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

Percentage Accurate: 95.0% → 97.8%

Time: 12.1s

Alternatives: 23

Speedup: 0.5×

• 36.0% 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: 95.0% 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: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(b - a), $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 t around inf 67.9%

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

4. Final simplification 98.8%

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

Alternative 2: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-define 97.2%

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

   3. associate--l+ 97.2%

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

   4. sub-neg 97.2%

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

   5. metadata-eval 97.2%

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

   6. sub-neg 97.2%

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

   7. associate-+l- 97.2%

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

   8. fmm-def 97.6%

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

   9. sub-neg 97.6%

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

   10. metadata-eval 97.6%

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

   11. remove-double-neg 97.6%

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

   12. sub-neg 97.6%

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

   13. metadata-eval 97.6%

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

3. Simplified 97.6%

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

5. Final simplification 97.6%

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

Alternative 3: 49.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-218}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.8e-27)
     t_1
     (if (<= y 1.06e-218)
       (* t (- b a))
       (if (<= y 1.9e-56)
         (* b (- t 2.0))
         (if (<= y 8.4e+21) (* a (- 1.0 t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.8e-27) {
		tmp = t_1;
	} else if (y <= 1.06e-218) {
		tmp = t * (b - a);
	} else if (y <= 1.9e-56) {
		tmp = b * (t - 2.0);
	} else if (y <= 8.4e+21) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1.8d-27)) then
        tmp = t_1
    else if (y <= 1.06d-218) then
        tmp = t * (b - a)
    else if (y <= 1.9d-56) then
        tmp = b * (t - 2.0d0)
    else if (y <= 8.4d+21) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.8e-27) {
		tmp = t_1;
	} else if (y <= 1.06e-218) {
		tmp = t * (b - a);
	} else if (y <= 1.9e-56) {
		tmp = b * (t - 2.0);
	} else if (y <= 8.4e+21) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.8e-27:
		tmp = t_1
	elif y <= 1.06e-218:
		tmp = t * (b - a)
	elif y <= 1.9e-56:
		tmp = b * (t - 2.0)
	elif y <= 8.4e+21:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.8e-27)
		tmp = t_1;
	elseif (y <= 1.06e-218)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 1.9e-56)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 8.4e+21)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.8e-27)
		tmp = t_1;
	elseif (y <= 1.06e-218)
		tmp = t * (b - a);
	elseif (y <= 1.9e-56)
		tmp = b * (t - 2.0);
	elseif (y <= 8.4e+21)
		tmp = a * (1.0 - t);
	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]}, If[LessEqual[y, -1.8e-27], t$95$1, If[LessEqual[y, 1.06e-218], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-56], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.4e+21], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7999999999999999e-27 or 8.4e21 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 65.4%

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

   if -1.7999999999999999e-27 < y < 1.0600000000000001e-218

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 45.8%

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

   if 1.0600000000000001e-218 < y < 1.9000000000000001e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 54.2%

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

      1. associate-*r* 54.2%

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

      2. neg-mul-1 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in y around 0 54.3%

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

   if 1.9000000000000001e-56 < y < 8.4e21

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 63.8%

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

Alternative 4: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+28} \lor \neg \left(b \leq 1560000000000\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.55e+28) (not (<= b 1560000000000.0)))
   (+ (- x (* b (- 2.0 (+ y t)))) (* z (- 1.0 y)))
   (+ x (- (* a (- 1.0 t)) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.55e+28) || !(b <= 1560000000000.0)) {
		tmp = (x - (b * (2.0 - (y + t)))) + (z * (1.0 - y));
	} else {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.55d+28)) .or. (.not. (b <= 1560000000000.0d0))) then
        tmp = (x - (b * (2.0d0 - (y + t)))) + (z * (1.0d0 - y))
    else
        tmp = x + ((a * (1.0d0 - t)) - (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.55e+28) || !(b <= 1560000000000.0)) {
		tmp = (x - (b * (2.0 - (y + t)))) + (z * (1.0 - y));
	} else {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.55e+28) or not (b <= 1560000000000.0):
		tmp = (x - (b * (2.0 - (y + t)))) + (z * (1.0 - y))
	else:
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.55e+28) || !(b <= 1560000000000.0))
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.55e+28) || ~((b <= 1560000000000.0)))
		tmp = (x - (b * (2.0 - (y + t)))) + (z * (1.0 - y));
	else
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.55e+28], N[Not[LessEqual[b, 1560000000000.0]], $MachinePrecision]], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5500000000000002e28 or 1.56e12 < b

   1. Initial program 91.8%

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

   3. Taylor expanded in a around 0 91.2%

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

   if -2.5500000000000002e28 < b < 1.56e12

   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 95.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+28} \lor \neg \left(b \leq 1560000000000\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-303}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 1080000000000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -3.3e+65)
     t_1
     (if (<= b -4.2e-303)
       (- x (* z (+ y -1.0)))
       (if (<= b 1080000000000.0) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -3.3e+65) {
		tmp = t_1;
	} else if (b <= -4.2e-303) {
		tmp = x - (z * (y + -1.0));
	} else if (b <= 1080000000000.0) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-3.3d+65)) then
        tmp = t_1
    else if (b <= (-4.2d-303)) then
        tmp = x - (z * (y + (-1.0d0)))
    else if (b <= 1080000000000.0d0) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -3.3e+65) {
		tmp = t_1;
	} else if (b <= -4.2e-303) {
		tmp = x - (z * (y + -1.0));
	} else if (b <= 1080000000000.0) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -3.3e+65:
		tmp = t_1
	elif b <= -4.2e-303:
		tmp = x - (z * (y + -1.0))
	elif b <= 1080000000000.0:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -3.3e+65)
		tmp = t_1;
	elseif (b <= -4.2e-303)
		tmp = Float64(x - Float64(z * Float64(y + -1.0)));
	elseif (b <= 1080000000000.0)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -3.3e+65)
		tmp = t_1;
	elseif (b <= -4.2e-303)
		tmp = x - (z * (y + -1.0));
	elseif (b <= 1080000000000.0)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+65], t$95$1, If[LessEqual[b, -4.2e-303], N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1080000000000.0], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.30000000000000023e65 or 1.08e12 < b

   1. Initial program 92.0%

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

   3. Taylor expanded in a around -inf 73.5%

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

      1. associate-*r* 73.5%

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

      2. neg-mul-1 73.5%

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

      3. sub-neg 73.5%

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

      4. mul-1-neg 73.5%

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

      5. div-sub 73.4%

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

      6. sub-neg 73.4%

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

      7. metadata-eval 73.4%

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

      8. div-sub 73.5%

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

      9. +-commutative 73.5%

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

      10. sub-neg 73.5%

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

      11. metadata-eval 73.5%

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

      12. mul-1-neg 73.5%

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

      13. remove-double-neg 73.5%

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

      14. +-commutative 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in x around inf 79.8%

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

   if -3.30000000000000023e65 < b < -4.2e-303

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0 91.1%

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

   4. Taylor expanded in a around 0 63.5%

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

   if -4.2e-303 < b < 1.08e12

   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 96.9%

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

   4. Taylor expanded in a around inf 64.3%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+65}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-303}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 1080000000000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+27} \lor \neg \left(b \leq 7.5 \cdot 10^{+30}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.2e+27) (not (<= b 7.5e+30)))
   (+ (* b (- (+ y t) 2.0)) (* z (- 1.0 y)))
   (+ x (- (* a (- 1.0 t)) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.2e+27) || !(b <= 7.5e+30)) {
		tmp = (b * ((y + t) - 2.0)) + (z * (1.0 - y));
	} else {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5.2d+27)) .or. (.not. (b <= 7.5d+30))) then
        tmp = (b * ((y + t) - 2.0d0)) + (z * (1.0d0 - y))
    else
        tmp = x + ((a * (1.0d0 - t)) - (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.2e+27) || !(b <= 7.5e+30)) {
		tmp = (b * ((y + t) - 2.0)) + (z * (1.0 - y));
	} else {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.2e+27) or not (b <= 7.5e+30):
		tmp = (b * ((y + t) - 2.0)) + (z * (1.0 - y))
	else:
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.2e+27) || !(b <= 7.5e+30))
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.2e+27) || ~((b <= 7.5e+30)))
		tmp = (b * ((y + t) - 2.0)) + (z * (1.0 - y));
	else
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.2e+27], N[Not[LessEqual[b, 7.5e+30]], $MachinePrecision]], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.20000000000000018e27 or 7.49999999999999973e30 < b

   1. Initial program 91.4%

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

   3. Taylor expanded in a around -inf 72.0%

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

      1. associate-*r* 72.0%

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

      2. neg-mul-1 72.0%

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

      3. sub-neg 72.0%

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

      4. mul-1-neg 72.0%

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

      5. div-sub 71.8%

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

      6. sub-neg 71.8%

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

      7. metadata-eval 71.8%

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

      8. div-sub 72.0%

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

      9. +-commutative 72.0%

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

      10. sub-neg 72.0%

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

      11. metadata-eval 72.0%

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

      12. mul-1-neg 72.0%

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

      13. remove-double-neg 72.0%

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

      14. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in z around -inf 87.1%

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

      1. associate-*r* 87.1%

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

      2. neg-mul-1 87.1%

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

      3. sub-neg 87.1%

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

      4. metadata-eval 87.1%

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

      5. +-commutative 87.1%

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

      6. distribute-lft-neg-in 87.1%

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

      7. distribute-rgt-neg-in 87.1%

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

      8. distribute-neg-in 87.1%

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

      9. metadata-eval 87.1%

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

      10. sub-neg 87.1%

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

   8. Simplified 87.1%

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

   if -5.20000000000000018e27 < b < 7.49999999999999973e30

   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 95.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+27} \lor \neg \left(b \leq 7.5 \cdot 10^{+30}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+27} \lor \neg \left(b \leq 1.4 \cdot 10^{+29}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z - a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.05e+27) (not (<= b 1.4e+29)))
   (+ (* b (- (+ y t) 2.0)) (* z (- 1.0 y)))
   (- x (- (* y z) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.05e+27) || !(b <= 1.4e+29)) {
		tmp = (b * ((y + t) - 2.0)) + (z * (1.0 - y));
	} else {
		tmp = x - ((y * z) - (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.05d+27)) .or. (.not. (b <= 1.4d+29))) then
        tmp = (b * ((y + t) - 2.0d0)) + (z * (1.0d0 - y))
    else
        tmp = x - ((y * z) - (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.05e+27) || !(b <= 1.4e+29)) {
		tmp = (b * ((y + t) - 2.0)) + (z * (1.0 - y));
	} else {
		tmp = x - ((y * z) - (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.05e+27) or not (b <= 1.4e+29):
		tmp = (b * ((y + t) - 2.0)) + (z * (1.0 - y))
	else:
		tmp = x - ((y * z) - (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.05e+27) || !(b <= 1.4e+29))
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(x - Float64(Float64(y * z) - Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.05e+27) || ~((b <= 1.4e+29)))
		tmp = (b * ((y + t) - 2.0)) + (z * (1.0 - y));
	else
		tmp = x - ((y * z) - (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.05e+27], N[Not[LessEqual[b, 1.4e+29]], $MachinePrecision]], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] - N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.0500000000000001e27 or 1.4e29 < b

   1. Initial program 91.4%

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

   3. Taylor expanded in a around -inf 72.0%

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

      1. associate-*r* 72.0%

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

      2. neg-mul-1 72.0%

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

      3. sub-neg 72.0%

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

      4. mul-1-neg 72.0%

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

      5. div-sub 71.8%

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

      6. sub-neg 71.8%

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

      7. metadata-eval 71.8%

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

      8. div-sub 72.0%

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

      9. +-commutative 72.0%

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

      10. sub-neg 72.0%

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

      11. metadata-eval 72.0%

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

      12. mul-1-neg 72.0%

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

      13. remove-double-neg 72.0%

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

      14. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in z around -inf 87.1%

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

      1. associate-*r* 87.1%

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

      2. neg-mul-1 87.1%

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

      3. sub-neg 87.1%

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

      4. metadata-eval 87.1%

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

      5. +-commutative 87.1%

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

      6. distribute-lft-neg-in 87.1%

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

      7. distribute-rgt-neg-in 87.1%

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

      8. distribute-neg-in 87.1%

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

      9. metadata-eval 87.1%

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

      10. sub-neg 87.1%

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

   8. Simplified 87.1%

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

   if -2.0500000000000001e27 < b < 1.4e29

   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 95.2%

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

   4. Taylor expanded in y around inf 85.2%

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

      1. *-commutative 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+27} \lor \neg \left(b \leq 1.4 \cdot 10^{+29}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z - a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-302}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+33}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -7.5e+69)
     t_1
     (if (<= b -1e-302)
       (- x (* z (+ y -1.0)))
       (if (<= b 6.5e+33) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -7.5e+69) {
		tmp = t_1;
	} else if (b <= -1e-302) {
		tmp = x - (z * (y + -1.0));
	} else if (b <= 6.5e+33) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-7.5d+69)) then
        tmp = t_1
    else if (b <= (-1d-302)) then
        tmp = x - (z * (y + (-1.0d0)))
    else if (b <= 6.5d+33) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -7.5e+69) {
		tmp = t_1;
	} else if (b <= -1e-302) {
		tmp = x - (z * (y + -1.0));
	} else if (b <= 6.5e+33) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -7.5e+69:
		tmp = t_1
	elif b <= -1e-302:
		tmp = x - (z * (y + -1.0))
	elif b <= 6.5e+33:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -7.5e+69)
		tmp = t_1;
	elseif (b <= -1e-302)
		tmp = Float64(x - Float64(z * Float64(y + -1.0)));
	elseif (b <= 6.5e+33)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -7.5e+69)
		tmp = t_1;
	elseif (b <= -1e-302)
		tmp = x - (z * (y + -1.0));
	elseif (b <= 6.5e+33)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+69], t$95$1, If[LessEqual[b, -1e-302], N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+33], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.49999999999999939e69 or 6.49999999999999993e33 < b

   1. Initial program 91.6%

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

   3. Taylor expanded in b around inf 78.2%

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

   if -7.49999999999999939e69 < b < -9.9999999999999996e-303

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0 91.1%

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

   4. Taylor expanded in a around 0 63.5%

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

   if -9.9999999999999996e-303 < b < 6.49999999999999993e33

   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 95.6%

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

   4. Taylor expanded in a around inf 63.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-302}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+33}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1000000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -4.8e+97)
     t_1
     (if (<= b -1.05e-302)
       (* z (- 1.0 y))
       (if (<= b 1000000000000.0) (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.8e+97) {
		tmp = t_1;
	} else if (b <= -1.05e-302) {
		tmp = z * (1.0 - y);
	} else if (b <= 1000000000000.0) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-4.8d+97)) then
        tmp = t_1
    else if (b <= (-1.05d-302)) then
        tmp = z * (1.0d0 - y)
    else if (b <= 1000000000000.0d0) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.8e+97) {
		tmp = t_1;
	} else if (b <= -1.05e-302) {
		tmp = z * (1.0 - y);
	} else if (b <= 1000000000000.0) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -4.8e+97:
		tmp = t_1
	elif b <= -1.05e-302:
		tmp = z * (1.0 - y)
	elif b <= 1000000000000.0:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -4.8e+97)
		tmp = t_1;
	elseif (b <= -1.05e-302)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 1000000000000.0)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -4.8e+97)
		tmp = t_1;
	elseif (b <= -1.05e-302)
		tmp = z * (1.0 - y);
	elseif (b <= 1000000000000.0)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+97], t$95$1, If[LessEqual[b, -1.05e-302], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1000000000000.0], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.8e97 or 1e12 < b

   1. Initial program 92.5%

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

   3. Taylor expanded in b around inf 78.0%

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

   if -4.8e97 < b < -1.05000000000000006e-302

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 42.8%

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

   if -1.05000000000000006e-302 < b < 1e12

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 49.8%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+97}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1000000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+27} \lor \neg \left(b \leq 8 \cdot 10^{+26}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z - a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.25e+27) (not (<= b 8e+26)))
   (- (* b (- (+ y t) 2.0)) (* y z))
   (- x (- (* y z) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.25e+27) || !(b <= 8e+26)) {
		tmp = (b * ((y + t) - 2.0)) - (y * z);
	} else {
		tmp = x - ((y * z) - (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.25d+27)) .or. (.not. (b <= 8d+26))) then
        tmp = (b * ((y + t) - 2.0d0)) - (y * z)
    else
        tmp = x - ((y * z) - (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.25e+27) || !(b <= 8e+26)) {
		tmp = (b * ((y + t) - 2.0)) - (y * z);
	} else {
		tmp = x - ((y * z) - (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.25e+27) or not (b <= 8e+26):
		tmp = (b * ((y + t) - 2.0)) - (y * z)
	else:
		tmp = x - ((y * z) - (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.25e+27) || !(b <= 8e+26))
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(y * z));
	else
		tmp = Float64(x - Float64(Float64(y * z) - Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.25e+27) || ~((b <= 8e+26)))
		tmp = (b * ((y + t) - 2.0)) - (y * z);
	else
		tmp = x - ((y * z) - (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.25e+27], N[Not[LessEqual[b, 8e+26]], $MachinePrecision]], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] - N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.25e27 or 8.00000000000000038e26 < b

   1. Initial program 91.4%

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

   3. Taylor expanded in y around inf 79.4%

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

      1. associate-*r* 79.4%

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

      2. neg-mul-1 79.4%

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

   5. Simplified 79.4%

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

   if -2.25e27 < b < 8.00000000000000038e26

   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 95.2%

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

   4. Taylor expanded in y around inf 85.2%

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

      1. *-commutative 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+27} \lor \neg \left(b \leq 8 \cdot 10^{+26}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z - a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+97} \lor \neg \left(b \leq 10500000000000\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z - a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.6e+97) (not (<= b 10500000000000.0)))
   (- x (* b (- 2.0 (+ y t))))
   (- x (- (* y z) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.6e+97) || !(b <= 10500000000000.0)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x - ((y * z) - (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5.6d+97)) .or. (.not. (b <= 10500000000000.0d0))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x - ((y * z) - (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.6e+97) || !(b <= 10500000000000.0)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x - ((y * z) - (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.6e+97) or not (b <= 10500000000000.0):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x - ((y * z) - (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.6e+97) || !(b <= 10500000000000.0))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x - Float64(Float64(y * z) - Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.6e+97) || ~((b <= 10500000000000.0)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x - ((y * z) - (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.6e+97], N[Not[LessEqual[b, 10500000000000.0]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] - N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5999999999999998e97 or 1.05e13 < b

   1. Initial program 92.5%

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

   3. Taylor expanded in a around -inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. neg-mul-1 75.7%

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

      3. sub-neg 75.7%

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

      4. mul-1-neg 75.7%

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

      5. div-sub 75.6%

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

      6. sub-neg 75.6%

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

      7. metadata-eval 75.6%

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

      8. div-sub 75.7%

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

      9. +-commutative 75.7%

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

      10. sub-neg 75.7%

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

      11. metadata-eval 75.7%

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

      12. mul-1-neg 75.7%

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

      13. remove-double-neg 75.7%

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

      14. +-commutative 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in x around inf 82.7%

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

   if -5.5999999999999998e97 < b < 1.05e13

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0 92.3%

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

   4. Taylor expanded in y around inf 82.1%

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

      1. *-commutative 82.1%

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

   6. Simplified 82.1%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+97} \lor \neg \left(b \leq 10500000000000\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z - a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-250}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 10^{+41}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1e+15)
     t_1
     (if (<= t 2.5e-250) (* y (- z)) (if (<= t 1e+41) (* y b) 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 <= -1e+15) {
		tmp = t_1;
	} else if (t <= 2.5e-250) {
		tmp = y * -z;
	} else if (t <= 1e+41) {
		tmp = y * 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 = t * (b - a)
    if (t <= (-1d+15)) then
        tmp = t_1
    else if (t <= 2.5d-250) then
        tmp = y * -z
    else if (t <= 1d+41) then
        tmp = y * 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 = t * (b - a);
	double tmp;
	if (t <= -1e+15) {
		tmp = t_1;
	} else if (t <= 2.5e-250) {
		tmp = y * -z;
	} else if (t <= 1e+41) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1e+15:
		tmp = t_1
	elif t <= 2.5e-250:
		tmp = y * -z
	elif t <= 1e+41:
		tmp = y * b
	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 <= -1e+15)
		tmp = t_1;
	elseif (t <= 2.5e-250)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 1e+41)
		tmp = Float64(y * b);
	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 <= -1e+15)
		tmp = t_1;
	elseif (t <= 2.5e-250)
		tmp = y * -z;
	elseif (t <= 1e+41)
		tmp = y * b;
	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, -1e+15], t$95$1, If[LessEqual[t, 2.5e-250], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 1e+41], N[(y * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1e15 or 1.00000000000000001e41 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf 62.9%

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

   if -1e15 < t < 2.50000000000000013e-250

   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 z around inf 44.3%

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

   4. Taylor expanded in y around inf 34.0%

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

      1. mul-1-neg 34.0%

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

   6. Simplified 34.0%

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

   if 2.50000000000000013e-250 < t < 1.00000000000000001e41

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 46.0%

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

   4. Taylor expanded in b around inf 33.5%

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

      1. *-commutative 33.5%

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

   6. Simplified 33.5%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-250}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 10^{+41}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 2400000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))))
   (if (<= b -3.2e+71)
     t_1
     (if (<= b -1.55e-303)
       (* y (- z))
       (if (<= b 2400000000000.0) (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -3.2e+71) {
		tmp = t_1;
	} else if (b <= -1.55e-303) {
		tmp = y * -z;
	} else if (b <= 2400000000000.0) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    if (b <= (-3.2d+71)) then
        tmp = t_1
    else if (b <= (-1.55d-303)) then
        tmp = y * -z
    else if (b <= 2400000000000.0d0) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -3.2e+71) {
		tmp = t_1;
	} else if (b <= -1.55e-303) {
		tmp = y * -z;
	} else if (b <= 2400000000000.0) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	tmp = 0
	if b <= -3.2e+71:
		tmp = t_1
	elif b <= -1.55e-303:
		tmp = y * -z
	elif b <= 2400000000000.0:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -3.2e+71)
		tmp = t_1;
	elseif (b <= -1.55e-303)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 2400000000000.0)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -3.2e+71)
		tmp = t_1;
	elseif (b <= -1.55e-303)
		tmp = y * -z;
	elseif (b <= 2400000000000.0)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+71], t$95$1, If[LessEqual[b, -1.55e-303], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 2400000000000.0], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.20000000000000023e71 or 2.4e12 < b

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 79.2%

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

      1. associate-*r* 79.2%

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

      2. neg-mul-1 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in y around 0 51.1%

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

   if -3.20000000000000023e71 < b < -1.55e-303

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 42.5%

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

   4. Taylor expanded in y around inf 32.4%

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

      1. mul-1-neg 32.4%

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

   6. Simplified 32.4%

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

   if -1.55e-303 < b < 2.4e12

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 49.8%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 2400000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+66} \lor \neg \left(b \leq 1.06 \cdot 10^{+73}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(z \cdot \left(y + -1\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.75e+66) (not (<= b 1.06e+73)))
   (- x (* b (- 2.0 (+ y t))))
   (- x (- (* z (+ y -1.0)) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.75e+66) || !(b <= 1.06e+73)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x - ((z * (y + -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 <= (-1.75d+66)) .or. (.not. (b <= 1.06d+73))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x - ((z * (y + (-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 <= -1.75e+66) || !(b <= 1.06e+73)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x - ((z * (y + -1.0)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.75e+66) or not (b <= 1.06e+73):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x - ((z * (y + -1.0)) - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.75e+66) || !(b <= 1.06e+73))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x - Float64(Float64(z * Float64(y + -1.0)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.75e+66) || ~((b <= 1.06e+73)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x - ((z * (y + -1.0)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.75e+66], N[Not[LessEqual[b, 1.06e+73]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7499999999999999e66 or 1.0600000000000001e73 < b

   1. Initial program 90.9%

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

   3. Taylor expanded in a around -inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

      3. sub-neg 71.0%

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

      4. mul-1-neg 71.0%

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

      5. div-sub 70.9%

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

      6. sub-neg 70.9%

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

      7. metadata-eval 70.9%

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

      8. div-sub 71.0%

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

      9. +-commutative 71.0%

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

      10. sub-neg 71.0%

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

      11. metadata-eval 71.0%

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

      12. mul-1-neg 71.0%

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

      13. remove-double-neg 71.0%

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

      14. +-commutative 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in x around inf 83.0%

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

   if -1.7499999999999999e66 < b < 1.0600000000000001e73

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0 93.0%

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

   4. Taylor expanded in t around 0 69.2%

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

      1. +-commutative 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

      4. mul-1-neg 69.2%

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

      5. unsub-neg 69.2%

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

      6. +-commutative 69.2%

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

   6. Simplified 69.2%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+66} \lor \neg \left(b \leq 1.06 \cdot 10^{+73}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(z \cdot \left(y + -1\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -9.5e+124)
     t_1
     (if (<= t 1.12e-249) (* y (- z)) (if (<= t 1.45e+41) (* y b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -9.5e+124) {
		tmp = t_1;
	} else if (t <= 1.12e-249) {
		tmp = y * -z;
	} else if (t <= 1.45e+41) {
		tmp = y * 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 = t * -a
    if (t <= (-9.5d+124)) then
        tmp = t_1
    else if (t <= 1.12d-249) then
        tmp = y * -z
    else if (t <= 1.45d+41) then
        tmp = y * 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 = t * -a;
	double tmp;
	if (t <= -9.5e+124) {
		tmp = t_1;
	} else if (t <= 1.12e-249) {
		tmp = y * -z;
	} else if (t <= 1.45e+41) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -9.5e+124:
		tmp = t_1
	elif t <= 1.12e-249:
		tmp = y * -z
	elif t <= 1.45e+41:
		tmp = y * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -9.5e+124)
		tmp = t_1;
	elseif (t <= 1.12e-249)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 1.45e+41)
		tmp = Float64(y * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -9.5e+124)
		tmp = t_1;
	elseif (t <= 1.12e-249)
		tmp = y * -z;
	elseif (t <= 1.45e+41)
		tmp = y * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -9.5e+124], t$95$1, If[LessEqual[t, 1.12e-249], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 1.45e+41], N[(y * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.50000000000000004e124 or 1.44999999999999994e41 < t

   1. Initial program 92.4%

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

   3. Taylor expanded in t around inf 70.3%

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

   4. Taylor expanded in b around 0 47.5%

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

      1. associate-*r* 47.5%

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

      2. neg-mul-1 47.5%

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

   6. Simplified 47.5%

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

   if -9.50000000000000004e124 < t < 1.12000000000000011e-249

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 41.2%

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

   4. Taylor expanded in y around inf 31.8%

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

      1. mul-1-neg 31.8%

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

   6. Simplified 31.8%

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

   if 1.12000000000000011e-249 < t < 1.44999999999999994e41

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 46.0%

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

   4. Taylor expanded in b around inf 33.5%

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

      1. *-commutative 33.5%

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

   6. Simplified 33.5%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 28.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+101}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+237}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.4e+101)
   (* y b)
   (if (<= b 1.85e+68) (* y (- z)) (if (<= b 1.8e+237) (* y b) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e+101) {
		tmp = y * b;
	} else if (b <= 1.85e+68) {
		tmp = y * -z;
	} else if (b <= 1.8e+237) {
		tmp = y * b;
	} else {
		tmp = t * 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 <= (-1.4d+101)) then
        tmp = y * b
    else if (b <= 1.85d+68) then
        tmp = y * -z
    else if (b <= 1.8d+237) then
        tmp = y * b
    else
        tmp = t * 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 <= -1.4e+101) {
		tmp = y * b;
	} else if (b <= 1.85e+68) {
		tmp = y * -z;
	} else if (b <= 1.8e+237) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.4e+101:
		tmp = y * b
	elif b <= 1.85e+68:
		tmp = y * -z
	elif b <= 1.8e+237:
		tmp = y * b
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.4e+101)
		tmp = Float64(y * b);
	elseif (b <= 1.85e+68)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 1.8e+237)
		tmp = Float64(y * b);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.4e+101)
		tmp = y * b;
	elseif (b <= 1.85e+68)
		tmp = y * -z;
	elseif (b <= 1.8e+237)
		tmp = y * b;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.4e+101], N[(y * b), $MachinePrecision], If[LessEqual[b, 1.85e+68], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 1.8e+237], N[(y * b), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.39999999999999991e101 or 1.84999999999999999e68 < b < 1.80000000000000007e237

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf 43.0%

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

   4. Taylor expanded in b around inf 39.6%

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

      1. *-commutative 39.6%

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

   6. Simplified 39.6%

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

   if -1.39999999999999991e101 < b < 1.84999999999999999e68

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 38.8%

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

   4. Taylor expanded in y around inf 28.9%

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

      1. mul-1-neg 28.9%

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

   6. Simplified 28.9%

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

   if 1.80000000000000007e237 < b

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf 73.2%

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

   4. Taylor expanded in b around inf 67.4%

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

      1. *-commutative 67.4%

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

   6. Simplified 67.4%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+101}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+237}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 24.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.35 \cdot 10^{+60}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-267}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 30000000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.35e+60)
   (* y b)
   (if (<= b 1.35e-267) x (if (<= b 30000000000.0) a (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.35e+60) {
		tmp = y * b;
	} else if (b <= 1.35e-267) {
		tmp = x;
	} else if (b <= 30000000000.0) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.35d+60)) then
        tmp = y * b
    else if (b <= 1.35d-267) then
        tmp = x
    else if (b <= 30000000000.0d0) then
        tmp = a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.35e+60) {
		tmp = y * b;
	} else if (b <= 1.35e-267) {
		tmp = x;
	} else if (b <= 30000000000.0) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.35e+60:
		tmp = y * b
	elif b <= 1.35e-267:
		tmp = x
	elif b <= 30000000000.0:
		tmp = a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.35e+60)
		tmp = Float64(y * b);
	elseif (b <= 1.35e-267)
		tmp = x;
	elseif (b <= 30000000000.0)
		tmp = a;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.35e+60)
		tmp = y * b;
	elseif (b <= 1.35e-267)
		tmp = x;
	elseif (b <= 30000000000.0)
		tmp = a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.35e+60], N[(y * b), $MachinePrecision], If[LessEqual[b, 1.35e-267], x, If[LessEqual[b, 30000000000.0], a, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.3499999999999999e60

   1. Initial program 88.6%

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

   3. Taylor expanded in y around inf 41.7%

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

   4. Taylor expanded in b around inf 32.9%

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

      1. *-commutative 32.9%

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

   6. Simplified 32.9%

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

   if -2.3499999999999999e60 < b < 1.34999999999999994e-267

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf 24.5%

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

   if 1.34999999999999994e-267 < b < 3e10

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 51.1%

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

   4. Taylor expanded in t around 0 24.5%

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

   if 3e10 < b

   1. Initial program 95.1%

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

   3. Taylor expanded in t around inf 41.8%

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

   4. Taylor expanded in b around inf 35.7%

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

      1. *-commutative 35.7%

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

   6. Simplified 35.7%

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

Alternative 18: 23.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+60}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 28000000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.2e+60)
   (* t b)
   (if (<= b 5.2e-271) x (if (<= b 28000000000.0) a (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e+60) {
		tmp = t * b;
	} else if (b <= 5.2e-271) {
		tmp = x;
	} else if (b <= 28000000000.0) {
		tmp = a;
	} else {
		tmp = t * 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 <= (-8.2d+60)) then
        tmp = t * b
    else if (b <= 5.2d-271) then
        tmp = x
    else if (b <= 28000000000.0d0) then
        tmp = a
    else
        tmp = t * 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 <= -8.2e+60) {
		tmp = t * b;
	} else if (b <= 5.2e-271) {
		tmp = x;
	} else if (b <= 28000000000.0) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.2e+60:
		tmp = t * b
	elif b <= 5.2e-271:
		tmp = x
	elif b <= 28000000000.0:
		tmp = a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.2e+60)
		tmp = Float64(t * b);
	elseif (b <= 5.2e-271)
		tmp = x;
	elseif (b <= 28000000000.0)
		tmp = a;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.2e+60)
		tmp = t * b;
	elseif (b <= 5.2e-271)
		tmp = x;
	elseif (b <= 28000000000.0)
		tmp = a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.2e+60], N[(t * b), $MachinePrecision], If[LessEqual[b, 5.2e-271], x, If[LessEqual[b, 28000000000.0], a, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.2e60 or 2.8e10 < b

   1. Initial program 92.3%

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

   3. Taylor expanded in t around inf 38.5%

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

   4. Taylor expanded in b around inf 33.9%

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

      1. *-commutative 33.9%

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

   6. Simplified 33.9%

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

   if -8.2e60 < b < 5.2e-271

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf 24.5%

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

   if 5.2e-271 < b < 2.8e10

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 51.1%

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

   4. Taylor expanded in t around 0 24.5%

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

Alternative 19: 62.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.9 \cdot 10^{+59} \lor \neg \left(b \leq 2.3 \cdot 10^{+32}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.9e+59) (not (<= b 2.3e+32)))
   (* b (- (+ y t) 2.0))
   (+ x (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.9e+59) || !(b <= 2.3e+32)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7.9d+59)) .or. (.not. (b <= 2.3d+32))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = x + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.9e+59) || !(b <= 2.3e+32)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.9e+59) or not (b <= 2.3e+32):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = x + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.9e+59) || !(b <= 2.3e+32))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.9e+59) || ~((b <= 2.3e+32)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = x + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.9e+59], N[Not[LessEqual[b, 2.3e+32]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.9000000000000001e59 or 2.3e32 < b

   1. Initial program 91.7%

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

   3. Taylor expanded in b around inf 76.7%

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

   if -7.9000000000000001e59 < b < 2.3e32

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 93.6%

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

   4. Taylor expanded in a around inf 57.6%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.9 \cdot 10^{+59} \lor \neg \left(b \leq 2.3 \cdot 10^{+32}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 20.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-148}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+146}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.2e+30) x (if (<= x -2.1e-148) z (if (<= x 3.7e+146) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.2e+30) {
		tmp = x;
	} else if (x <= -2.1e-148) {
		tmp = z;
	} else if (x <= 3.7e+146) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.2d+30)) then
        tmp = x
    else if (x <= (-2.1d-148)) then
        tmp = z
    else if (x <= 3.7d+146) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.2e+30) {
		tmp = x;
	} else if (x <= -2.1e-148) {
		tmp = z;
	} else if (x <= 3.7e+146) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.2e+30:
		tmp = x
	elif x <= -2.1e-148:
		tmp = z
	elif x <= 3.7e+146:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.2e+30)
		tmp = x;
	elseif (x <= -2.1e-148)
		tmp = z;
	elseif (x <= 3.7e+146)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.2e+30)
		tmp = x;
	elseif (x <= -2.1e-148)
		tmp = z;
	elseif (x <= 3.7e+146)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.2e+30], x, If[LessEqual[x, -2.1e-148], z, If[LessEqual[x, 3.7e+146], a, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.19999999999999973e30 or 3.70000000000000004e146 < x

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf 34.9%

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

   if -3.19999999999999973e30 < x < -2.1e-148

   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 z around inf 35.1%

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

   4. Taylor expanded in y around 0 23.6%

      \[\leadsto z \cdot \color{blue}{1} \]

   5. Taylor expanded in z around 0 23.6%

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

   if -2.1e-148 < x < 3.70000000000000004e146

   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 inf 33.0%

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

   4. Taylor expanded in t around 0 14.3%

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

Alternative 21: 35.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+15} \lor \neg \left(a \leq 5.5 \cdot 10^{+37}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.8e+15) (not (<= a 5.5e+37))) (* a (- 1.0 t)) (* y (- z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.8e+15) || !(a <= 5.5e+37)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * -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 ((a <= (-1.8d+15)) .or. (.not. (a <= 5.5d+37))) then
        tmp = a * (1.0d0 - t)
    else
        tmp = y * -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 ((a <= -1.8e+15) || !(a <= 5.5e+37)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.8e+15) or not (a <= 5.5e+37):
		tmp = a * (1.0 - t)
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.8e+15) || !(a <= 5.5e+37))
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.8e+15) || ~((a <= 5.5e+37)))
		tmp = a * (1.0 - t);
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.8e+15], N[Not[LessEqual[a, 5.5e+37]], $MachinePrecision]], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8e15 or 5.50000000000000016e37 < a

   1. Initial program 92.8%

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

   3. Taylor expanded in a around inf 57.6%

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

   if -1.8e15 < a < 5.50000000000000016e37

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 42.1%

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

   4. Taylor expanded in y around inf 30.5%

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

      1. mul-1-neg 30.5%

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

   6. Simplified 30.5%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+15} \lor \neg \left(a \leq 5.5 \cdot 10^{+37}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 20.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+147}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.2e-22) x (if (<= x 1.05e+147) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.2e-22) {
		tmp = x;
	} else if (x <= 1.05e+147) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.2d-22)) then
        tmp = x
    else if (x <= 1.05d+147) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.2e-22) {
		tmp = x;
	} else if (x <= 1.05e+147) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.2e-22:
		tmp = x
	elif x <= 1.05e+147:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.2e-22)
		tmp = x;
	elseif (x <= 1.05e+147)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.2e-22)
		tmp = x;
	elseif (x <= 1.05e+147)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.2e-22], x, If[LessEqual[x, 1.05e+147], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2000000000000001e-22 or 1.05000000000000003e147 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 31.0%

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

   if -2.2000000000000001e-22 < x < 1.05000000000000003e147

   1. Initial program 95.3%

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

   3. Taylor expanded in a around inf 34.2%

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

   4. Taylor expanded in t around 0 14.4%

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

Alternative 23: 11.3% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

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 = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in a around inf 28.7%

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

4. Taylor expanded in t around 0 10.6%

   \[\leadsto \color{blue}{a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024181 
(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)))