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

Percentage Accurate: 95.3% → 98.0%

Time: 19.9s

Alternatives: 29

Speedup: 0.5×

• 35.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 63.8%

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

4. Final simplification 98.9%

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

Alternative 2: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-define 98.0%

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

   3. associate--l+ 98.0%

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

   4. sub-neg 98.0%

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

   5. metadata-eval 98.0%

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

   6. sub-neg 98.0%

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

   7. associate-+l- 98.0%

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

   8. fma-neg 98.0%

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

   9. sub-neg 98.0%

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

   10. metadata-eval 98.0%

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

   11. remove-double-neg 98.0%

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

   12. sub-neg 98.0%

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

   13. metadata-eval 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 3: 35.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-72}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-144}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -4.5e+43)
     t_1
     (if (<= a -1.3e-72)
       (* y b)
       (if (<= a -4.8e-144)
         z
         (if (<= a -3.6e-223) (* y (- z)) (if (<= a 3.5e-10) (* t b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.5e+43) {
		tmp = t_1;
	} else if (a <= -1.3e-72) {
		tmp = y * b;
	} else if (a <= -4.8e-144) {
		tmp = z;
	} else if (a <= -3.6e-223) {
		tmp = y * -z;
	} else if (a <= 3.5e-10) {
		tmp = t * 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 = a * (1.0d0 - t)
    if (a <= (-4.5d+43)) then
        tmp = t_1
    else if (a <= (-1.3d-72)) then
        tmp = y * b
    else if (a <= (-4.8d-144)) then
        tmp = z
    else if (a <= (-3.6d-223)) then
        tmp = y * -z
    else if (a <= 3.5d-10) then
        tmp = t * 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 = a * (1.0 - t);
	double tmp;
	if (a <= -4.5e+43) {
		tmp = t_1;
	} else if (a <= -1.3e-72) {
		tmp = y * b;
	} else if (a <= -4.8e-144) {
		tmp = z;
	} else if (a <= -3.6e-223) {
		tmp = y * -z;
	} else if (a <= 3.5e-10) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -4.5e+43:
		tmp = t_1
	elif a <= -1.3e-72:
		tmp = y * b
	elif a <= -4.8e-144:
		tmp = z
	elif a <= -3.6e-223:
		tmp = y * -z
	elif a <= 3.5e-10:
		tmp = t * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -4.5e+43)
		tmp = t_1;
	elseif (a <= -1.3e-72)
		tmp = Float64(y * b);
	elseif (a <= -4.8e-144)
		tmp = z;
	elseif (a <= -3.6e-223)
		tmp = Float64(y * Float64(-z));
	elseif (a <= 3.5e-10)
		tmp = Float64(t * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -4.5e+43)
		tmp = t_1;
	elseif (a <= -1.3e-72)
		tmp = y * b;
	elseif (a <= -4.8e-144)
		tmp = z;
	elseif (a <= -3.6e-223)
		tmp = y * -z;
	elseif (a <= 3.5e-10)
		tmp = t * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+43], t$95$1, If[LessEqual[a, -1.3e-72], N[(y * b), $MachinePrecision], If[LessEqual[a, -4.8e-144], z, If[LessEqual[a, -3.6e-223], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, 3.5e-10], N[(t * b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.5e43 or 3.4999999999999998e-10 < a

   1. Initial program 94.0%

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

   3. Taylor expanded in a around inf 56.0%

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

   if -4.5e43 < a < -1.29999999999999998e-72

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 56.8%

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

   4. Taylor expanded in y around inf 36.3%

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

   if -1.29999999999999998e-72 < a < -4.79999999999999988e-144

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 40.4%

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

   4. Taylor expanded in y around 0 34.9%

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

   if -4.79999999999999988e-144 < a < -3.6000000000000004e-223

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 60.8%

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

   4. Taylor expanded in y around inf 55.5%

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

      1. mul-1-neg 55.5%

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

   6. Simplified 55.5%

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

   if -3.6000000000000004e-223 < a < 3.4999999999999998e-10

   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 t around inf 34.0%

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

   4. Taylor expanded in b around inf 32.8%

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

      1. *-commutative 32.8%

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

   6. Simplified 32.8%

      \[\leadsto \color{blue}{t \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-72}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-144}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-71}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -9.8e+23)
     t_2
     (if (<= b 2.8e-183)
       t_1
       (if (<= b 1.7e-71)
         (+ x (* z (- 1.0 y)))
         (if (<= b 6.6e+94) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9.8e+23) {
		tmp = t_2;
	} else if (b <= 2.8e-183) {
		tmp = t_1;
	} else if (b <= 1.7e-71) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 6.6e+94) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-9.8d+23)) then
        tmp = t_2
    else if (b <= 2.8d-183) then
        tmp = t_1
    else if (b <= 1.7d-71) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 6.6d+94) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9.8e+23) {
		tmp = t_2;
	} else if (b <= 2.8e-183) {
		tmp = t_1;
	} else if (b <= 1.7e-71) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 6.6e+94) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -9.8e+23:
		tmp = t_2
	elif b <= 2.8e-183:
		tmp = t_1
	elif b <= 1.7e-71:
		tmp = x + (z * (1.0 - y))
	elif b <= 6.6e+94:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -9.8e+23)
		tmp = t_2;
	elseif (b <= 2.8e-183)
		tmp = t_1;
	elseif (b <= 1.7e-71)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 6.6e+94)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -9.8e+23)
		tmp = t_2;
	elseif (b <= 2.8e-183)
		tmp = t_1;
	elseif (b <= 1.7e-71)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 6.6e+94)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.8e+23], t$95$2, If[LessEqual[b, 2.8e-183], t$95$1, If[LessEqual[b, 1.7e-71], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e+94], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.8000000000000006e23 or 6.6e94 < b

   1. Initial program 92.9%

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

   3. Taylor expanded in b around inf 71.3%

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

   if -9.8000000000000006e23 < b < 2.79999999999999985e-183 or 1.70000000000000002e-71 < b < 6.6e94

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 69.7%

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

   4. Taylor expanded in b around 0 59.9%

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

   if 2.79999999999999985e-183 < b < 1.70000000000000002e-71

   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 96.0%

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

   4. Taylor expanded in a around 0 70.6%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-183}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-71}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+94}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-183}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 16200:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -5.5e+24)
     t_1
     (if (<= b 4.5e-183)
       (- x (* t a))
       (if (<= b 1.95e-72)
         (* z (- 1.0 y))
         (if (<= b 16200.0) (* 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 <= -5.5e+24) {
		tmp = t_1;
	} else if (b <= 4.5e-183) {
		tmp = x - (t * a);
	} else if (b <= 1.95e-72) {
		tmp = z * (1.0 - y);
	} else if (b <= 16200.0) {
		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 <= (-5.5d+24)) then
        tmp = t_1
    else if (b <= 4.5d-183) then
        tmp = x - (t * a)
    else if (b <= 1.95d-72) then
        tmp = z * (1.0d0 - y)
    else if (b <= 16200.0d0) 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 <= -5.5e+24) {
		tmp = t_1;
	} else if (b <= 4.5e-183) {
		tmp = x - (t * a);
	} else if (b <= 1.95e-72) {
		tmp = z * (1.0 - y);
	} else if (b <= 16200.0) {
		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 <= -5.5e+24:
		tmp = t_1
	elif b <= 4.5e-183:
		tmp = x - (t * a)
	elif b <= 1.95e-72:
		tmp = z * (1.0 - y)
	elif b <= 16200.0:
		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 <= -5.5e+24)
		tmp = t_1;
	elseif (b <= 4.5e-183)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 1.95e-72)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 16200.0)
		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 <= -5.5e+24)
		tmp = t_1;
	elseif (b <= 4.5e-183)
		tmp = x - (t * a);
	elseif (b <= 1.95e-72)
		tmp = z * (1.0 - y);
	elseif (b <= 16200.0)
		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, -5.5e+24], t$95$1, If[LessEqual[b, 4.5e-183], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e-72], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 16200.0], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.5000000000000002e24 or 16200 < b

   1. Initial program 94.0%

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

   3. Taylor expanded in b around inf 66.2%

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

   if -5.5000000000000002e24 < b < 4.49999999999999971e-183

   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 95.7%

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

   4. Taylor expanded in t around inf 54.7%

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

      1. *-commutative 54.7%

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

   6. Simplified 54.7%

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

   if 4.49999999999999971e-183 < b < 1.95e-72

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 59.0%

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

   if 1.95e-72 < b < 16200

   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 59.0%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-183}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 16200:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot a\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-160}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* t a))) (t_2 (* y (- b z))))
   (if (<= y -5.8e+98)
     t_2
     (if (<= y -1.3e+17)
       t_1
       (if (<= y 2.7e-160) (* t (- b a)) (if (<= y 4e+26) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (t * a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -5.8e+98) {
		tmp = t_2;
	} else if (y <= -1.3e+17) {
		tmp = t_1;
	} else if (y <= 2.7e-160) {
		tmp = t * (b - a);
	} else if (y <= 4e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (t * a)
    t_2 = y * (b - z)
    if (y <= (-5.8d+98)) then
        tmp = t_2
    else if (y <= (-1.3d+17)) then
        tmp = t_1
    else if (y <= 2.7d-160) then
        tmp = t * (b - a)
    else if (y <= 4d+26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (t * a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -5.8e+98) {
		tmp = t_2;
	} else if (y <= -1.3e+17) {
		tmp = t_1;
	} else if (y <= 2.7e-160) {
		tmp = t * (b - a);
	} else if (y <= 4e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (t * a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -5.8e+98:
		tmp = t_2
	elif y <= -1.3e+17:
		tmp = t_1
	elif y <= 2.7e-160:
		tmp = t * (b - a)
	elif y <= 4e+26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(t * a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -5.8e+98)
		tmp = t_2;
	elseif (y <= -1.3e+17)
		tmp = t_1;
	elseif (y <= 2.7e-160)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 4e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (t * a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -5.8e+98)
		tmp = t_2;
	elseif (y <= -1.3e+17)
		tmp = t_1;
	elseif (y <= 2.7e-160)
		tmp = t * (b - a);
	elseif (y <= 4e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+98], t$95$2, If[LessEqual[y, -1.3e+17], t$95$1, If[LessEqual[y, 2.7e-160], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+26], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000002e98 or 4.00000000000000019e26 < y

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 70.2%

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

   if -5.8000000000000002e98 < y < -1.3e17 or 2.7000000000000001e-160 < y < 4.00000000000000019e26

   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 b around 0 79.7%

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

   4. Taylor expanded in t around inf 50.7%

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

      1. *-commutative 50.7%

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

   6. Simplified 50.7%

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

   if -1.3e17 < y < 2.7000000000000001e-160

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 51.4%

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

Alternative 7: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+44} \lor \neg \left(a \leq 1.02 \cdot 10^{-10}\right):\\ \;\;\;\;x + \left(t\_1 + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= a -1.6e+44) (not (<= a 1.02e-10)))
     (+ x (+ t_1 (* a (- 1.0 t))))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((a <= -1.6e+44) || !(a <= 1.02e-10)) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((a <= (-1.6d+44)) .or. (.not. (a <= 1.02d-10))) then
        tmp = x + (t_1 + (a * (1.0d0 - t)))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((a <= -1.6e+44) || !(a <= 1.02e-10)) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (a <= -1.6e+44) or not (a <= 1.02e-10):
		tmp = x + (t_1 + (a * (1.0 - t)))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((a <= -1.6e+44) || !(a <= 1.02e-10))
		tmp = Float64(x + Float64(t_1 + Float64(a * Float64(1.0 - t))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((a <= -1.6e+44) || ~((a <= 1.02e-10)))
		tmp = x + (t_1 + (a * (1.0 - t)));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -1.6e+44], N[Not[LessEqual[a, 1.02e-10]], $MachinePrecision]], N[(x + N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.60000000000000002e44 or 1.01999999999999997e-10 < a

   1. Initial program 94.0%

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

   3. Taylor expanded in b around 0 85.8%

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

   if -1.60000000000000002e44 < a < 1.01999999999999997e-10

   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 a around 0 96.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+44} \lor \neg \left(a \leq 1.02 \cdot 10^{-10}\right):\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(\left(1 + \frac{x}{a}\right) - \left(t + \frac{z \cdot \left(y + -1\right)}{a}\right)\right)\\ \mathbf{elif}\;a \leq 10^{-10}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= a -1.75e+42)
     (* a (- (+ 1.0 (/ x a)) (+ t (/ (* z (+ y -1.0)) a))))
     (if (<= a 1e-10)
       (+ (+ x (* b (- (+ y t) 2.0))) t_1)
       (+ x (+ t_1 (* a (- 1.0 t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (a <= -1.75e+42) {
		tmp = a * ((1.0 + (x / a)) - (t + ((z * (y + -1.0)) / a)));
	} else if (a <= 1e-10) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (a <= (-1.75d+42)) then
        tmp = a * ((1.0d0 + (x / a)) - (t + ((z * (y + (-1.0d0))) / a)))
    else if (a <= 1d-10) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + (t_1 + (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 t_1 = z * (1.0 - y);
	double tmp;
	if (a <= -1.75e+42) {
		tmp = a * ((1.0 + (x / a)) - (t + ((z * (y + -1.0)) / a)));
	} else if (a <= 1e-10) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if a <= -1.75e+42:
		tmp = a * ((1.0 + (x / a)) - (t + ((z * (y + -1.0)) / a)))
	elif a <= 1e-10:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + (t_1 + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (a <= -1.75e+42)
		tmp = Float64(a * Float64(Float64(1.0 + Float64(x / a)) - Float64(t + Float64(Float64(z * Float64(y + -1.0)) / a))));
	elseif (a <= 1e-10)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(t_1 + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (a <= -1.75e+42)
		tmp = a * ((1.0 + (x / a)) - (t + ((z * (y + -1.0)) / a)));
	elseif (a <= 1e-10)
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + (t_1 + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+42], N[(a * N[(N[(1.0 + N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(t + N[(N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-10], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.75000000000000012e42

   1. Initial program 96.3%

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

   3. Taylor expanded in a around inf 96.3%

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

   4. Taylor expanded in b around 0 87.6%

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

   if -1.75000000000000012e42 < a < 1.00000000000000004e-10

   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 a around 0 96.4%

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

   if 1.00000000000000004e-10 < a

   1. Initial program 92.1%

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

   3. Taylor expanded in b around 0 85.9%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(\left(1 + \frac{x}{a}\right) - \left(t + \frac{z \cdot \left(y + -1\right)}{a}\right)\right)\\ \mathbf{elif}\;a \leq 10^{-10}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+162}:\\ \;\;\;\;x + \left(t\_1 - t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+103}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 + t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* a (- 1.0 t))))
   (if (<= z -2.05e+162)
     (+ x (- t_1 (* t a)))
     (if (<= z 1.55e+103)
       (+ (+ x (* b (- (+ y t) 2.0))) t_2)
       (+ x (+ t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (z <= -2.05e+162) {
		tmp = x + (t_1 - (t * a));
	} else if (z <= 1.55e+103) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_2;
	} else {
		tmp = x + (t_1 + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = a * (1.0d0 - t)
    if (z <= (-2.05d+162)) then
        tmp = x + (t_1 - (t * a))
    else if (z <= 1.55d+103) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_2
    else
        tmp = x + (t_1 + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (z <= -2.05e+162) {
		tmp = x + (t_1 - (t * a));
	} else if (z <= 1.55e+103) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_2;
	} else {
		tmp = x + (t_1 + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = a * (1.0 - t)
	tmp = 0
	if z <= -2.05e+162:
		tmp = x + (t_1 - (t * a))
	elif z <= 1.55e+103:
		tmp = (x + (b * ((y + t) - 2.0))) + t_2
	else:
		tmp = x + (t_1 + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (z <= -2.05e+162)
		tmp = Float64(x + Float64(t_1 - Float64(t * a)));
	elseif (z <= 1.55e+103)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_2);
	else
		tmp = Float64(x + Float64(t_1 + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (z <= -2.05e+162)
		tmp = x + (t_1 - (t * a));
	elseif (z <= 1.55e+103)
		tmp = (x + (b * ((y + t) - 2.0))) + t_2;
	else
		tmp = x + (t_1 + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+162], N[(x + N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+103], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(x + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e162

   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 b around 0 91.4%

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

   4. Taylor expanded in t around inf 91.4%

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

      1. *-commutative 91.4%

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

   6. Simplified 91.4%

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

   if -2.05e162 < z < 1.5500000000000001e103

   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 z around 0 91.2%

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

   if 1.5500000000000001e103 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in b around 0 91.4%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+162}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+103}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 26.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-305}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+109}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= z -2.8e-51)
     t_1
     (if (<= z 2.1e-305)
       (* y b)
       (if (<= z 5.8e-57) x (if (<= z 5.2e+109) (* t b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (z <= -2.8e-51) {
		tmp = t_1;
	} else if (z <= 2.1e-305) {
		tmp = y * b;
	} else if (z <= 5.8e-57) {
		tmp = x;
	} else if (z <= 5.2e+109) {
		tmp = t * 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 = y * -z
    if (z <= (-2.8d-51)) then
        tmp = t_1
    else if (z <= 2.1d-305) then
        tmp = y * b
    else if (z <= 5.8d-57) then
        tmp = x
    else if (z <= 5.2d+109) then
        tmp = t * 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 = y * -z;
	double tmp;
	if (z <= -2.8e-51) {
		tmp = t_1;
	} else if (z <= 2.1e-305) {
		tmp = y * b;
	} else if (z <= 5.8e-57) {
		tmp = x;
	} else if (z <= 5.2e+109) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if z <= -2.8e-51:
		tmp = t_1
	elif z <= 2.1e-305:
		tmp = y * b
	elif z <= 5.8e-57:
		tmp = x
	elif z <= 5.2e+109:
		tmp = t * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -2.8e-51)
		tmp = t_1;
	elseif (z <= 2.1e-305)
		tmp = Float64(y * b);
	elseif (z <= 5.8e-57)
		tmp = x;
	elseif (z <= 5.2e+109)
		tmp = Float64(t * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (z <= -2.8e-51)
		tmp = t_1;
	elseif (z <= 2.1e-305)
		tmp = y * b;
	elseif (z <= 5.8e-57)
		tmp = x;
	elseif (z <= 5.2e+109)
		tmp = t * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.8e-51], t$95$1, If[LessEqual[z, 2.1e-305], N[(y * b), $MachinePrecision], If[LessEqual[z, 5.8e-57], x, If[LessEqual[z, 5.2e+109], N[(t * b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8e-51 or 5.1999999999999997e109 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf 57.7%

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

   4. Taylor expanded in y around inf 41.0%

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

      1. mul-1-neg 41.0%

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

   6. Simplified 41.0%

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

   if -2.8e-51 < z < 2.1e-305

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 52.2%

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

   4. Taylor expanded in y around inf 35.8%

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

   if 2.1e-305 < z < 5.8000000000000005e-57

   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 x around inf 33.3%

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

   if 5.8000000000000005e-57 < z < 5.1999999999999997e109

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf 52.3%

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

   4. Taylor expanded in b around inf 34.9%

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

      1. *-commutative 34.9%

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

   6. Simplified 34.9%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-305}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+109}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-82}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -1.9e+16)
     t_1
     (if (<= b -1.6e-82)
       (+ x (+ a (* z (- 1.0 y))))
       (if (<= b 1.05e+48) (- x (- (* a (+ t -1.0)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.9e+16) {
		tmp = t_1;
	} else if (b <= -1.6e-82) {
		tmp = x + (a + (z * (1.0 - y)));
	} else if (b <= 1.05e+48) {
		tmp = x - ((a * (t + -1.0)) - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-1.9d+16)) then
        tmp = t_1
    else if (b <= (-1.6d-82)) then
        tmp = x + (a + (z * (1.0d0 - y)))
    else if (b <= 1.05d+48) then
        tmp = x - ((a * (t + (-1.0d0))) - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.9e+16) {
		tmp = t_1;
	} else if (b <= -1.6e-82) {
		tmp = x + (a + (z * (1.0 - y)));
	} else if (b <= 1.05e+48) {
		tmp = x - ((a * (t + -1.0)) - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -1.9e+16:
		tmp = t_1
	elif b <= -1.6e-82:
		tmp = x + (a + (z * (1.0 - y)))
	elif b <= 1.05e+48:
		tmp = x - ((a * (t + -1.0)) - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -1.9e+16)
		tmp = t_1;
	elseif (b <= -1.6e-82)
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	elseif (b <= 1.05e+48)
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -1.9e+16)
		tmp = t_1;
	elseif (b <= -1.6e-82)
		tmp = x + (a + (z * (1.0 - y)));
	elseif (b <= 1.05e+48)
		tmp = x - ((a * (t + -1.0)) - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+16], t$95$1, If[LessEqual[b, -1.6e-82], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+48], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9e16 or 1.0499999999999999e48 < b

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 77.3%

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

   4. Taylor expanded in x around inf 75.2%

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

   if -1.9e16 < b < -1.6000000000000001e-82

   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 84.9%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. +-commutative 71.0%

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

      2. sub-neg 71.0%

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

      3. metadata-eval 71.0%

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

      4. mul-1-neg 71.0%

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

      5. unsub-neg 71.0%

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

      6. +-commutative 71.0%

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

   6. Simplified 71.0%

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

   if -1.6000000000000001e-82 < b < 1.0499999999999999e48

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 93.3%

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

   4. Taylor expanded in y around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. sub-neg 71.1%

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

      3. metadata-eval 71.1%

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

      4. neg-mul-1 71.1%

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

      5. unsub-neg 71.1%

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

      6. +-commutative 71.1%

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

   6. Simplified 71.1%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+16}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-82}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.9 \cdot 10^{+23} \lor \neg \left(b \leq 1.05 \cdot 10^{+48}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.9e+23) (not (<= b 1.05e+48)))
   (+ (* b (- (+ y t) 2.0)) (* a (- 1.0 t)))
   (+ x (- (* z (- 1.0 y)) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.9e+23) || !(b <= 1.05e+48)) {
		tmp = (b * ((y + t) - 2.0)) + (a * (1.0 - t));
	} else {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5.9d+23)) .or. (.not. (b <= 1.05d+48))) then
        tmp = (b * ((y + t) - 2.0d0)) + (a * (1.0d0 - t))
    else
        tmp = x + ((z * (1.0d0 - y)) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.9e+23) || !(b <= 1.05e+48)) {
		tmp = (b * ((y + t) - 2.0)) + (a * (1.0 - t));
	} else {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.9e+23) or not (b <= 1.05e+48):
		tmp = (b * ((y + t) - 2.0)) + (a * (1.0 - t))
	else:
		tmp = x + ((z * (1.0 - y)) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.9e+23) || !(b <= 1.05e+48))
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.9e+23) || ~((b <= 1.05e+48)))
		tmp = (b * ((y + t) - 2.0)) + (a * (1.0 - t));
	else
		tmp = x + ((z * (1.0 - y)) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.9e+23], N[Not[LessEqual[b, 1.05e+48]], $MachinePrecision]], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.89999999999999987e23 or 1.0499999999999999e48 < b

   1. Initial program 93.4%

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

   3. Taylor expanded in a around inf 77.0%

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

   4. Taylor expanded in a around inf 77.4%

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

   if -5.89999999999999987e23 < b < 1.0499999999999999e48

   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 92.2%

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

   4. Taylor expanded in t around inf 82.6%

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

      1. *-commutative 82.6%

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

   6. Simplified 82.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.9 \cdot 10^{+23} \lor \neg \left(b \leq 1.05 \cdot 10^{+48}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+24}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+101}:\\ \;\;\;\;x + \left(t\_1 + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -4.6e+24)
     (+ t_2 t_1)
     (if (<= b 5.2e+101) (+ x (+ t_1 (* a (- 1.0 t)))) (+ x t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.6e+24) {
		tmp = t_2 + t_1;
	} else if (b <= 5.2e+101) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-4.6d+24)) then
        tmp = t_2 + t_1
    else if (b <= 5.2d+101) then
        tmp = x + (t_1 + (a * (1.0d0 - t)))
    else
        tmp = x + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.6e+24) {
		tmp = t_2 + t_1;
	} else if (b <= 5.2e+101) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -4.6e+24:
		tmp = t_2 + t_1
	elif b <= 5.2e+101:
		tmp = x + (t_1 + (a * (1.0 - t)))
	else:
		tmp = x + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -4.6e+24)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 5.2e+101)
		tmp = Float64(x + Float64(t_1 + Float64(a * Float64(1.0 - t))));
	else
		tmp = Float64(x + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -4.6e+24)
		tmp = t_2 + t_1;
	elseif (b <= 5.2e+101)
		tmp = x + (t_1 + (a * (1.0 - t)));
	else
		tmp = x + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.6e+24], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 5.2e+101], N[(x + N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.5999999999999998e24

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf 79.8%

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

   4. Taylor expanded in z around -inf 77.8%

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

      1. mul-1-neg 77.8%

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

      2. sub-neg 77.8%

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

      3. metadata-eval 77.8%

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

      4. distribute-rgt-neg-in 77.8%

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

      5. mul-1-neg 77.8%

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

      6. distribute-lft-in 77.8%

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

      7. metadata-eval 77.8%

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

      8. +-commutative 77.8%

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

      9. mul-1-neg 77.8%

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

      10. unsub-neg 77.8%

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

   6. Simplified 77.8%

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

   if -4.5999999999999998e24 < b < 5.2e101

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 90.1%

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

   if 5.2e101 < b

   1. Initial program 90.0%

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

   3. Taylor expanded in a around inf 74.5%

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

   4. Taylor expanded in x around inf 85.8%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+101}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -5.6 \cdot 10^{+23}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+47}:\\ \;\;\;\;x + \left(t\_1 - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -5.6e+23)
     (+ t_2 t_1)
     (if (<= b 6.8e+47) (+ x (- t_1 (* t a))) (+ t_2 (* a (- 1.0 t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -5.6e+23) {
		tmp = t_2 + t_1;
	} else if (b <= 6.8e+47) {
		tmp = x + (t_1 - (t * a));
	} else {
		tmp = t_2 + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-5.6d+23)) then
        tmp = t_2 + t_1
    else if (b <= 6.8d+47) then
        tmp = x + (t_1 - (t * a))
    else
        tmp = t_2 + (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 t_1 = z * (1.0 - y);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -5.6e+23) {
		tmp = t_2 + t_1;
	} else if (b <= 6.8e+47) {
		tmp = x + (t_1 - (t * a));
	} else {
		tmp = t_2 + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -5.6e+23:
		tmp = t_2 + t_1
	elif b <= 6.8e+47:
		tmp = x + (t_1 - (t * a))
	else:
		tmp = t_2 + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -5.6e+23)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 6.8e+47)
		tmp = Float64(x + Float64(t_1 - Float64(t * a)));
	else
		tmp = Float64(t_2 + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -5.6e+23)
		tmp = t_2 + t_1;
	elseif (b <= 6.8e+47)
		tmp = x + (t_1 - (t * a));
	else
		tmp = t_2 + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.6e+23], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 6.8e+47], N[(x + N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.6e23

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf 79.8%

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

   4. Taylor expanded in z around -inf 77.8%

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

      1. mul-1-neg 77.8%

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

      2. sub-neg 77.8%

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

      3. metadata-eval 77.8%

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

      4. distribute-rgt-neg-in 77.8%

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

      5. mul-1-neg 77.8%

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

      6. distribute-lft-in 77.8%

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

      7. metadata-eval 77.8%

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

      8. +-commutative 77.8%

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

      9. mul-1-neg 77.8%

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

      10. unsub-neg 77.8%

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

   6. Simplified 77.8%

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

   if -5.6e23 < b < 6.7999999999999996e47

   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 92.2%

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

   4. Taylor expanded in t around inf 82.6%

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

      1. *-commutative 82.6%

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

   6. Simplified 82.6%

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

   if 6.7999999999999996e47 < 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 a around inf 74.0%

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

   4. Taylor expanded in a around inf 79.1%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+47}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+18}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+29}:\\ \;\;\;\;z + \left(t + -2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.55e+99)
     t_1
     (if (<= y -1.8e+18)
       (- x (* t a))
       (if (<= y 5e+29) (+ z (* (+ t -2.0) b)) 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 <= -2.55e+99) {
		tmp = t_1;
	} else if (y <= -1.8e+18) {
		tmp = x - (t * a);
	} else if (y <= 5e+29) {
		tmp = z + ((t + -2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-2.55d+99)) then
        tmp = t_1
    else if (y <= (-1.8d+18)) then
        tmp = x - (t * a)
    else if (y <= 5d+29) then
        tmp = z + ((t + (-2.0d0)) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.55e+99) {
		tmp = t_1;
	} else if (y <= -1.8e+18) {
		tmp = x - (t * a);
	} else if (y <= 5e+29) {
		tmp = z + ((t + -2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2.55e+99:
		tmp = t_1
	elif y <= -1.8e+18:
		tmp = x - (t * a)
	elif y <= 5e+29:
		tmp = z + ((t + -2.0) * b)
	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 <= -2.55e+99)
		tmp = t_1;
	elseif (y <= -1.8e+18)
		tmp = Float64(x - Float64(t * a));
	elseif (y <= 5e+29)
		tmp = Float64(z + Float64(Float64(t + -2.0) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.55e+99)
		tmp = t_1;
	elseif (y <= -1.8e+18)
		tmp = x - (t * a);
	elseif (y <= 5e+29)
		tmp = z + ((t + -2.0) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+99], t$95$1, If[LessEqual[y, -1.8e+18], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+29], N[(z + N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.54999999999999976e99 or 5.0000000000000001e29 < y

   1. Initial program 94.3%

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

   3. Taylor expanded in y around inf 70.8%

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

   if -2.54999999999999976e99 < y < -1.8e18

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 86.7%

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

   4. Taylor expanded in t around inf 64.5%

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

      1. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   if -1.8e18 < y < 5.0000000000000001e29

   1. Initial program 98.4%

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

   3. Taylor expanded in a around inf 79.5%

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

   4. Taylor expanded in z around -inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. sub-neg 54.5%

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

      3. metadata-eval 54.5%

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

      4. distribute-rgt-neg-in 54.5%

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

      5. mul-1-neg 54.5%

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

      6. distribute-lft-in 54.5%

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

      7. metadata-eval 54.5%

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

      8. +-commutative 54.5%

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

      9. mul-1-neg 54.5%

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

      10. unsub-neg 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in y around 0 52.4%

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

      1. +-commutative 52.4%

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

      2. sub-neg 52.4%

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

      3. metadata-eval 52.4%

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

   9. Simplified 52.4%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+18}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+29}:\\ \;\;\;\;z + \left(t + -2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+24} \lor \neg \left(b \leq 1.25 \cdot 10^{+48}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6e+24) (not (<= b 1.25e+48)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (- (* z (- 1.0 y)) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6e+24) || !(b <= 1.25e+48)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6d+24)) .or. (.not. (b <= 1.25d+48))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((z * (1.0d0 - y)) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6e+24) || !(b <= 1.25e+48)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6e+24) or not (b <= 1.25e+48):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((z * (1.0 - y)) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6e+24) || !(b <= 1.25e+48))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6e+24) || ~((b <= 1.25e+48)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((z * (1.0 - y)) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6e+24], N[Not[LessEqual[b, 1.25e+48]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.9999999999999999e24 or 1.24999999999999993e48 < b

   1. Initial program 93.4%

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

   3. Taylor expanded in a around inf 77.0%

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

   4. Taylor expanded in x around inf 75.6%

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

   if -5.9999999999999999e24 < b < 1.24999999999999993e48

   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 92.2%

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

   4. Taylor expanded in t around inf 82.6%

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

      1. *-commutative 82.6%

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

   6. Simplified 82.6%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+24} \lor \neg \left(b \leq 1.25 \cdot 10^{+48}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-23}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -4.6e+43)
     t_1
     (if (<= a -7.8e-23)
       (* b (- y 2.0))
       (if (<= a 1.7e-10) (* b (- t 2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.6e+43) {
		tmp = t_1;
	} else if (a <= -7.8e-23) {
		tmp = b * (y - 2.0);
	} else if (a <= 1.7e-10) {
		tmp = b * (t - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-4.6d+43)) then
        tmp = t_1
    else if (a <= (-7.8d-23)) then
        tmp = b * (y - 2.0d0)
    else if (a <= 1.7d-10) then
        tmp = b * (t - 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.6e+43) {
		tmp = t_1;
	} else if (a <= -7.8e-23) {
		tmp = b * (y - 2.0);
	} else if (a <= 1.7e-10) {
		tmp = b * (t - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -4.6e+43:
		tmp = t_1
	elif a <= -7.8e-23:
		tmp = b * (y - 2.0)
	elif a <= 1.7e-10:
		tmp = b * (t - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -4.6e+43)
		tmp = t_1;
	elseif (a <= -7.8e-23)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (a <= 1.7e-10)
		tmp = Float64(b * Float64(t - 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -4.6e+43)
		tmp = t_1;
	elseif (a <= -7.8e-23)
		tmp = b * (y - 2.0);
	elseif (a <= 1.7e-10)
		tmp = b * (t - 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e+43], t$95$1, If[LessEqual[a, -7.8e-23], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-10], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.6000000000000005e43 or 1.70000000000000007e-10 < a

   1. Initial program 94.0%

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

   3. Taylor expanded in a around inf 56.0%

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

   if -4.6000000000000005e43 < a < -7.8e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 51.0%

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

   4. Taylor expanded in t around 0 45.3%

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

   if -7.8e-23 < a < 1.70000000000000007e-10

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. *-commutative 66.9%

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

      3. distribute-rgt-neg-in 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in y around 0 35.7%

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

Alternative 18: 39.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -4.5e+41)
     t_1
     (if (<= a -1.05e-21) (* y b) (if (<= a 3.5e-10) (* b (- t 2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.5e+41) {
		tmp = t_1;
	} else if (a <= -1.05e-21) {
		tmp = y * b;
	} else if (a <= 3.5e-10) {
		tmp = b * (t - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-4.5d+41)) then
        tmp = t_1
    else if (a <= (-1.05d-21)) then
        tmp = y * b
    else if (a <= 3.5d-10) then
        tmp = b * (t - 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.5e+41) {
		tmp = t_1;
	} else if (a <= -1.05e-21) {
		tmp = y * b;
	} else if (a <= 3.5e-10) {
		tmp = b * (t - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -4.5e+41:
		tmp = t_1
	elif a <= -1.05e-21:
		tmp = y * b
	elif a <= 3.5e-10:
		tmp = b * (t - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -4.5e+41)
		tmp = t_1;
	elseif (a <= -1.05e-21)
		tmp = Float64(y * b);
	elseif (a <= 3.5e-10)
		tmp = Float64(b * Float64(t - 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -4.5e+41)
		tmp = t_1;
	elseif (a <= -1.05e-21)
		tmp = y * b;
	elseif (a <= 3.5e-10)
		tmp = b * (t - 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+41], t$95$1, If[LessEqual[a, -1.05e-21], N[(y * b), $MachinePrecision], If[LessEqual[a, 3.5e-10], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5000000000000001e41 or 3.4999999999999998e-10 < a

   1. Initial program 94.0%

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

   3. Taylor expanded in a around inf 56.0%

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

   if -4.5000000000000001e41 < a < -1.05000000000000006e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 51.0%

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

   4. Taylor expanded in y around inf 40.0%

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

   if -1.05000000000000006e-21 < a < 3.4999999999999998e-10

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. *-commutative 66.9%

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

      3. distribute-rgt-neg-in 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in y around 0 35.7%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+24} \lor \neg \left(b \leq 1.2 \cdot 10^{+48}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.2e+24) (not (<= b 1.2e+48)))
   (+ x (* b (- (+ y t) 2.0)))
   (- x (- (* a (+ t -1.0)) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.2e+24) || !(b <= 1.2e+48)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x - ((a * (t + -1.0)) - 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 ((b <= (-4.2d+24)) .or. (.not. (b <= 1.2d+48))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x - ((a * (t + (-1.0d0))) - 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 ((b <= -4.2e+24) || !(b <= 1.2e+48)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x - ((a * (t + -1.0)) - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.2e+24) or not (b <= 1.2e+48):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x - ((a * (t + -1.0)) - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.2e+24) || !(b <= 1.2e+48))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.2e+24) || ~((b <= 1.2e+48)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x - ((a * (t + -1.0)) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.2e+24], N[Not[LessEqual[b, 1.2e+48]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.2000000000000003e24 or 1.2000000000000001e48 < b

   1. Initial program 93.4%

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

   3. Taylor expanded in a around inf 77.0%

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

   4. Taylor expanded in x around inf 75.6%

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

   if -4.2000000000000003e24 < b < 1.2000000000000001e48

   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 92.2%

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

   4. Taylor expanded in y around 0 67.7%

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

      1. +-commutative 67.7%

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

      2. sub-neg 67.7%

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

      3. metadata-eval 67.7%

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

      4. neg-mul-1 67.7%

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

      5. unsub-neg 67.7%

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

      6. +-commutative 67.7%

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

   6. Simplified 67.7%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+24} \lor \neg \left(b \leq 1.2 \cdot 10^{+48}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 63.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+162} \lor \neg \left(z \leq 10^{+110}\right):\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.9e+162) (not (<= z 1e+110)))
   (+ x (* z (- 1.0 y)))
   (+ x (* b (- (+ y t) 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e+162) || !(z <= 1e+110)) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = x + (b * ((y + t) - 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.9d+162)) .or. (.not. (z <= 1d+110))) then
        tmp = x + (z * (1.0d0 - y))
    else
        tmp = x + (b * ((y + t) - 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e+162) || !(z <= 1e+110)) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = x + (b * ((y + t) - 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.9e+162) or not (z <= 1e+110):
		tmp = x + (z * (1.0 - y))
	else:
		tmp = x + (b * ((y + t) - 2.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.9e+162) || !(z <= 1e+110))
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.9e+162) || ~((z <= 1e+110)))
		tmp = x + (z * (1.0 - y));
	else
		tmp = x + (b * ((y + t) - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.9e+162], N[Not[LessEqual[z, 1e+110]], $MachinePrecision]], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000012e162 or 1e110 < z

   1. Initial program 93.7%

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

   3. Taylor expanded in b around 0 92.6%

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

   4. Taylor expanded in a around 0 76.6%

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

   if -1.90000000000000012e162 < z < 1e110

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf 82.8%

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

   4. Taylor expanded in x around inf 64.7%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+162} \lor \neg \left(z \leq 10^{+110}\right):\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 27.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+33}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+220}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -2.4e+75)
     t_1
     (if (<= t 4.2e+33) (* y b) (if (<= t 5e+220) (* t 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 <= -2.4e+75) {
		tmp = t_1;
	} else if (t <= 4.2e+33) {
		tmp = y * b;
	} else if (t <= 5e+220) {
		tmp = t * 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 <= (-2.4d+75)) then
        tmp = t_1
    else if (t <= 4.2d+33) then
        tmp = y * b
    else if (t <= 5d+220) then
        tmp = t * 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 <= -2.4e+75) {
		tmp = t_1;
	} else if (t <= 4.2e+33) {
		tmp = y * b;
	} else if (t <= 5e+220) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -2.4e+75:
		tmp = t_1
	elif t <= 4.2e+33:
		tmp = y * b
	elif t <= 5e+220:
		tmp = t * 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 <= -2.4e+75)
		tmp = t_1;
	elseif (t <= 4.2e+33)
		tmp = Float64(y * b);
	elseif (t <= 5e+220)
		tmp = Float64(t * 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 <= -2.4e+75)
		tmp = t_1;
	elseif (t <= 4.2e+33)
		tmp = y * b;
	elseif (t <= 5e+220)
		tmp = t * 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, -2.4e+75], t$95$1, If[LessEqual[t, 4.2e+33], N[(y * b), $MachinePrecision], If[LessEqual[t, 5e+220], N[(t * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4e75 or 5.0000000000000002e220 < t

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf 74.7%

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

   4. Taylor expanded in b around 0 49.8%

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

      1. neg-mul-1 49.8%

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

   6. Simplified 49.8%

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

   if -2.4e75 < t < 4.2000000000000001e33

   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 inf 36.7%

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

   4. Taylor expanded in y around inf 27.0%

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

   if 4.2000000000000001e33 < t < 5.0000000000000002e220

   1. Initial program 95.7%

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

   3. Taylor expanded in t around inf 57.8%

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

   4. Taylor expanded in b around inf 40.7%

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

      1. *-commutative 40.7%

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

   6. Simplified 40.7%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+33}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+220}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 61.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+23} \lor \neg \left(b \leq 1.4 \cdot 10^{+97}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.8e+23) (not (<= b 1.4e+97)))
   (* 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 <= -9.8e+23) || !(b <= 1.4e+97)) {
		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 <= (-9.8d+23)) .or. (.not. (b <= 1.4d+97))) 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 <= -9.8e+23) || !(b <= 1.4e+97)) {
		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 <= -9.8e+23) or not (b <= 1.4e+97):
		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 <= -9.8e+23) || !(b <= 1.4e+97))
		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 <= -9.8e+23) || ~((b <= 1.4e+97)))
		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, -9.8e+23], N[Not[LessEqual[b, 1.4e+97]], $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 < -9.8000000000000006e23 or 1.4e97 < b

   1. Initial program 92.9%

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

   3. Taylor expanded in b around inf 71.3%

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

   if -9.8000000000000006e23 < b < 1.4e97

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 64.7%

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

   4. Taylor expanded in b around 0 55.9%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+23} \lor \neg \left(b \leq 1.4 \cdot 10^{+97}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 50.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+68} \lor \neg \left(t \leq 1.02 \cdot 10^{+35}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.4e+68) (not (<= t 1.02e+35))) (* t (- b a)) (* y (- b z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.4e+68) || !(t <= 1.02e+35)) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - 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 ((t <= (-1.4d+68)) .or. (.not. (t <= 1.02d+35))) then
        tmp = t * (b - a)
    else
        tmp = y * (b - 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 ((t <= -1.4e+68) || !(t <= 1.02e+35)) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.4e+68) or not (t <= 1.02e+35):
		tmp = t * (b - a)
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.4e+68) || !(t <= 1.02e+35))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.4e+68) || ~((t <= 1.02e+35)))
		tmp = t * (b - a);
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.4e+68], N[Not[LessEqual[t, 1.02e+35]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e68 or 1.02000000000000007e35 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf 68.8%

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

   if -1.4e68 < t < 1.02000000000000007e35

   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 y around inf 43.4%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+68} \lor \neg \left(t \leq 1.02 \cdot 10^{+35}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 46.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+66} \lor \neg \left(t \leq 9.6 \cdot 10^{+29}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.45e+66) (not (<= t 9.6e+29))) (* t (- b a)) (* b (- y 2.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.45e+66) || !(t <= 9.6e+29)) {
		tmp = t * (b - a);
	} else {
		tmp = b * (y - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.45d+66)) .or. (.not. (t <= 9.6d+29))) then
        tmp = t * (b - a)
    else
        tmp = b * (y - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.45e+66) || !(t <= 9.6e+29)) {
		tmp = t * (b - a);
	} else {
		tmp = b * (y - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.45e+66) or not (t <= 9.6e+29):
		tmp = t * (b - a)
	else:
		tmp = b * (y - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.45e+66) || !(t <= 9.6e+29))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(b * Float64(y - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.45e+66) || ~((t <= 9.6e+29)))
		tmp = t * (b - a);
	else
		tmp = b * (y - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.45e+66], N[Not[LessEqual[t, 9.6e+29]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.44999999999999993e66 or 9.6000000000000003e29 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf 68.5%

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

   if -1.44999999999999993e66 < t < 9.6000000000000003e29

   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 inf 36.5%

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

   4. Taylor expanded in t around 0 35.8%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+66} \lor \neg \left(t \leq 9.6 \cdot 10^{+29}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 27.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+68} \lor \neg \left(t \leq 4.4 \cdot 10^{+33}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.5e+68) (not (<= t 4.4e+33))) (* t b) (* y b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.5e+68) || !(t <= 4.4e+33)) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.5d+68)) .or. (.not. (t <= 4.4d+33))) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.5e+68) || !(t <= 4.4e+33)) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.5e+68) or not (t <= 4.4e+33):
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.5e+68) || !(t <= 4.4e+33))
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.5e+68) || ~((t <= 4.4e+33)))
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.5e+68], N[Not[LessEqual[t, 4.4e+33]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5000000000000003e68 or 4.39999999999999988e33 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf 68.2%

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

   4. Taylor expanded in b around inf 36.8%

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

      1. *-commutative 36.8%

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

   6. Simplified 36.8%

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

   if -4.5000000000000003e68 < t < 4.39999999999999988e33

   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 inf 36.2%

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

   4. Taylor expanded in y around inf 27.2%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+68} \lor \neg \left(t \leq 4.4 \cdot 10^{+33}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 27.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+116} \lor \neg \left(y \leq 1.5 \cdot 10^{+83}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e+116) (not (<= y 1.5e+83))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+116) || !(y <= 1.5e+83)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.15d+116)) .or. (.not. (y <= 1.5d+83))) then
        tmp = y * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+116) || !(y <= 1.5e+83)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.15e+116) or not (y <= 1.5e+83):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e+116) || !(y <= 1.5e+83))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.15e+116) || ~((y <= 1.5e+83)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e+116], N[Not[LessEqual[y, 1.5e+83]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.14999999999999997e116 or 1.5e83 < y

   1. Initial program 93.3%

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

   3. Taylor expanded in b around inf 47.3%

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

   4. Taylor expanded in y around inf 41.5%

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

   if -1.14999999999999997e116 < y < 1.5e83

   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 x around inf 19.8%

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

4. Final simplification 27.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+116} \lor \neg \left(y \leq 1.5 \cdot 10^{+83}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 21.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+162}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.55e+162) z (if (<= z 4.6e+57) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.55e+162) {
		tmp = z;
	} else if (z <= 4.6e+57) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.55d+162)) then
        tmp = z
    else if (z <= 4.6d+57) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.55e+162) {
		tmp = z;
	} else if (z <= 4.6e+57) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.55e+162:
		tmp = z
	elif z <= 4.6e+57:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.55e+162)
		tmp = z;
	elseif (z <= 4.6e+57)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.55e+162)
		tmp = z;
	elseif (z <= 4.6e+57)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.55e+162], z, If[LessEqual[z, 4.6e+57], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5499999999999999e162 or 4.5999999999999998e57 < z

   1. Initial program 93.3%

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

   3. Taylor expanded in z around inf 67.5%

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

   4. Taylor expanded in y around 0 26.0%

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

   if -2.5499999999999999e162 < z < 4.5999999999999998e57

   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 x around inf 19.5%

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

Alternative 28: 18.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= a 7.5e+126) x a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 7.5e+126) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 7.5d+126) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 7.5e+126) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 7.5e+126:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 7.5e+126)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 7.5e+126)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 7.5e+126], x, a]

Derivation

1. Split input into 2 regimes

2. if a < 7.5000000000000006e126

   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 x around inf 16.1%

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

   if 7.5000000000000006e126 < a

   1. Initial program 91.2%

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

   3. Taylor expanded in a around inf 68.1%

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

   4. Taylor expanded in t around 0 38.4%

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

Alternative 29: 11.1% 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 96.9%

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

3. Taylor expanded in a around inf 28.1%

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

4. Taylor expanded in t around 0 10.0%

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

Reproduce

herbie shell --seed 2024146 
(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)))