) 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 + (a * (1.0 - t));
	double t_2 = y * (b - z);
	double t_3 = x + (z + (b * -2.0));
	double tmp;
	if (y <= -4.5e+80) {
		tmp = t_2;
	} else if (y <= -2.8e-20) {
		tmp = t_1;
	} else if (y <= -3.65e-100) {
		tmp = t_3;
	} else if (y <= -8.5e-121) {
		tmp = t * (b - a);
	} else if (y <= -8.2e-140) {
		tmp = t_3;
	} else if (y <= 6e-152) {
		tmp = t_1;
	} else if (y <= 1.95e-70) {
		tmp = t_3;
	} else if (y <= 3.5e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = y * (b - z)
	t_3 = x + (z + (b * -2.0))
	tmp = 0
	if y <= -4.5e+80:
		tmp = t_2
	elif y <= -2.8e-20:
		tmp = t_1
	elif y <= -3.65e-100:
		tmp = t_3
	elif y <= -8.5e-121:
		tmp = t * (b - a)
	elif y <= -8.2e-140:
		tmp = t_3
	elif y <= 6e-152:
		tmp = t_1
	elif y <= 1.95e-70:
		tmp = t_3
	elif y <= 3.5e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(x + Float64(z + Float64(b * -2.0)))
	tmp = 0.0
	if (y <= -4.5e+80)
		tmp = t_2;
	elseif (y <= -2.8e-20)
		tmp = t_1;
	elseif (y <= -3.65e-100)
		tmp = t_3;
	elseif (y <= -8.5e-121)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= -8.2e-140)
		tmp = t_3;
	elseif (y <= 6e-152)
		tmp = t_1;
	elseif (y <= 1.95e-70)
		tmp = t_3;
	elseif (y <= 3.5e+24)
		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 + (a * (1.0 - t));
	t_2 = y * (b - z);
	t_3 = x + (z + (b * -2.0));
	tmp = 0.0;
	if (y <= -4.5e+80)
		tmp = t_2;
	elseif (y <= -2.8e-20)
		tmp = t_1;
	elseif (y <= -3.65e-100)
		tmp = t_3;
	elseif (y <= -8.5e-121)
		tmp = t * (b - a);
	elseif (y <= -8.2e-140)
		tmp = t_3;
	elseif (y <= 6e-152)
		tmp = t_1;
	elseif (y <= 1.95e-70)
		tmp = t_3;
	elseif (y <= 3.5e+24)
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+80], t$95$2, If[LessEqual[y, -2.8e-20], t$95$1, If[LessEqual[y, -3.65e-100], t$95$3, If[LessEqual[y, -8.5e-121], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e-140], t$95$3, If[LessEqual[y, 6e-152], t$95$1, If[LessEqual[y, 1.95e-70], t$95$3, If[LessEqual[y, 3.5e+24], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.50000000000000007e80 or 3.5000000000000002e24 < y

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 77.2%

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

   if -4.50000000000000007e80 < y < -2.8000000000000003e-20 or -8.2000000000000003e-140 < y < 6e-152 or 1.9500000000000001e-70 < y < 3.5000000000000002e24

   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 78.0%

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

   4. Taylor expanded in a around inf 65.2%

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

   if -2.8000000000000003e-20 < y < -3.6499999999999998e-100 or -8.50000000000000025e-121 < y < -8.2000000000000003e-140 or 6e-152 < y < 1.9500000000000001e-70

   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 0 84.6%

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

   4. Taylor expanded in y around 0 84.6%

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

      1. associate--l+ 84.6%

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

      2. sub-neg 84.6%

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

      3. metadata-eval 84.6%

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

      4. neg-mul-1 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in t around 0 73.5%

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

   if -3.6499999999999998e-100 < y < -8.50000000000000025e-121

   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 90.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-20}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{-100}:\\ \;\;\;\;x + \left(z + b \cdot -2\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-140}:\\ \;\;\;\;x + \left(z + b \cdot -2\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-152}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-70}:\\ \;\;\;\;x + \left(z + b \cdot -2\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+24}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-54}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-150}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 32000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -1.25e+123)
     t_2
     (if (<= y -7e+72)
       t_1
       (if (<= y -6.8e+50)
         t_2
         (if (<= y -6.5e-54)
           (+ x a)
           (if (<= y -3.4e-122)
             t_1
             (if (<= y -2.9e-150) z (if (<= y 32000.0) (+ x a) 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 = y * (b - z);
	double tmp;
	if (y <= -1.25e+123) {
		tmp = t_2;
	} else if (y <= -7e+72) {
		tmp = t_1;
	} else if (y <= -6.8e+50) {
		tmp = t_2;
	} else if (y <= -6.5e-54) {
		tmp = x + a;
	} else if (y <= -3.4e-122) {
		tmp = t_1;
	} else if (y <= -2.9e-150) {
		tmp = z;
	} else if (y <= 32000.0) {
		tmp = x + a;
	} 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 = y * (b - z)
    if (y <= (-1.25d+123)) then
        tmp = t_2
    else if (y <= (-7d+72)) then
        tmp = t_1
    else if (y <= (-6.8d+50)) then
        tmp = t_2
    else if (y <= (-6.5d-54)) then
        tmp = x + a
    else if (y <= (-3.4d-122)) then
        tmp = t_1
    else if (y <= (-2.9d-150)) then
        tmp = z
    else if (y <= 32000.0d0) then
        tmp = x + a
    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 = y * (b - z);
	double tmp;
	if (y <= -1.25e+123) {
		tmp = t_2;
	} else if (y <= -7e+72) {
		tmp = t_1;
	} else if (y <= -6.8e+50) {
		tmp = t_2;
	} else if (y <= -6.5e-54) {
		tmp = x + a;
	} else if (y <= -3.4e-122) {
		tmp = t_1;
	} else if (y <= -2.9e-150) {
		tmp = z;
	} else if (y <= 32000.0) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -1.25e+123:
		tmp = t_2
	elif y <= -7e+72:
		tmp = t_1
	elif y <= -6.8e+50:
		tmp = t_2
	elif y <= -6.5e-54:
		tmp = x + a
	elif y <= -3.4e-122:
		tmp = t_1
	elif y <= -2.9e-150:
		tmp = z
	elif y <= 32000.0:
		tmp = x + a
	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(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.25e+123)
		tmp = t_2;
	elseif (y <= -7e+72)
		tmp = t_1;
	elseif (y <= -6.8e+50)
		tmp = t_2;
	elseif (y <= -6.5e-54)
		tmp = Float64(x + a);
	elseif (y <= -3.4e-122)
		tmp = t_1;
	elseif (y <= -2.9e-150)
		tmp = z;
	elseif (y <= 32000.0)
		tmp = Float64(x + a);
	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 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.25e+123)
		tmp = t_2;
	elseif (y <= -7e+72)
		tmp = t_1;
	elseif (y <= -6.8e+50)
		tmp = t_2;
	elseif (y <= -6.5e-54)
		tmp = x + a;
	elseif (y <= -3.4e-122)
		tmp = t_1;
	elseif (y <= -2.9e-150)
		tmp = z;
	elseif (y <= 32000.0)
		tmp = x + a;
	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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+123], t$95$2, If[LessEqual[y, -7e+72], t$95$1, If[LessEqual[y, -6.8e+50], t$95$2, If[LessEqual[y, -6.5e-54], N[(x + a), $MachinePrecision], If[LessEqual[y, -3.4e-122], t$95$1, If[LessEqual[y, -2.9e-150], z, If[LessEqual[y, 32000.0], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.24999999999999994e123 or -7.0000000000000002e72 < y < -6.7999999999999997e50 or 32000 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf 78.6%

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

   if -1.24999999999999994e123 < y < -7.0000000000000002e72 or -6.49999999999999991e-54 < y < -3.3999999999999998e-122

   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 t around inf 63.4%

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

   if -6.7999999999999997e50 < y < -6.49999999999999991e-54 or -2.8999999999999998e-150 < y < 32000

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0 75.8%

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

   4. Taylor expanded in a around inf 62.1%

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

   5. Taylor expanded in t around 0 43.6%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 43.6%

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

      2. metadata-eval 43.6%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 43.6%

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

      4. +-commutative 43.6%

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

   7. Simplified 43.6%

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

   if -3.3999999999999998e-122 < y < -2.8999999999999998e-150

   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 0 90.4%

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

   4. Taylor expanded in y around 0 90.4%

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

      1. associate--l+ 90.4%

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

      2. sub-neg 90.4%

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

      3. metadata-eval 90.4%

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

      4. neg-mul-1 90.4%

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

   6. Simplified 90.4%

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

   7. Taylor expanded in z around inf 61.1%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-54}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-150}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 32000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := x + \left(z + b \cdot -2\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+72}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 60000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (+ x (+ z (* b -2.0)))))
   (if (<= y -5.8e+146)
     t_1
     (if (<= y -6.4e+72)
       (* (- (+ y t) 2.0) b)
       (if (<= y -5.7e+50)
         t_1
         (if (<= y -8e-100)
           t_2
           (if (<= y -3.6e-120)
             (* t (- b a))
             (if (<= y 60000.0) t_2 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 = x + (z + (b * -2.0));
	double tmp;
	if (y <= -5.8e+146) {
		tmp = t_1;
	} else if (y <= -6.4e+72) {
		tmp = ((y + t) - 2.0) * b;
	} else if (y <= -5.7e+50) {
		tmp = t_1;
	} else if (y <= -8e-100) {
		tmp = t_2;
	} else if (y <= -3.6e-120) {
		tmp = t * (b - a);
	} else if (y <= 60000.0) {
		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 = y * (b - z)
    t_2 = x + (z + (b * (-2.0d0)))
    if (y <= (-5.8d+146)) then
        tmp = t_1
    else if (y <= (-6.4d+72)) then
        tmp = ((y + t) - 2.0d0) * b
    else if (y <= (-5.7d+50)) then
        tmp = t_1
    else if (y <= (-8d-100)) then
        tmp = t_2
    else if (y <= (-3.6d-120)) then
        tmp = t * (b - a)
    else if (y <= 60000.0d0) 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 = y * (b - z);
	double t_2 = x + (z + (b * -2.0));
	double tmp;
	if (y <= -5.8e+146) {
		tmp = t_1;
	} else if (y <= -6.4e+72) {
		tmp = ((y + t) - 2.0) * b;
	} else if (y <= -5.7e+50) {
		tmp = t_1;
	} else if (y <= -8e-100) {
		tmp = t_2;
	} else if (y <= -3.6e-120) {
		tmp = t * (b - a);
	} else if (y <= 60000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = x + (z + (b * -2.0))
	tmp = 0
	if y <= -5.8e+146:
		tmp = t_1
	elif y <= -6.4e+72:
		tmp = ((y + t) - 2.0) * b
	elif y <= -5.7e+50:
		tmp = t_1
	elif y <= -8e-100:
		tmp = t_2
	elif y <= -3.6e-120:
		tmp = t * (b - a)
	elif y <= 60000.0:
		tmp = t_2
	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(x + Float64(z + Float64(b * -2.0)))
	tmp = 0.0
	if (y <= -5.8e+146)
		tmp = t_1;
	elseif (y <= -6.4e+72)
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	elseif (y <= -5.7e+50)
		tmp = t_1;
	elseif (y <= -8e-100)
		tmp = t_2;
	elseif (y <= -3.6e-120)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 60000.0)
		tmp = t_2;
	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 = x + (z + (b * -2.0));
	tmp = 0.0;
	if (y <= -5.8e+146)
		tmp = t_1;
	elseif (y <= -6.4e+72)
		tmp = ((y + t) - 2.0) * b;
	elseif (y <= -5.7e+50)
		tmp = t_1;
	elseif (y <= -8e-100)
		tmp = t_2;
	elseif (y <= -3.6e-120)
		tmp = t * (b - a);
	elseif (y <= 60000.0)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+146], t$95$1, If[LessEqual[y, -6.4e+72], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[y, -5.7e+50], t$95$1, If[LessEqual[y, -8e-100], t$95$2, If[LessEqual[y, -3.6e-120], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 60000.0], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.7999999999999997e146 or -6.4000000000000003e72 < y < -5.7000000000000002e50 or 6e4 < y

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 79.6%

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

   if -5.7999999999999997e146 < y < -6.4000000000000003e72

   1. Initial program 88.9%

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

   3. Taylor expanded in b around inf 67.1%

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

   if -5.7000000000000002e50 < y < -8.0000000000000002e-100 or -3.6000000000000003e-120 < y < 6e4

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0 71.8%

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

   4. Taylor expanded in y around 0 70.7%

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

      1. associate--l+ 70.7%

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

      2. sub-neg 70.7%

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

      3. metadata-eval 70.7%

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

      4. neg-mul-1 70.7%

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

   6. Simplified 70.7%

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

   7. Taylor expanded in t around 0 58.3%

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

   if -8.0000000000000002e-100 < y < -3.6000000000000003e-120

   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 90.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+72}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-100}:\\ \;\;\;\;x + \left(z + b \cdot -2\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 60000:\\ \;\;\;\;x + \left(z + b \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 34.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -y \cdot z\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+126}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -96000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-238}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* y z))))
   (if (<= t -1.25e+126)
     (* t b)
     (if (<= t -96000000.0)
       (+ x a)
       (if (<= t -5.8e-83)
         t_1
         (if (<= t -2.6e-238)
           (+ x a)
           (if (<= t 3.5e-288)
             t_1
             (if (<= t 2.3e+43) (+ x a) (* t (- a))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(y * z);
	double tmp;
	if (t <= -1.25e+126) {
		tmp = t * b;
	} else if (t <= -96000000.0) {
		tmp = x + a;
	} else if (t <= -5.8e-83) {
		tmp = t_1;
	} else if (t <= -2.6e-238) {
		tmp = x + a;
	} else if (t <= 3.5e-288) {
		tmp = t_1;
	} else if (t <= 2.3e+43) {
		tmp = x + a;
	} else {
		tmp = t * -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(y * z)
    if (t <= (-1.25d+126)) then
        tmp = t * b
    else if (t <= (-96000000.0d0)) then
        tmp = x + a
    else if (t <= (-5.8d-83)) then
        tmp = t_1
    else if (t <= (-2.6d-238)) then
        tmp = x + a
    else if (t <= 3.5d-288) then
        tmp = t_1
    else if (t <= 2.3d+43) then
        tmp = x + a
    else
        tmp = t * -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(y * z);
	double tmp;
	if (t <= -1.25e+126) {
		tmp = t * b;
	} else if (t <= -96000000.0) {
		tmp = x + a;
	} else if (t <= -5.8e-83) {
		tmp = t_1;
	} else if (t <= -2.6e-238) {
		tmp = x + a;
	} else if (t <= 3.5e-288) {
		tmp = t_1;
	} else if (t <= 2.3e+43) {
		tmp = x + a;
	} else {
		tmp = t * -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -(y * z)
	tmp = 0
	if t <= -1.25e+126:
		tmp = t * b
	elif t <= -96000000.0:
		tmp = x + a
	elif t <= -5.8e-83:
		tmp = t_1
	elif t <= -2.6e-238:
		tmp = x + a
	elif t <= 3.5e-288:
		tmp = t_1
	elif t <= 2.3e+43:
		tmp = x + a
	else:
		tmp = t * -a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-Float64(y * z))
	tmp = 0.0
	if (t <= -1.25e+126)
		tmp = Float64(t * b);
	elseif (t <= -96000000.0)
		tmp = Float64(x + a);
	elseif (t <= -5.8e-83)
		tmp = t_1;
	elseif (t <= -2.6e-238)
		tmp = Float64(x + a);
	elseif (t <= 3.5e-288)
		tmp = t_1;
	elseif (t <= 2.3e+43)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -(y * z);
	tmp = 0.0;
	if (t <= -1.25e+126)
		tmp = t * b;
	elseif (t <= -96000000.0)
		tmp = x + a;
	elseif (t <= -5.8e-83)
		tmp = t_1;
	elseif (t <= -2.6e-238)
		tmp = x + a;
	elseif (t <= 3.5e-288)
		tmp = t_1;
	elseif (t <= 2.3e+43)
		tmp = x + a;
	else
		tmp = t * -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = (-N[(y * z), $MachinePrecision])}, If[LessEqual[t, -1.25e+126], N[(t * b), $MachinePrecision], If[LessEqual[t, -96000000.0], N[(x + a), $MachinePrecision], If[LessEqual[t, -5.8e-83], t$95$1, If[LessEqual[t, -2.6e-238], N[(x + a), $MachinePrecision], If[LessEqual[t, 3.5e-288], t$95$1, If[LessEqual[t, 2.3e+43], N[(x + a), $MachinePrecision], N[(t * (-a)), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.24999999999999994e126

   1. Initial program 84.6%

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

   3. Taylor expanded in a around 0 77.2%

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

   4. Taylor expanded in t around inf 51.0%

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

   if -1.24999999999999994e126 < t < -9.6e7 or -5.7999999999999998e-83 < t < -2.6000000000000001e-238 or 3.5000000000000003e-288 < t < 2.3000000000000002e43

   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 b around 0 73.0%

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

   4. Taylor expanded in a around inf 46.8%

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

   5. Taylor expanded in t around 0 42.8%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 42.8%

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

      2. metadata-eval 42.8%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 42.8%

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

      4. +-commutative 42.8%

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

   7. Simplified 42.8%

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

   if -9.6e7 < t < -5.7999999999999998e-83 or -2.6000000000000001e-238 < t < 3.5000000000000003e-288

   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 74.8%

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

   4. Taylor expanded in y around inf 48.4%

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

      1. mul-1-neg 48.4%

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

      2. distribute-rgt-neg-in 48.4%

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

   6. Simplified 48.4%

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

   if 2.3000000000000002e43 < t

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf 78.5%

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

   4. Taylor expanded in b around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. distribute-rgt-neg-in 51.6%

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

   6. Simplified 51.6%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+126}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -96000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-83}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-238}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-288}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-43}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+95}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 1.52 \cdot 10^{+143}:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -4.8e+20)
     t_1
     (if (<= b 5e-43)
       (+ x (+ a (* z (- 1.0 y))))
       (if (<= b 5.1e+95)
         (+ x (* a (- 1.0 t)))
         (if (<= b 3.8e+119)
           (+ x (+ a (* b (+ y -2.0))))
           (if (<= b 1.52e+143) (+ x (+ z (* b (+ t -2.0)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -4.8e+20) {
		tmp = t_1;
	} else if (b <= 5e-43) {
		tmp = x + (a + (z * (1.0 - y)));
	} else if (b <= 5.1e+95) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 3.8e+119) {
		tmp = x + (a + (b * (y + -2.0)));
	} else if (b <= 1.52e+143) {
		tmp = x + (z + (b * (t + -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 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-4.8d+20)) then
        tmp = t_1
    else if (b <= 5d-43) then
        tmp = x + (a + (z * (1.0d0 - y)))
    else if (b <= 5.1d+95) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 3.8d+119) then
        tmp = x + (a + (b * (y + (-2.0d0))))
    else if (b <= 1.52d+143) then
        tmp = x + (z + (b * (t + (-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 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -4.8e+20) {
		tmp = t_1;
	} else if (b <= 5e-43) {
		tmp = x + (a + (z * (1.0 - y)));
	} else if (b <= 5.1e+95) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 3.8e+119) {
		tmp = x + (a + (b * (y + -2.0)));
	} else if (b <= 1.52e+143) {
		tmp = x + (z + (b * (t + -2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -4.8e+20:
		tmp = t_1
	elif b <= 5e-43:
		tmp = x + (a + (z * (1.0 - y)))
	elif b <= 5.1e+95:
		tmp = x + (a * (1.0 - t))
	elif b <= 3.8e+119:
		tmp = x + (a + (b * (y + -2.0)))
	elif b <= 1.52e+143:
		tmp = x + (z + (b * (t + -2.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -4.8e+20)
		tmp = t_1;
	elseif (b <= 5e-43)
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	elseif (b <= 5.1e+95)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 3.8e+119)
		tmp = Float64(x + Float64(a + Float64(b * Float64(y + -2.0))));
	elseif (b <= 1.52e+143)
		tmp = Float64(x + Float64(z + Float64(b * Float64(t + -2.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -4.8e+20)
		tmp = t_1;
	elseif (b <= 5e-43)
		tmp = x + (a + (z * (1.0 - y)));
	elseif (b <= 5.1e+95)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 3.8e+119)
		tmp = x + (a + (b * (y + -2.0)));
	elseif (b <= 1.52e+143)
		tmp = x + (z + (b * (t + -2.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+20], t$95$1, If[LessEqual[b, 5e-43], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.1e+95], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+119], N[(x + N[(a + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.52e+143], N[(x + N[(z + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.8e20 or 1.51999999999999996e143 < b

   1. Initial program 86.6%

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

   3. Taylor expanded in a around 0 82.0%

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

   4. Taylor expanded in z around 0 82.2%

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

   if -4.8e20 < b < 5.00000000000000019e-43

   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 96.1%

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

   4. Taylor expanded in t around 0 82.1%

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

      1. +-commutative 82.1%

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

      2. sub-neg 82.1%

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

      3. metadata-eval 82.1%

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

      4. neg-mul-1 82.1%

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

      5. unsub-neg 82.1%

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

   6. Simplified 82.1%

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

   if 5.00000000000000019e-43 < b < 5.10000000000000003e95

   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 77.8%

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

   4. Taylor expanded in a around inf 55.9%

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

   if 5.10000000000000003e95 < b < 3.7999999999999999e119

   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 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 t around 0 64.8%

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

      1. associate--l+ 64.8%

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

      2. sub-neg 64.8%

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

      3. metadata-eval 64.8%

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

      4. neg-mul-1 64.8%

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

   6. Simplified 64.8%

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

   if 3.7999999999999999e119 < b < 1.51999999999999996e143

   1. Initial program 85.7%

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

   3. Taylor expanded in a around 0 58.2%

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

   4. Taylor expanded in y around 0 73.3%

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

      1. associate--l+ 73.3%

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

      2. sub-neg 73.3%

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

      3. metadata-eval 73.3%

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

      4. neg-mul-1 73.3%

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

   6. Simplified 73.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+20}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-43}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+95}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 1.52 \cdot 10^{+143}:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.18 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-303}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-31}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -1.18e+17)
     t_2
     (if (<= b -6.5e-251)
       t_1
       (if (<= b 2.55e-303)
         (+ x a)
         (if (<= b 2.2e-195) t_1 (if (<= b 1.9e-31) (+ x a) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.18e+17) {
		tmp = t_2;
	} else if (b <= -6.5e-251) {
		tmp = t_1;
	} else if (b <= 2.55e-303) {
		tmp = x + a;
	} else if (b <= 2.2e-195) {
		tmp = t_1;
	} else if (b <= 1.9e-31) {
		tmp = x + a;
	} 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 = z * (1.0d0 - y)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-1.18d+17)) then
        tmp = t_2
    else if (b <= (-6.5d-251)) then
        tmp = t_1
    else if (b <= 2.55d-303) then
        tmp = x + a
    else if (b <= 2.2d-195) then
        tmp = t_1
    else if (b <= 1.9d-31) then
        tmp = x + a
    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 = z * (1.0 - y);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.18e+17) {
		tmp = t_2;
	} else if (b <= -6.5e-251) {
		tmp = t_1;
	} else if (b <= 2.55e-303) {
		tmp = x + a;
	} else if (b <= 2.2e-195) {
		tmp = t_1;
	} else if (b <= 1.9e-31) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1.18e+17:
		tmp = t_2
	elif b <= -6.5e-251:
		tmp = t_1
	elif b <= 2.55e-303:
		tmp = x + a
	elif b <= 2.2e-195:
		tmp = t_1
	elif b <= 1.9e-31:
		tmp = x + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.18e+17)
		tmp = t_2;
	elseif (b <= -6.5e-251)
		tmp = t_1;
	elseif (b <= 2.55e-303)
		tmp = Float64(x + a);
	elseif (b <= 2.2e-195)
		tmp = t_1;
	elseif (b <= 1.9e-31)
		tmp = Float64(x + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.18e+17)
		tmp = t_2;
	elseif (b <= -6.5e-251)
		tmp = t_1;
	elseif (b <= 2.55e-303)
		tmp = x + a;
	elseif (b <= 2.2e-195)
		tmp = t_1;
	elseif (b <= 1.9e-31)
		tmp = x + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.18e+17], t$95$2, If[LessEqual[b, -6.5e-251], t$95$1, If[LessEqual[b, 2.55e-303], N[(x + a), $MachinePrecision], If[LessEqual[b, 2.2e-195], t$95$1, If[LessEqual[b, 1.9e-31], N[(x + a), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.18e17 or 1.9e-31 < b

   1. Initial program 89.2%

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

   3. Taylor expanded in b around inf 64.4%

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

   if -1.18e17 < b < -6.5000000000000002e-251 or 2.55e-303 < b < 2.20000000000000005e-195

   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 57.1%

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

   if -6.5000000000000002e-251 < b < 2.55e-303 or 2.20000000000000005e-195 < b < 1.9e-31

   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 97.9%

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

   4. Taylor expanded in a around inf 71.1%

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

   5. Taylor expanded in t around 0 57.5%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 57.5%

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

      2. metadata-eval 57.5%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 57.5%

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

      4. +-commutative 57.5%

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

   7. Simplified 57.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.18 \cdot 10^{+17}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-251}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-303}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-195}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-31}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-238}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{-283}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+42}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -8e+98)
     t_1
     (if (<= t -2.8e-238)
       (+ x a)
       (if (<= t 1.82e-283) (- (* y z)) (if (<= t 1.3e+42) (+ x a) 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 <= -8e+98) {
		tmp = t_1;
	} else if (t <= -2.8e-238) {
		tmp = x + a;
	} else if (t <= 1.82e-283) {
		tmp = -(y * z);
	} else if (t <= 1.3e+42) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-8d+98)) then
        tmp = t_1
    else if (t <= (-2.8d-238)) then
        tmp = x + a
    else if (t <= 1.82d-283) then
        tmp = -(y * z)
    else if (t <= 1.3d+42) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -8e+98) {
		tmp = t_1;
	} else if (t <= -2.8e-238) {
		tmp = x + a;
	} else if (t <= 1.82e-283) {
		tmp = -(y * z);
	} else if (t <= 1.3e+42) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -8e+98:
		tmp = t_1
	elif t <= -2.8e-238:
		tmp = x + a
	elif t <= 1.82e-283:
		tmp = -(y * z)
	elif t <= 1.3e+42:
		tmp = x + a
	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 <= -8e+98)
		tmp = t_1;
	elseif (t <= -2.8e-238)
		tmp = Float64(x + a);
	elseif (t <= 1.82e-283)
		tmp = Float64(-Float64(y * z));
	elseif (t <= 1.3e+42)
		tmp = Float64(x + a);
	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 <= -8e+98)
		tmp = t_1;
	elseif (t <= -2.8e-238)
		tmp = x + a;
	elseif (t <= 1.82e-283)
		tmp = -(y * z);
	elseif (t <= 1.3e+42)
		tmp = x + a;
	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, -8e+98], t$95$1, If[LessEqual[t, -2.8e-238], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.82e-283], (-N[(y * z), $MachinePrecision]), If[LessEqual[t, 1.3e+42], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.99999999999999998e98 or 1.29999999999999995e42 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 73.8%

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

   if -7.99999999999999998e98 < t < -2.80000000000000004e-238 or 1.81999999999999994e-283 < t < 1.29999999999999995e42

   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 b around 0 72.5%

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

   4. Taylor expanded in a around inf 42.6%

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

   5. Taylor expanded in t around 0 40.9%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 40.9%

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

      2. metadata-eval 40.9%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 40.9%

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

      4. +-commutative 40.9%

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

   7. Simplified 40.9%

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

   if -2.80000000000000004e-238 < t < 1.81999999999999994e-283

   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 79.7%

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

   4. Taylor expanded in y around inf 48.3%

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

      1. mul-1-neg 48.3%

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

      2. distribute-rgt-neg-in 48.3%

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

   6. Simplified 48.3%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-238}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{-283}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+42}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+20} \lor \neg \left(b \leq 1.15 \cdot 10^{+70}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + \left(t + -1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.6e+20) (not (<= b 1.15e+70)))
   (+ (+ x (* (- (+ y t) 2.0) b)) (* a (- 1.0 t)))
   (- x (+ (* (+ y -1.0) z) (* (+ t -1.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.6e+20) || !(b <= 1.15e+70)) {
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	} else {
		tmp = x - (((y + -1.0) * z) + ((t + -1.0) * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-8.6d+20)) .or. (.not. (b <= 1.15d+70))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + (a * (1.0d0 - t))
    else
        tmp = x - (((y + (-1.0d0)) * z) + ((t + (-1.0d0)) * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.6e+20) || !(b <= 1.15e+70)) {
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	} else {
		tmp = x - (((y + -1.0) * z) + ((t + -1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8.6e+20) or not (b <= 1.15e+70):
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t))
	else:
		tmp = x - (((y + -1.0) * z) + ((t + -1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.6e+20) || !(b <= 1.15e+70))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x - Float64(Float64(Float64(y + -1.0) * z) + Float64(Float64(t + -1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8.6e+20) || ~((b <= 1.15e+70)))
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	else
		tmp = x - (((y + -1.0) * z) + ((t + -1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.6e+20], N[Not[LessEqual[b, 1.15e+70]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.6e20 or 1.14999999999999997e70 < b

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 86.3%

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

   if -8.6e20 < b < 1.14999999999999997e70

   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 93.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+20} \lor \neg \left(b \leq 1.15 \cdot 10^{+70}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + \left(t + -1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-75}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+190}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= z -3.3e+93)
     t_1
     (if (<= z -6.8e-75)
       (+ x (* a (- 1.0 t)))
       (if (<= z 1.65e+190) (+ x (* (- (+ y t) 2.0) b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -3.3e+93) {
		tmp = t_1;
	} else if (z <= -6.8e-75) {
		tmp = x + (a * (1.0 - t));
	} else if (z <= 1.65e+190) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (z <= (-3.3d+93)) then
        tmp = t_1
    else if (z <= (-6.8d-75)) then
        tmp = x + (a * (1.0d0 - t))
    else if (z <= 1.65d+190) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -3.3e+93) {
		tmp = t_1;
	} else if (z <= -6.8e-75) {
		tmp = x + (a * (1.0 - t));
	} else if (z <= 1.65e+190) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if z <= -3.3e+93:
		tmp = t_1
	elif z <= -6.8e-75:
		tmp = x + (a * (1.0 - t))
	elif z <= 1.65e+190:
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -3.3e+93)
		tmp = t_1;
	elseif (z <= -6.8e-75)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (z <= 1.65e+190)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (z <= -3.3e+93)
		tmp = t_1;
	elseif (z <= -6.8e-75)
		tmp = x + (a * (1.0 - t));
	elseif (z <= 1.65e+190)
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+93], t$95$1, If[LessEqual[z, -6.8e-75], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+190], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000009e93 or 1.65e190 < z

   1. Initial program 89.3%

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

   3. Taylor expanded in z around inf 71.4%

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

   if -3.30000000000000009e93 < z < -6.8000000000000003e-75

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0 84.3%

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

   4. Taylor expanded in a around inf 65.3%

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

   if -6.8000000000000003e-75 < z < 1.65e190

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0 77.3%

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

   4. Taylor expanded in z around 0 66.8%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+93}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-75}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+190}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+45} \lor \neg \left(b \leq 1.35 \cdot 10^{+121}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + \left(t + -1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.5e+45) (not (<= b 1.35e+121)))
   (+ x (* (- (+ y t) 2.0) b))
   (- x (+ (* (+ y -1.0) z) (* (+ t -1.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e+45) || !(b <= 1.35e+121)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x - (((y + -1.0) * z) + ((t + -1.0) * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.5d+45)) .or. (.not. (b <= 1.35d+121))) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = x - (((y + (-1.0d0)) * z) + ((t + (-1.0d0)) * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e+45) || !(b <= 1.35e+121)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x - (((y + -1.0) * z) + ((t + -1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.5e+45) or not (b <= 1.35e+121):
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = x - (((y + -1.0) * z) + ((t + -1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.5e+45) || !(b <= 1.35e+121))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(x - Float64(Float64(Float64(y + -1.0) * z) + Float64(Float64(t + -1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.5e+45) || ~((b <= 1.35e+121)))
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = x - (((y + -1.0) * z) + ((t + -1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.5e+45], N[Not[LessEqual[b, 1.35e+121]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.50000000000000005e45 or 1.3500000000000001e121 < b

   1. Initial program 85.1%

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

   3. Taylor expanded in a around 0 82.4%

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

   4. Taylor expanded in z around 0 84.4%

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

   if -1.50000000000000005e45 < b < 1.3500000000000001e121

   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 90.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+45} \lor \neg \left(b \leq 1.35 \cdot 10^{+121}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + \left(t + -1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+18} \lor \neg \left(b \leq 10^{-30}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.9e+18) (not (<= b 1e-30)))
   (+ x (* (- (+ y t) 2.0) b))
   (+ x (+ a (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+18) || !(b <= 1e-30)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.9d+18)) .or. (.not. (b <= 1d-30))) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = x + (a + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+18) || !(b <= 1e-30)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.9e+18) or not (b <= 1e-30):
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = x + (a + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.9e+18) || !(b <= 1e-30))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.9e+18) || ~((b <= 1e-30)))
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = x + (a + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.9e+18], N[Not[LessEqual[b, 1e-30]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.9e18 or 1e-30 < b

   1. Initial program 89.2%

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

   3. Taylor expanded in a around 0 78.3%

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

   4. Taylor expanded in z around 0 73.9%

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

   if -1.9e18 < b < 1e-30

   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 96.2%

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

   4. Taylor expanded in t around 0 81.2%

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

      1. +-commutative 81.2%

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

      2. sub-neg 81.2%

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

      3. metadata-eval 81.2%

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

      4. neg-mul-1 81.2%

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

      5. unsub-neg 81.2%

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

   6. Simplified 81.2%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+18} \lor \neg \left(b \leq 10^{-30}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+124}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.05e+124) (* t b) (if (<= t 2.6e+43) (+ x a) (* t (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e+124) {
		tmp = t * b;
	} else if (t <= 2.6e+43) {
		tmp = x + a;
	} else {
		tmp = t * -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.05d+124)) then
        tmp = t * b
    else if (t <= 2.6d+43) then
        tmp = x + a
    else
        tmp = t * -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e+124) {
		tmp = t * b;
	} else if (t <= 2.6e+43) {
		tmp = x + a;
	} else {
		tmp = t * -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.05e+124:
		tmp = t * b
	elif t <= 2.6e+43:
		tmp = x + a
	else:
		tmp = t * -a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.05e+124)
		tmp = Float64(t * b);
	elseif (t <= 2.6e+43)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.05e+124)
		tmp = t * b;
	elseif (t <= 2.6e+43)
		tmp = x + a;
	else
		tmp = t * -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.05e+124], N[(t * b), $MachinePrecision], If[LessEqual[t, 2.6e+43], N[(x + a), $MachinePrecision], N[(t * (-a)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000006e124

   1. Initial program 84.6%

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

   3. Taylor expanded in a around 0 77.2%

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

   4. Taylor expanded in t around inf 51.0%

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

   if -1.05000000000000006e124 < t < 2.60000000000000021e43

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0 73.4%

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

   4. Taylor expanded in a around inf 40.0%

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

   5. Taylor expanded in t around 0 36.9%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 36.9%

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

      2. metadata-eval 36.9%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 36.9%

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

      4. +-commutative 36.9%

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

   7. Simplified 36.9%

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

   if 2.60000000000000021e43 < t

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf 78.5%

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

   4. Taylor expanded in b around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. distribute-rgt-neg-in 51.6%

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

   6. Simplified 51.6%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+124}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+123} \lor \neg \left(t \leq 2.3 \cdot 10^{+42}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8e+123) (not (<= t 2.3e+42))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8e+123) || !(t <= 2.3e+42)) {
		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 ((t <= (-8d+123)) .or. (.not. (t <= 2.3d+42))) 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 ((t <= -8e+123) || !(t <= 2.3e+42)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8e+123) or not (t <= 2.3e+42):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8e+123) || !(t <= 2.3e+42))
		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 ((t <= -8e+123) || ~((t <= 2.3e+42)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8e+123], N[Not[LessEqual[t, 2.3e+42]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -7.99999999999999982e123 or 2.3e42 < t

   1. Initial program 89.1%

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

   3. Taylor expanded in a around 0 66.0%

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

   4. Taylor expanded in t around inf 39.4%

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

   if -7.99999999999999982e123 < t < 2.3e42

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf 23.9%

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

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+123} \lor \neg \left(t \leq 2.3 \cdot 10^{+42}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+128} \lor \neg \left(t \leq 1.35 \cdot 10^{+42}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2e+128) (not (<= t 1.35e+42))) (* t b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e+128) || !(t <= 1.35e+42)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2d+128)) .or. (.not. (t <= 1.35d+42))) then
        tmp = t * b
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e+128) || !(t <= 1.35e+42)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2e+128) or not (t <= 1.35e+42):
		tmp = t * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2e+128) || !(t <= 1.35e+42))
		tmp = Float64(t * b);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2e+128) || ~((t <= 1.35e+42)))
		tmp = t * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2e+128], N[Not[LessEqual[t, 1.35e+42]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0000000000000002e128 or 1.35e42 < t

   1. Initial program 89.1%

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

   3. Taylor expanded in a around 0 66.0%

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

   4. Taylor expanded in t around inf 39.4%

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

   if -2.0000000000000002e128 < t < 1.35e42

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0 74.2%

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

   4. Taylor expanded in a around inf 40.4%

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

   5. Taylor expanded in t around 0 37.3%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 37.3%

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

      2. metadata-eval 37.3%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 37.3%

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

      4. +-commutative 37.3%

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

   7. Simplified 37.3%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+128} \lor \neg \left(t \leq 1.35 \cdot 10^{+42}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 25.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+143}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9e+143) (* t b) (if (<= b 8.6e-33) x (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9e+143) {
		tmp = t * b;
	} else if (b <= 8.6e-33) {
		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 <= (-9d+143)) then
        tmp = t * b
    else if (b <= 8.6d-33) 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 <= -9e+143) {
		tmp = t * b;
	} else if (b <= 8.6e-33) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9e+143:
		tmp = t * b
	elif b <= 8.6e-33:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9e+143)
		tmp = Float64(t * b);
	elseif (b <= 8.6e-33)
		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 <= -9e+143)
		tmp = t * b;
	elseif (b <= 8.6e-33)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9e+143], N[(t * b), $MachinePrecision], If[LessEqual[b, 8.6e-33], x, N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.9999999999999993e143

   1. Initial program 82.9%

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

   3. Taylor expanded in a around 0 77.8%

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

   4. Taylor expanded in t around inf 44.7%

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

   if -8.9999999999999993e143 < b < 8.60000000000000062e-33

   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 25.4%

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

   if 8.60000000000000062e-33 < b

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 80.7%

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

   4. Taylor expanded in y around inf 32.6%

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

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+143}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 21.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+178}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.95e+178) z (if (<= z 2.9e+76) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.95e+178) {
		tmp = z;
	} else if (z <= 2.9e+76) {
		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 <= (-2.95d+178)) then
        tmp = z
    else if (z <= 2.9d+76) 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 <= -2.95e+178) {
		tmp = z;
	} else if (z <= 2.9e+76) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.95e+178:
		tmp = z
	elif z <= 2.9e+76:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.95e+178)
		tmp = z;
	elseif (z <= 2.9e+76)
		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 <= -2.95e+178)
		tmp = z;
	elseif (z <= 2.9e+76)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.95e+178], z, If[LessEqual[z, 2.9e+76], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.94999999999999992e178 or 2.9000000000000002e76 < z

   1. Initial program 90.2%

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

   3. Taylor expanded in a around 0 75.1%

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

   4. Taylor expanded in y around 0 46.7%

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

      1. associate--l+ 46.7%

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

      2. sub-neg 46.7%

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

      3. metadata-eval 46.7%

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

      4. neg-mul-1 46.7%

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

   6. Simplified 46.7%

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

   7. Taylor expanded in z around inf 27.5%

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

   if -2.94999999999999992e178 < z < 2.9000000000000002e76

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf 24.4%

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

4. Final simplification 25.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+178}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 16.1% 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 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 x around inf 17.7%

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

4. Final simplification 17.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(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)))