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

Percentage Accurate: 94.9% → 97.8%

Time: 16.4s

Alternatives: 22

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: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.5× speedup

Math

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

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 64.5%

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

4. Final simplification 98.0%

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

Alternative 2: 97.4% 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 94.5%

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

   1. +-commutative 94.5%

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

   2. fma-define 96.1%

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

   3. associate--l+ 96.1%

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

   4. sub-neg 96.1%

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

   5. metadata-eval 96.1%

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

   6. sub-neg 96.1%

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

   7. associate-+l- 96.1%

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

   8. fma-neg 96.8%

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

   9. sub-neg 96.8%

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

   10. metadata-eval 96.8%

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

   11. remove-double-neg 96.8%

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

   12. sub-neg 96.8%

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

   13. metadata-eval 96.8%

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

3. Simplified 96.8%

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

5. Final simplification 96.8%

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

Alternative 3: 47.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.66 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-262}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-84}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -1.66e-15)
     t_2
     (if (<= t -1.45e-229)
       t_1
       (if (<= t 1.18e-262)
         (+ x z)
         (if (<= t 4.6e-164)
           t_1
           (if (<= t 2.4e-84)
             (+ x z)
             (if (<= t 1.52e-34)
               t_1
               (if (<= t 1.65e+17) (* y (- z)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.66e-15) {
		tmp = t_2;
	} else if (t <= -1.45e-229) {
		tmp = t_1;
	} else if (t <= 1.18e-262) {
		tmp = x + z;
	} else if (t <= 4.6e-164) {
		tmp = t_1;
	} else if (t <= 2.4e-84) {
		tmp = x + z;
	} else if (t <= 1.52e-34) {
		tmp = t_1;
	} else if (t <= 1.65e+17) {
		tmp = y * -z;
	} 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 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-1.66d-15)) then
        tmp = t_2
    else if (t <= (-1.45d-229)) then
        tmp = t_1
    else if (t <= 1.18d-262) then
        tmp = x + z
    else if (t <= 4.6d-164) then
        tmp = t_1
    else if (t <= 2.4d-84) then
        tmp = x + z
    else if (t <= 1.52d-34) then
        tmp = t_1
    else if (t <= 1.65d+17) then
        tmp = y * -z
    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 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.66e-15) {
		tmp = t_2;
	} else if (t <= -1.45e-229) {
		tmp = t_1;
	} else if (t <= 1.18e-262) {
		tmp = x + z;
	} else if (t <= 4.6e-164) {
		tmp = t_1;
	} else if (t <= 2.4e-84) {
		tmp = x + z;
	} else if (t <= 1.52e-34) {
		tmp = t_1;
	} else if (t <= 1.65e+17) {
		tmp = y * -z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1.66e-15:
		tmp = t_2
	elif t <= -1.45e-229:
		tmp = t_1
	elif t <= 1.18e-262:
		tmp = x + z
	elif t <= 4.6e-164:
		tmp = t_1
	elif t <= 2.4e-84:
		tmp = x + z
	elif t <= 1.52e-34:
		tmp = t_1
	elif t <= 1.65e+17:
		tmp = y * -z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.66e-15)
		tmp = t_2;
	elseif (t <= -1.45e-229)
		tmp = t_1;
	elseif (t <= 1.18e-262)
		tmp = Float64(x + z);
	elseif (t <= 4.6e-164)
		tmp = t_1;
	elseif (t <= 2.4e-84)
		tmp = Float64(x + z);
	elseif (t <= 1.52e-34)
		tmp = t_1;
	elseif (t <= 1.65e+17)
		tmp = Float64(y * Float64(-z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.66e-15)
		tmp = t_2;
	elseif (t <= -1.45e-229)
		tmp = t_1;
	elseif (t <= 1.18e-262)
		tmp = x + z;
	elseif (t <= 4.6e-164)
		tmp = t_1;
	elseif (t <= 2.4e-84)
		tmp = x + z;
	elseif (t <= 1.52e-34)
		tmp = t_1;
	elseif (t <= 1.65e+17)
		tmp = y * -z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.66e-15], t$95$2, If[LessEqual[t, -1.45e-229], t$95$1, If[LessEqual[t, 1.18e-262], N[(x + z), $MachinePrecision], If[LessEqual[t, 4.6e-164], t$95$1, If[LessEqual[t, 2.4e-84], N[(x + z), $MachinePrecision], If[LessEqual[t, 1.52e-34], t$95$1, If[LessEqual[t, 1.65e+17], N[(y * (-z)), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.65999999999999996e-15 or 1.65e17 < t

   1. Initial program 91.4%

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

   3. Taylor expanded in t around inf 65.5%

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

   if -1.65999999999999996e-15 < t < -1.45e-229 or 1.17999999999999994e-262 < t < 4.59999999999999971e-164 or 2.40000000000000017e-84 < t < 1.52e-34

   1. Initial program 95.9%

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

   3. Taylor expanded in t around -inf 60.6%

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

      1. associate-*r* 60.6%

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

      2. neg-mul-1 60.6%

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

      3. distribute-lft-out-- 60.6%

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

      4. associate-*r* 60.6%

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

      5. distribute-lft-neg-in 60.6%

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

      6. *-commutative 60.6%

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

      7. neg-mul-1 60.6%

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

      8. remove-double-neg 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in x around inf 43.5%

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

   7. Taylor expanded in t around 0 62.5%

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

   8. Taylor expanded in x around 0 46.4%

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

   if -1.45e-229 < t < 1.17999999999999994e-262 or 4.59999999999999971e-164 < t < 2.40000000000000017e-84

   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 85.3%

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

   4. Taylor expanded in a around 0 67.3%

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

   5. Taylor expanded in y around 0 46.6%

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

      1. cancel-sign-sub-inv 46.6%

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

      2. metadata-eval 46.6%

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

      3. *-lft-identity 46.6%

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

   7. Simplified 46.6%

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

   if 1.52e-34 < t < 1.65e17

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 73.6%

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

   4. Taylor expanded in y around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. distribute-rgt-neg-in 63.5%

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

   6. Simplified 63.5%

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

Alternative 4: 39.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.3 \cdot 10^{-233}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-274}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-291}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+35}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))) (t_2 (* a (- 1.0 t))))
   (if (<= a -1.25e-33)
     t_2
     (if (<= a -8.5e-84)
       t_1
       (if (<= a -7.3e-233)
         (+ x z)
         (if (<= a -4.4e-274)
           (* y b)
           (if (<= a -2.45e-291)
             (* b (- t 2.0))
             (if (<= a 3.3e-304) t_1 (if (<= a 6e+35) (+ x z) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -1.25e-33) {
		tmp = t_2;
	} else if (a <= -8.5e-84) {
		tmp = t_1;
	} else if (a <= -7.3e-233) {
		tmp = x + z;
	} else if (a <= -4.4e-274) {
		tmp = y * b;
	} else if (a <= -2.45e-291) {
		tmp = b * (t - 2.0);
	} else if (a <= 3.3e-304) {
		tmp = t_1;
	} else if (a <= 6e+35) {
		tmp = x + z;
	} 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 = y * -z
    t_2 = a * (1.0d0 - t)
    if (a <= (-1.25d-33)) then
        tmp = t_2
    else if (a <= (-8.5d-84)) then
        tmp = t_1
    else if (a <= (-7.3d-233)) then
        tmp = x + z
    else if (a <= (-4.4d-274)) then
        tmp = y * b
    else if (a <= (-2.45d-291)) then
        tmp = b * (t - 2.0d0)
    else if (a <= 3.3d-304) then
        tmp = t_1
    else if (a <= 6d+35) then
        tmp = x + z
    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 = y * -z;
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -1.25e-33) {
		tmp = t_2;
	} else if (a <= -8.5e-84) {
		tmp = t_1;
	} else if (a <= -7.3e-233) {
		tmp = x + z;
	} else if (a <= -4.4e-274) {
		tmp = y * b;
	} else if (a <= -2.45e-291) {
		tmp = b * (t - 2.0);
	} else if (a <= 3.3e-304) {
		tmp = t_1;
	} else if (a <= 6e+35) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -1.25e-33:
		tmp = t_2
	elif a <= -8.5e-84:
		tmp = t_1
	elif a <= -7.3e-233:
		tmp = x + z
	elif a <= -4.4e-274:
		tmp = y * b
	elif a <= -2.45e-291:
		tmp = b * (t - 2.0)
	elif a <= 3.3e-304:
		tmp = t_1
	elif a <= 6e+35:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.25e-33)
		tmp = t_2;
	elseif (a <= -8.5e-84)
		tmp = t_1;
	elseif (a <= -7.3e-233)
		tmp = Float64(x + z);
	elseif (a <= -4.4e-274)
		tmp = Float64(y * b);
	elseif (a <= -2.45e-291)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (a <= 3.3e-304)
		tmp = t_1;
	elseif (a <= 6e+35)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.25e-33)
		tmp = t_2;
	elseif (a <= -8.5e-84)
		tmp = t_1;
	elseif (a <= -7.3e-233)
		tmp = x + z;
	elseif (a <= -4.4e-274)
		tmp = y * b;
	elseif (a <= -2.45e-291)
		tmp = b * (t - 2.0);
	elseif (a <= 3.3e-304)
		tmp = t_1;
	elseif (a <= 6e+35)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e-33], t$95$2, If[LessEqual[a, -8.5e-84], t$95$1, If[LessEqual[a, -7.3e-233], N[(x + z), $MachinePrecision], If[LessEqual[a, -4.4e-274], N[(y * b), $MachinePrecision], If[LessEqual[a, -2.45e-291], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-304], t$95$1, If[LessEqual[a, 6e+35], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.25000000000000007e-33 or 5.99999999999999981e35 < 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 a around inf 57.4%

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

   if -1.25000000000000007e-33 < a < -8.4999999999999994e-84 or -2.44999999999999997e-291 < a < 3.30000000000000013e-304

   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 z around inf 72.6%

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

   4. Taylor expanded in y around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. distribute-rgt-neg-in 72.7%

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

   6. Simplified 72.7%

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

   if -8.4999999999999994e-84 < a < -7.3000000000000003e-233 or 3.30000000000000013e-304 < a < 5.99999999999999981e35

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0 57.9%

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

   4. Taylor expanded in a around 0 54.0%

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

   5. Taylor expanded in y around 0 36.1%

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

      1. cancel-sign-sub-inv 36.1%

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

      2. metadata-eval 36.1%

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

      3. *-lft-identity 36.1%

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

   7. Simplified 36.1%

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

   if -7.3000000000000003e-233 < a < -4.3999999999999999e-274

   1. Initial program 88.9%

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

   3. Taylor expanded in y around inf 85.8%

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

   4. Taylor expanded in b around inf 64.6%

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

   if -4.3999999999999999e-274 < a < -2.44999999999999997e-291

   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 26.3%

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

   4. Taylor expanded in b around -inf 26.3%

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

      1. associate-*r/ 26.3%

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

      2. associate-+r- 26.3%

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

      3. associate-+r- 26.3%

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

      4. +-commutative 26.3%

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

      5. associate--l+ 26.3%

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

      6. sub-neg 26.3%

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

      7. metadata-eval 26.3%

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

   6. Simplified 26.3%

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

   7. Taylor expanded in y around 0 80.8%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -7.3 \cdot 10^{-233}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-274}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-291}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-304}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+35}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-239}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+31}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.04 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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)))
        (t_3 (+ x (* z (- 1.0 y)))))
   (if (<= b -5.2e+14)
     t_2
     (if (<= b -7e-256)
       t_1
       (if (<= b 4e-239)
         t_3
         (if (<= b 1.45e-211)
           t_1
           (if (<= b 6.4e+31) t_3 (if (<= b 1.04e+105) 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 t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -5.2e+14) {
		tmp = t_2;
	} else if (b <= -7e-256) {
		tmp = t_1;
	} else if (b <= 4e-239) {
		tmp = t_3;
	} else if (b <= 1.45e-211) {
		tmp = t_1;
	} else if (b <= 6.4e+31) {
		tmp = t_3;
	} else if (b <= 1.04e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x + (z * (1.0d0 - y))
    if (b <= (-5.2d+14)) then
        tmp = t_2
    else if (b <= (-7d-256)) then
        tmp = t_1
    else if (b <= 4d-239) then
        tmp = t_3
    else if (b <= 1.45d-211) then
        tmp = t_1
    else if (b <= 6.4d+31) then
        tmp = t_3
    else if (b <= 1.04d+105) 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 t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -5.2e+14) {
		tmp = t_2;
	} else if (b <= -7e-256) {
		tmp = t_1;
	} else if (b <= 4e-239) {
		tmp = t_3;
	} else if (b <= 1.45e-211) {
		tmp = t_1;
	} else if (b <= 6.4e+31) {
		tmp = t_3;
	} else if (b <= 1.04e+105) {
		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)
	t_3 = x + (z * (1.0 - y))
	tmp = 0
	if b <= -5.2e+14:
		tmp = t_2
	elif b <= -7e-256:
		tmp = t_1
	elif b <= 4e-239:
		tmp = t_3
	elif b <= 1.45e-211:
		tmp = t_1
	elif b <= 6.4e+31:
		tmp = t_3
	elif b <= 1.04e+105:
		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))
	t_3 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -5.2e+14)
		tmp = t_2;
	elseif (b <= -7e-256)
		tmp = t_1;
	elseif (b <= 4e-239)
		tmp = t_3;
	elseif (b <= 1.45e-211)
		tmp = t_1;
	elseif (b <= 6.4e+31)
		tmp = t_3;
	elseif (b <= 1.04e+105)
		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);
	t_3 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -5.2e+14)
		tmp = t_2;
	elseif (b <= -7e-256)
		tmp = t_1;
	elseif (b <= 4e-239)
		tmp = t_3;
	elseif (b <= 1.45e-211)
		tmp = t_1;
	elseif (b <= 6.4e+31)
		tmp = t_3;
	elseif (b <= 1.04e+105)
		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]}, Block[{t$95$3 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+14], t$95$2, If[LessEqual[b, -7e-256], t$95$1, If[LessEqual[b, 4e-239], t$95$3, If[LessEqual[b, 1.45e-211], t$95$1, If[LessEqual[b, 6.4e+31], t$95$3, If[LessEqual[b, 1.04e+105], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.2e14 or 1.04e105 < b

   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 b around inf 78.3%

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

   if -5.2e14 < b < -7.00000000000000028e-256 or 4.0000000000000003e-239 < b < 1.45000000000000007e-211 or 6.4000000000000001e31 < b < 1.04e105

   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 b around 0 87.2%

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

   4. Taylor expanded in a around inf 63.3%

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

   if -7.00000000000000028e-256 < b < 4.0000000000000003e-239 or 1.45000000000000007e-211 < b < 6.4000000000000001e31

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0 89.1%

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

   4. Taylor expanded in a around 0 65.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-256}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-239}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-211}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+31}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.04 \cdot 10^{+105}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+30}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- y 2.0))))
   (if (<= b -8e+68)
     t_2
     (if (<= b 2.6e-211)
       t_1
       (if (<= b 5.4e-171)
         (* y (- z))
         (if (<= b 1.8e-86)
           t_1
           (if (<= b 9.8e+30) (+ x z) (if (<= b 3.2e+105) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -8e+68) {
		tmp = t_2;
	} else if (b <= 2.6e-211) {
		tmp = t_1;
	} else if (b <= 5.4e-171) {
		tmp = y * -z;
	} else if (b <= 1.8e-86) {
		tmp = t_1;
	} else if (b <= 9.8e+30) {
		tmp = x + z;
	} else if (b <= 3.2e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * (y - 2.0d0)
    if (b <= (-8d+68)) then
        tmp = t_2
    else if (b <= 2.6d-211) then
        tmp = t_1
    else if (b <= 5.4d-171) then
        tmp = y * -z
    else if (b <= 1.8d-86) then
        tmp = t_1
    else if (b <= 9.8d+30) then
        tmp = x + z
    else if (b <= 3.2d+105) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -8e+68) {
		tmp = t_2;
	} else if (b <= 2.6e-211) {
		tmp = t_1;
	} else if (b <= 5.4e-171) {
		tmp = y * -z;
	} else if (b <= 1.8e-86) {
		tmp = t_1;
	} else if (b <= 9.8e+30) {
		tmp = x + z;
	} else if (b <= 3.2e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * (y - 2.0)
	tmp = 0
	if b <= -8e+68:
		tmp = t_2
	elif b <= 2.6e-211:
		tmp = t_1
	elif b <= 5.4e-171:
		tmp = y * -z
	elif b <= 1.8e-86:
		tmp = t_1
	elif b <= 9.8e+30:
		tmp = x + z
	elif b <= 3.2e+105:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -8e+68)
		tmp = t_2;
	elseif (b <= 2.6e-211)
		tmp = t_1;
	elseif (b <= 5.4e-171)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 1.8e-86)
		tmp = t_1;
	elseif (b <= 9.8e+30)
		tmp = Float64(x + z);
	elseif (b <= 3.2e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -8e+68)
		tmp = t_2;
	elseif (b <= 2.6e-211)
		tmp = t_1;
	elseif (b <= 5.4e-171)
		tmp = y * -z;
	elseif (b <= 1.8e-86)
		tmp = t_1;
	elseif (b <= 9.8e+30)
		tmp = x + z;
	elseif (b <= 3.2e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+68], t$95$2, If[LessEqual[b, 2.6e-211], t$95$1, If[LessEqual[b, 5.4e-171], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 1.8e-86], t$95$1, If[LessEqual[b, 9.8e+30], N[(x + z), $MachinePrecision], If[LessEqual[b, 3.2e+105], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.99999999999999962e68 or 3.2e105 < b

   1. Initial program 90.2%

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

   3. Taylor expanded in t around -inf 75.5%

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

      1. associate-*r* 75.5%

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

      2. neg-mul-1 75.5%

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

      3. distribute-lft-out-- 75.5%

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

      4. associate-*r* 75.5%

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

      5. distribute-lft-neg-in 75.5%

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

      6. *-commutative 75.5%

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

      7. neg-mul-1 75.5%

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

      8. remove-double-neg 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in x around inf 75.7%

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

   7. Taylor expanded in t around 0 62.8%

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

   8. Taylor expanded in x around 0 55.5%

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

   if -7.99999999999999962e68 < b < 2.6e-211 or 5.40000000000000028e-171 < b < 1.79999999999999983e-86 or 9.79999999999999969e30 < b < 3.2e105

   1. Initial program 97.0%

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

   3. Taylor expanded in a around inf 44.9%

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

   if 2.6e-211 < b < 5.40000000000000028e-171

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 66.9%

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

   4. Taylor expanded in y around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. distribute-rgt-neg-in 59.4%

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

   6. Simplified 59.4%

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

   if 1.79999999999999983e-86 < b < 9.79999999999999969e30

   1. Initial program 96.1%

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

   3. Taylor expanded in b around 0 70.0%

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

   4. Taylor expanded in a around 0 58.9%

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

   5. Taylor expanded in y around 0 40.7%

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

      1. cancel-sign-sub-inv 40.7%

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

      2. metadata-eval 40.7%

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

      3. *-lft-identity 40.7%

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

   7. Simplified 40.7%

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

Alternative 7: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1400000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-239}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+29}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (+ x (* z (- 1.0 y)))))
   (if (<= b -1400000000000.0)
     t_2
     (if (<= b -2.6e-254)
       t_1
       (if (<= b 7.2e-239)
         t_3
         (if (<= b 1e-211) t_1 (if (<= b 1.05e+29) t_3 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 = x + (b * ((y + t) - 2.0));
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -1400000000000.0) {
		tmp = t_2;
	} else if (b <= -2.6e-254) {
		tmp = t_1;
	} else if (b <= 7.2e-239) {
		tmp = t_3;
	} else if (b <= 1e-211) {
		tmp = t_1;
	} else if (b <= 1.05e+29) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = x + (z * (1.0d0 - y))
    if (b <= (-1400000000000.0d0)) then
        tmp = t_2
    else if (b <= (-2.6d-254)) then
        tmp = t_1
    else if (b <= 7.2d-239) then
        tmp = t_3
    else if (b <= 1d-211) then
        tmp = t_1
    else if (b <= 1.05d+29) then
        tmp = t_3
    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 = x + (b * ((y + t) - 2.0));
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -1400000000000.0) {
		tmp = t_2;
	} else if (b <= -2.6e-254) {
		tmp = t_1;
	} else if (b <= 7.2e-239) {
		tmp = t_3;
	} else if (b <= 1e-211) {
		tmp = t_1;
	} else if (b <= 1.05e+29) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = x + (z * (1.0 - y))
	tmp = 0
	if b <= -1400000000000.0:
		tmp = t_2
	elif b <= -2.6e-254:
		tmp = t_1
	elif b <= 7.2e-239:
		tmp = t_3
	elif b <= 1e-211:
		tmp = t_1
	elif b <= 1.05e+29:
		tmp = t_3
	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(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -1400000000000.0)
		tmp = t_2;
	elseif (b <= -2.6e-254)
		tmp = t_1;
	elseif (b <= 7.2e-239)
		tmp = t_3;
	elseif (b <= 1e-211)
		tmp = t_1;
	elseif (b <= 1.05e+29)
		tmp = t_3;
	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 = x + (b * ((y + t) - 2.0));
	t_3 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -1400000000000.0)
		tmp = t_2;
	elseif (b <= -2.6e-254)
		tmp = t_1;
	elseif (b <= 7.2e-239)
		tmp = t_3;
	elseif (b <= 1e-211)
		tmp = t_1;
	elseif (b <= 1.05e+29)
		tmp = t_3;
	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[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1400000000000.0], t$95$2, If[LessEqual[b, -2.6e-254], t$95$1, If[LessEqual[b, 7.2e-239], t$95$3, If[LessEqual[b, 1e-211], t$95$1, If[LessEqual[b, 1.05e+29], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4e12 or 1.0500000000000001e29 < b

   1. Initial program 90.6%

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

   3. Taylor expanded in t around -inf 74.1%

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

      1. associate-*r* 74.1%

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

      2. neg-mul-1 74.1%

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

      3. distribute-lft-out-- 74.1%

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

      4. associate-*r* 74.1%

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

      5. distribute-lft-neg-in 74.1%

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

      6. *-commutative 74.1%

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

      7. neg-mul-1 74.1%

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

      8. remove-double-neg 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in x around inf 72.0%

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

   7. Taylor expanded in a around 0 76.1%

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

   if -1.4e12 < b < -2.6e-254 or 7.2000000000000002e-239 < b < 1.00000000000000009e-211

   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 b around 0 95.0%

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

   4. Taylor expanded in a around inf 66.1%

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

   if -2.6e-254 < b < 7.2000000000000002e-239 or 1.00000000000000009e-211 < b < 1.0500000000000001e29

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0 90.2%

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

   4. Taylor expanded in a around 0 66.2%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1400000000000:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-254}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-239}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 10^{-211}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+29}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-92}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.58 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- y 2.0)))) (t_2 (* t (- b a))) (t_3 (* z (- 1.0 y))))
   (if (<= t -7.5e+85)
     t_2
     (if (<= t 4e-142)
       t_1
       (if (<= t 8.8e-92)
         t_3
         (if (<= t 1.58e-34) t_1 (if (<= t 1.85e+21) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (y - 2.0));
	double t_2 = t * (b - a);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (t <= -7.5e+85) {
		tmp = t_2;
	} else if (t <= 4e-142) {
		tmp = t_1;
	} else if (t <= 8.8e-92) {
		tmp = t_3;
	} else if (t <= 1.58e-34) {
		tmp = t_1;
	} else if (t <= 1.85e+21) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (b * (y - 2.0d0))
    t_2 = t * (b - a)
    t_3 = z * (1.0d0 - y)
    if (t <= (-7.5d+85)) then
        tmp = t_2
    else if (t <= 4d-142) then
        tmp = t_1
    else if (t <= 8.8d-92) then
        tmp = t_3
    else if (t <= 1.58d-34) then
        tmp = t_1
    else if (t <= 1.85d+21) then
        tmp = t_3
    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 + (b * (y - 2.0));
	double t_2 = t * (b - a);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (t <= -7.5e+85) {
		tmp = t_2;
	} else if (t <= 4e-142) {
		tmp = t_1;
	} else if (t <= 8.8e-92) {
		tmp = t_3;
	} else if (t <= 1.58e-34) {
		tmp = t_1;
	} else if (t <= 1.85e+21) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * (y - 2.0))
	t_2 = t * (b - a)
	t_3 = z * (1.0 - y)
	tmp = 0
	if t <= -7.5e+85:
		tmp = t_2
	elif t <= 4e-142:
		tmp = t_1
	elif t <= 8.8e-92:
		tmp = t_3
	elif t <= 1.58e-34:
		tmp = t_1
	elif t <= 1.85e+21:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(y - 2.0)))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -7.5e+85)
		tmp = t_2;
	elseif (t <= 4e-142)
		tmp = t_1;
	elseif (t <= 8.8e-92)
		tmp = t_3;
	elseif (t <= 1.58e-34)
		tmp = t_1;
	elseif (t <= 1.85e+21)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * (y - 2.0));
	t_2 = t * (b - a);
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (t <= -7.5e+85)
		tmp = t_2;
	elseif (t <= 4e-142)
		tmp = t_1;
	elseif (t <= 8.8e-92)
		tmp = t_3;
	elseif (t <= 1.58e-34)
		tmp = t_1;
	elseif (t <= 1.85e+21)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+85], t$95$2, If[LessEqual[t, 4e-142], t$95$1, If[LessEqual[t, 8.8e-92], t$95$3, If[LessEqual[t, 1.58e-34], t$95$1, If[LessEqual[t, 1.85e+21], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.49999999999999942e85 or 1.85e21 < t

   1. Initial program 90.4%

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

   3. Taylor expanded in t around inf 69.6%

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

   if -7.49999999999999942e85 < t < 4.0000000000000002e-142 or 8.79999999999999949e-92 < t < 1.57999999999999997e-34

   1. Initial program 97.3%

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

   3. Taylor expanded in t around -inf 59.0%

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

      1. associate-*r* 59.0%

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

      2. neg-mul-1 59.0%

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

      3. distribute-lft-out-- 59.0%

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

      4. associate-*r* 59.0%

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

      5. distribute-lft-neg-in 59.0%

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

      6. *-commutative 59.0%

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

      7. neg-mul-1 59.0%

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

      8. remove-double-neg 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in x around inf 42.1%

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

   7. Taylor expanded in t around 0 57.7%

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

   if 4.0000000000000002e-142 < t < 8.79999999999999949e-92 or 1.57999999999999997e-34 < t < 1.85e21

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 66.0%

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

Alternative 9: 39.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-233}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-273}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+34}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.2e-33)
     t_1
     (if (<= a -2.2e-83)
       (* y (- z))
       (if (<= a -5.2e-233)
         (+ x z)
         (if (<= a 2.2e-273) (* y b) (if (<= a 7e+34) (+ x z) 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 <= -1.2e-33) {
		tmp = t_1;
	} else if (a <= -2.2e-83) {
		tmp = y * -z;
	} else if (a <= -5.2e-233) {
		tmp = x + z;
	} else if (a <= 2.2e-273) {
		tmp = y * b;
	} else if (a <= 7e+34) {
		tmp = x + 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 = a * (1.0d0 - t)
    if (a <= (-1.2d-33)) then
        tmp = t_1
    else if (a <= (-2.2d-83)) then
        tmp = y * -z
    else if (a <= (-5.2d-233)) then
        tmp = x + z
    else if (a <= 2.2d-273) then
        tmp = y * b
    else if (a <= 7d+34) then
        tmp = x + 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 = a * (1.0 - t);
	double tmp;
	if (a <= -1.2e-33) {
		tmp = t_1;
	} else if (a <= -2.2e-83) {
		tmp = y * -z;
	} else if (a <= -5.2e-233) {
		tmp = x + z;
	} else if (a <= 2.2e-273) {
		tmp = y * b;
	} else if (a <= 7e+34) {
		tmp = x + z;
	} 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 <= -1.2e-33:
		tmp = t_1
	elif a <= -2.2e-83:
		tmp = y * -z
	elif a <= -5.2e-233:
		tmp = x + z
	elif a <= 2.2e-273:
		tmp = y * b
	elif a <= 7e+34:
		tmp = x + z
	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 <= -1.2e-33)
		tmp = t_1;
	elseif (a <= -2.2e-83)
		tmp = Float64(y * Float64(-z));
	elseif (a <= -5.2e-233)
		tmp = Float64(x + z);
	elseif (a <= 2.2e-273)
		tmp = Float64(y * b);
	elseif (a <= 7e+34)
		tmp = Float64(x + z);
	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 <= -1.2e-33)
		tmp = t_1;
	elseif (a <= -2.2e-83)
		tmp = y * -z;
	elseif (a <= -5.2e-233)
		tmp = x + z;
	elseif (a <= 2.2e-273)
		tmp = y * b;
	elseif (a <= 7e+34)
		tmp = x + z;
	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, -1.2e-33], t$95$1, If[LessEqual[a, -2.2e-83], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, -5.2e-233], N[(x + z), $MachinePrecision], If[LessEqual[a, 2.2e-273], N[(y * b), $MachinePrecision], If[LessEqual[a, 7e+34], N[(x + z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.2e-33 or 6.99999999999999996e34 < 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 a around inf 57.4%

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

   if -1.2e-33 < a < -2.20000000000000008e-83

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 68.1%

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

   4. Taylor expanded in y around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. distribute-rgt-neg-in 68.2%

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

   6. Simplified 68.2%

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

   if -2.20000000000000008e-83 < a < -5.1999999999999996e-233 or 2.1999999999999998e-273 < a < 6.99999999999999996e34

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0 59.0%

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

   4. Taylor expanded in a around 0 54.8%

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

   5. Taylor expanded in y around 0 37.3%

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

      1. cancel-sign-sub-inv 37.3%

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

      2. metadata-eval 37.3%

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

      3. *-lft-identity 37.3%

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

   7. Simplified 37.3%

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

   if -5.1999999999999996e-233 < a < 2.1999999999999998e-273

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf 64.5%

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

   4. Taylor expanded in b around inf 38.7%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-233}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-273}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+34}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -21000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-171}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -21000000000000.0)
     t_2
     (if (<= b 2.7e-211)
       t_1
       (if (<= b 1.1e-171)
         (+ x (* z (- 1.0 y)))
         (if (<= b 5.5e+106) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -21000000000000.0) {
		tmp = t_2;
	} else if (b <= 2.7e-211) {
		tmp = t_1;
	} else if (b <= 1.1e-171) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 5.5e+106) {
		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 + (z + (a * (1.0d0 - t)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-21000000000000.0d0)) then
        tmp = t_2
    else if (b <= 2.7d-211) then
        tmp = t_1
    else if (b <= 1.1d-171) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 5.5d+106) 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 + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -21000000000000.0) {
		tmp = t_2;
	} else if (b <= 2.7e-211) {
		tmp = t_1;
	} else if (b <= 1.1e-171) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 5.5e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -21000000000000.0:
		tmp = t_2
	elif b <= 2.7e-211:
		tmp = t_1
	elif b <= 1.1e-171:
		tmp = x + (z * (1.0 - y))
	elif b <= 5.5e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -21000000000000.0)
		tmp = t_2;
	elseif (b <= 2.7e-211)
		tmp = t_1;
	elseif (b <= 1.1e-171)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 5.5e+106)
		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 + (z + (a * (1.0 - t)));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -21000000000000.0)
		tmp = t_2;
	elseif (b <= 2.7e-211)
		tmp = t_1;
	elseif (b <= 1.1e-171)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 5.5e+106)
		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[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -21000000000000.0], t$95$2, If[LessEqual[b, 2.7e-211], t$95$1, If[LessEqual[b, 1.1e-171], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+106], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1e13 or 5.5e106 < b

   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 t around -inf 77.2%

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

      1. associate-*r* 77.2%

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

      2. neg-mul-1 77.2%

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

      3. distribute-lft-out-- 77.2%

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

      4. associate-*r* 77.2%

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

      5. distribute-lft-neg-in 77.2%

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

      6. *-commutative 77.2%

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

      7. neg-mul-1 77.2%

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

      8. remove-double-neg 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in x around inf 77.4%

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

   7. Taylor expanded in a around 0 86.0%

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

   if -2.1e13 < b < 2.6999999999999999e-211 or 1.1000000000000001e-171 < b < 5.5e106

   1. Initial program 96.7%

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

   3. Taylor expanded in b around 0 87.8%

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

   4. Taylor expanded in y around 0 67.4%

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

      1. +-commutative 67.4%

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

      2. sub-neg 67.4%

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

      3. metadata-eval 67.4%

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

      4. neg-mul-1 67.4%

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

      5. unsub-neg 67.4%

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

   6. Simplified 67.4%

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

   if 2.6999999999999999e-211 < b < 1.1000000000000001e-171

   1. Initial program 92.3%

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

   3. Taylor expanded in b around 0 92.3%

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

   4. Taylor expanded in a around 0 71.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -21000000000000:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-211}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-171}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+106}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1.55e+14)
     t_2
     (if (<= b 2.7e-211)
       t_1
       (if (<= b 8.6e-171) (* z (- 1.0 y)) (if (<= b 6.6e+108) 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 <= -1.55e+14) {
		tmp = t_2;
	} else if (b <= 2.7e-211) {
		tmp = t_1;
	} else if (b <= 8.6e-171) {
		tmp = z * (1.0 - y);
	} else if (b <= 6.6e+108) {
		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 <= (-1.55d+14)) then
        tmp = t_2
    else if (b <= 2.7d-211) then
        tmp = t_1
    else if (b <= 8.6d-171) then
        tmp = z * (1.0d0 - y)
    else if (b <= 6.6d+108) 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 <= -1.55e+14) {
		tmp = t_2;
	} else if (b <= 2.7e-211) {
		tmp = t_1;
	} else if (b <= 8.6e-171) {
		tmp = z * (1.0 - y);
	} else if (b <= 6.6e+108) {
		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 <= -1.55e+14:
		tmp = t_2
	elif b <= 2.7e-211:
		tmp = t_1
	elif b <= 8.6e-171:
		tmp = z * (1.0 - y)
	elif b <= 6.6e+108:
		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 <= -1.55e+14)
		tmp = t_2;
	elseif (b <= 2.7e-211)
		tmp = t_1;
	elseif (b <= 8.6e-171)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 6.6e+108)
		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 <= -1.55e+14)
		tmp = t_2;
	elseif (b <= 2.7e-211)
		tmp = t_1;
	elseif (b <= 8.6e-171)
		tmp = z * (1.0 - y);
	elseif (b <= 6.6e+108)
		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, -1.55e+14], t$95$2, If[LessEqual[b, 2.7e-211], t$95$1, If[LessEqual[b, 8.6e-171], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e+108], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.55e14 or 6.60000000000000038e108 < b

   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 b around inf 78.3%

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

   if -1.55e14 < b < 2.6999999999999999e-211 or 8.6000000000000004e-171 < b < 6.60000000000000038e108

   1. Initial program 96.7%

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

   3. Taylor expanded in b around 0 87.8%

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

   4. Taylor expanded in a around inf 57.3%

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

   if 2.6999999999999999e-211 < b < 8.6000000000000004e-171

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 66.9%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-211}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+108}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -27000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -27000000000000.0)
     t_1
     (if (<= y -5.2e-63)
       (* b (- t 2.0))
       (if (<= y -1.8e-271)
         (* a (- 1.0 t))
         (if (<= y 2e+20) (* t (- b a)) 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 <= -27000000000000.0) {
		tmp = t_1;
	} else if (y <= -5.2e-63) {
		tmp = b * (t - 2.0);
	} else if (y <= -1.8e-271) {
		tmp = a * (1.0 - t);
	} else if (y <= 2e+20) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-27000000000000.0d0)) then
        tmp = t_1
    else if (y <= (-5.2d-63)) then
        tmp = b * (t - 2.0d0)
    else if (y <= (-1.8d-271)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 2d+20) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -27000000000000.0) {
		tmp = t_1;
	} else if (y <= -5.2e-63) {
		tmp = b * (t - 2.0);
	} else if (y <= -1.8e-271) {
		tmp = a * (1.0 - t);
	} else if (y <= 2e+20) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -27000000000000.0:
		tmp = t_1
	elif y <= -5.2e-63:
		tmp = b * (t - 2.0)
	elif y <= -1.8e-271:
		tmp = a * (1.0 - t)
	elif y <= 2e+20:
		tmp = t * (b - a)
	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 <= -27000000000000.0)
		tmp = t_1;
	elseif (y <= -5.2e-63)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= -1.8e-271)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 2e+20)
		tmp = Float64(t * Float64(b - a));
	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 <= -27000000000000.0)
		tmp = t_1;
	elseif (y <= -5.2e-63)
		tmp = b * (t - 2.0);
	elseif (y <= -1.8e-271)
		tmp = a * (1.0 - t);
	elseif (y <= 2e+20)
		tmp = t * (b - a);
	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, -27000000000000.0], t$95$1, If[LessEqual[y, -5.2e-63], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.8e-271], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+20], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7e13 or 2e20 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 64.9%

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

   if -2.7e13 < y < -5.2000000000000003e-63

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 70.5%

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

   4. Taylor expanded in b around -inf 39.7%

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

      1. associate-*r/ 39.6%

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

      2. associate-+r- 39.6%

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

      3. associate-+r- 39.6%

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

      4. +-commutative 39.6%

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

      5. associate--l+ 39.6%

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

      6. sub-neg 39.6%

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

      7. metadata-eval 39.6%

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

   6. Simplified 39.6%

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

   7. Taylor expanded in y around 0 49.3%

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

   if -5.2000000000000003e-63 < y < -1.7999999999999999e-271

   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 57.0%

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

   if -1.7999999999999999e-271 < y < 2e20

   1. Initial program 97.2%

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

   3. Taylor expanded in t around inf 45.4%

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

Alternative 13: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+16} \lor \neg \left(t \leq 3.3 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \left(\frac{x}{t} - a\right) + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(b \cdot \left(y - 2\right) + z \cdot \left(1 - y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.4e+16) (not (<= t 3.3e+16)))
   (+ (* t (- (/ x t) a)) (* b (- (+ y t) 2.0)))
   (+ a (+ x (+ (* b (- y 2.0)) (* z (- 1.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.4e+16) || !(t <= 3.3e+16)) {
		tmp = (t * ((x / t) - a)) + (b * ((y + t) - 2.0));
	} else {
		tmp = a + (x + ((b * (y - 2.0)) + (z * (1.0 - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-6.4d+16)) .or. (.not. (t <= 3.3d+16))) then
        tmp = (t * ((x / t) - a)) + (b * ((y + t) - 2.0d0))
    else
        tmp = a + (x + ((b * (y - 2.0d0)) + (z * (1.0d0 - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.4e+16) || !(t <= 3.3e+16)) {
		tmp = (t * ((x / t) - a)) + (b * ((y + t) - 2.0));
	} else {
		tmp = a + (x + ((b * (y - 2.0)) + (z * (1.0 - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.4e+16) or not (t <= 3.3e+16):
		tmp = (t * ((x / t) - a)) + (b * ((y + t) - 2.0))
	else:
		tmp = a + (x + ((b * (y - 2.0)) + (z * (1.0 - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.4e+16) || !(t <= 3.3e+16))
		tmp = Float64(Float64(t * Float64(Float64(x / t) - a)) + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(a + Float64(x + Float64(Float64(b * Float64(y - 2.0)) + Float64(z * Float64(1.0 - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.4e+16) || ~((t <= 3.3e+16)))
		tmp = (t * ((x / t) - a)) + (b * ((y + t) - 2.0));
	else
		tmp = a + (x + ((b * (y - 2.0)) + (z * (1.0 - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.4e+16], N[Not[LessEqual[t, 3.3e+16]], $MachinePrecision]], N[(N[(t * N[(N[(x / t), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(x + N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4e16 or 3.3e16 < t

   1. Initial program 91.1%

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

   3. Taylor expanded in t around -inf 92.7%

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

      1. associate-*r* 92.7%

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

      2. neg-mul-1 92.7%

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

      3. distribute-lft-out-- 92.7%

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

      4. associate-*r* 92.7%

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

      5. distribute-lft-neg-in 92.7%

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

      6. *-commutative 92.7%

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

      7. neg-mul-1 92.7%

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

      8. remove-double-neg 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in x around inf 80.2%

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

   if -6.4e16 < t < 3.3e16

   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 t around -inf 61.0%

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

      1. associate-*r* 61.0%

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

      2. neg-mul-1 61.0%

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

      3. distribute-lft-out-- 61.0%

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

      4. associate-*r* 61.0%

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

      5. distribute-lft-neg-in 61.0%

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

      6. *-commutative 61.0%

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

      7. neg-mul-1 61.0%

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

      8. remove-double-neg 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in t around 0 95.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+16} \lor \neg \left(t \leq 3.3 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \left(\frac{x}{t} - a\right) + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(b \cdot \left(y - 2\right) + z \cdot \left(1 - y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+176}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+112} \lor \neg \left(y \leq 42000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -2.5e+208)
     t_1
     (if (<= y -6.2e+176)
       (* y b)
       (if (or (<= y -9.8e+112) (not (<= y 42000.0))) t_1 (+ x z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -2.5e+208) {
		tmp = t_1;
	} else if (y <= -6.2e+176) {
		tmp = y * b;
	} else if ((y <= -9.8e+112) || !(y <= 42000.0)) {
		tmp = t_1;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-2.5d+208)) then
        tmp = t_1
    else if (y <= (-6.2d+176)) then
        tmp = y * b
    else if ((y <= (-9.8d+112)) .or. (.not. (y <= 42000.0d0))) then
        tmp = t_1
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -2.5e+208) {
		tmp = t_1;
	} else if (y <= -6.2e+176) {
		tmp = y * b;
	} else if ((y <= -9.8e+112) || !(y <= 42000.0)) {
		tmp = t_1;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -2.5e+208:
		tmp = t_1
	elif y <= -6.2e+176:
		tmp = y * b
	elif (y <= -9.8e+112) or not (y <= 42000.0):
		tmp = t_1
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -2.5e+208)
		tmp = t_1;
	elseif (y <= -6.2e+176)
		tmp = Float64(y * b);
	elseif ((y <= -9.8e+112) || !(y <= 42000.0))
		tmp = t_1;
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -2.5e+208)
		tmp = t_1;
	elseif (y <= -6.2e+176)
		tmp = y * b;
	elseif ((y <= -9.8e+112) || ~((y <= 42000.0)))
		tmp = t_1;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -2.5e+208], t$95$1, If[LessEqual[y, -6.2e+176], N[(y * b), $MachinePrecision], If[Or[LessEqual[y, -9.8e+112], N[Not[LessEqual[y, 42000.0]], $MachinePrecision]], t$95$1, N[(x + z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5000000000000002e208 or -6.1999999999999998e176 < y < -9.80000000000000008e112 or 42000 < y

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf 48.5%

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

   4. Taylor expanded in y around inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. distribute-rgt-neg-in 47.9%

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

   6. Simplified 47.9%

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

   if -2.5000000000000002e208 < y < -6.1999999999999998e176

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 85.7%

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

   4. Taylor expanded in b around inf 73.1%

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

   if -9.80000000000000008e112 < y < 42000

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0 67.8%

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

   4. Taylor expanded in a around 0 34.4%

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

   5. Taylor expanded in y around 0 31.9%

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

      1. cancel-sign-sub-inv 31.9%

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

      2. metadata-eval 31.9%

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

      3. *-lft-identity 31.9%

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

   7. Simplified 31.9%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+208}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+176}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+112} \lor \neg \left(y \leq 42000\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 82.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+14} \lor \neg \left(b \leq 1.2 \cdot 10^{+119}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.2e+14) (not (<= b 1.2e+119)))
   (+ x (* b (- (+ y t) 2.0)))
   (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.2e+14) || !(b <= 1.2e+119)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.2d+14)) .or. (.not. (b <= 1.2d+119))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.2e+14) || !(b <= 1.2e+119)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.2e+14) or not (b <= 1.2e+119):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.2e+14) || !(b <= 1.2e+119))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.2e+14) || ~((b <= 1.2e+119)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.2e+14], N[Not[LessEqual[b, 1.2e+119]], $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] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.2e14 or 1.2e119 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in t around -inf 77.0%

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

      1. associate-*r* 77.0%

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

      2. neg-mul-1 77.0%

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

      3. distribute-lft-out-- 77.0%

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

      4. associate-*r* 77.0%

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

      5. distribute-lft-neg-in 77.0%

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

      6. *-commutative 77.0%

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

      7. neg-mul-1 77.0%

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

      8. remove-double-neg 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in x around inf 78.1%

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

   7. Taylor expanded in a around 0 86.8%

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

   if -6.2e14 < b < 1.2e119

   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 b around 0 88.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+14} \lor \neg \left(b \leq 1.2 \cdot 10^{+119}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -48000000000000 \lor \neg \left(b \leq 9.4 \cdot 10^{+114}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -48000000000000.0) (not (<= b 9.4e+114)))
   (+ 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 <= -48000000000000.0) || !(b <= 9.4e+114)) {
		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 <= (-48000000000000.0d0)) .or. (.not. (b <= 9.4d+114))) 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 <= -48000000000000.0) || !(b <= 9.4e+114)) {
		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 <= -48000000000000.0) or not (b <= 9.4e+114):
		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 <= -48000000000000.0) || !(b <= 9.4e+114))
		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 <= -48000000000000.0) || ~((b <= 9.4e+114)))
		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, -48000000000000.0], N[Not[LessEqual[b, 9.4e+114]], $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 < -4.8e13 or 9.4000000000000001e114 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in t around -inf 77.0%

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

      1. associate-*r* 77.0%

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

      2. neg-mul-1 77.0%

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

      3. distribute-lft-out-- 77.0%

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

      4. associate-*r* 77.0%

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

      5. distribute-lft-neg-in 77.0%

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

      6. *-commutative 77.0%

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

      7. neg-mul-1 77.0%

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

      8. remove-double-neg 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in x around inf 78.1%

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

   7. Taylor expanded in a around 0 86.8%

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

   if -4.8e13 < b < 9.4000000000000001e114

   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 b around 0 88.2%

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

   4. Taylor expanded in t around inf 77.4%

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

      1. *-commutative 77.4%

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

   6. Simplified 77.4%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -48000000000000 \lor \neg \left(b \leq 9.4 \cdot 10^{+114}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-34}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -7.2e+98)
     t_1
     (if (<= t 1.32e-34) (+ x z) (if (<= t 9.2e+18) (* y (- z)) 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 <= -7.2e+98) {
		tmp = t_1;
	} else if (t <= 1.32e-34) {
		tmp = x + z;
	} else if (t <= 9.2e+18) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-7.2d+98)) then
        tmp = t_1
    else if (t <= 1.32d-34) then
        tmp = x + z
    else if (t <= 9.2d+18) then
        tmp = y * -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -7.2e+98) {
		tmp = t_1;
	} else if (t <= 1.32e-34) {
		tmp = x + z;
	} else if (t <= 9.2e+18) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -7.2e+98:
		tmp = t_1
	elif t <= 1.32e-34:
		tmp = x + z
	elif t <= 9.2e+18:
		tmp = y * -z
	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 <= -7.2e+98)
		tmp = t_1;
	elseif (t <= 1.32e-34)
		tmp = Float64(x + z);
	elseif (t <= 9.2e+18)
		tmp = Float64(y * Float64(-z));
	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 <= -7.2e+98)
		tmp = t_1;
	elseif (t <= 1.32e-34)
		tmp = x + z;
	elseif (t <= 9.2e+18)
		tmp = y * -z;
	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, -7.2e+98], t$95$1, If[LessEqual[t, 1.32e-34], N[(x + z), $MachinePrecision], If[LessEqual[t, 9.2e+18], N[(y * (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.19999999999999962e98 or 9.2e18 < t

   1. Initial program 90.3%

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

   3. Taylor expanded in b around 0 66.7%

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

   4. Taylor expanded in t around inf 48.0%

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

      1. associate-*r* 48.0%

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

      2. mul-1-neg 48.0%

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

   6. Simplified 48.0%

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

   if -7.19999999999999962e98 < t < 1.32e-34

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0 68.1%

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

   4. Taylor expanded in a around 0 50.9%

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

   5. Taylor expanded in y around 0 29.4%

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

      1. cancel-sign-sub-inv 29.4%

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

      2. metadata-eval 29.4%

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

      3. *-lft-identity 29.4%

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

   7. Simplified 29.4%

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

   if 1.32e-34 < t < 9.2e18

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 73.6%

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

   4. Taylor expanded in y around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. distribute-rgt-neg-in 63.5%

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

   6. Simplified 63.5%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-34}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+45} \lor \neg \left(t \leq 3.9 \cdot 10^{+19}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.2e+45) (not (<= t 3.9e+19))) (* t (- b a)) (- x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e+45) || !(t <= 3.9e+19)) {
		tmp = t * (b - a);
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.2d+45)) .or. (.not. (t <= 3.9d+19))) then
        tmp = t * (b - a)
    else
        tmp = x - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e+45) || !(t <= 3.9e+19)) {
		tmp = t * (b - a);
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.2e+45) or not (t <= 3.9e+19):
		tmp = t * (b - a)
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.2e+45) || !(t <= 3.9e+19))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.2e+45) || ~((t <= 3.9e+19)))
		tmp = t * (b - a);
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.2e+45], N[Not[LessEqual[t, 3.9e+19]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.19999999999999995e45 or 3.9e19 < t

   1. Initial program 91.0%

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

   3. Taylor expanded in t around inf 68.2%

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

   if -1.19999999999999995e45 < t < 3.9e19

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0 72.7%

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

   4. Taylor expanded in y around inf 48.4%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+45} \lor \neg \left(t \leq 3.9 \cdot 10^{+19}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+19} \lor \neg \left(y \leq 1.06 \cdot 10^{+68}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.2e+19) (not (<= y 1.06e+68))) (* y b) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.2e+19) || !(y <= 1.06e+68)) {
		tmp = y * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.2d+19)) .or. (.not. (y <= 1.06d+68))) then
        tmp = y * b
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.2e+19) || !(y <= 1.06e+68)) {
		tmp = y * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.2e+19) or not (y <= 1.06e+68):
		tmp = y * b
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.2e+19) || !(y <= 1.06e+68))
		tmp = Float64(y * b);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.2e+19) || ~((y <= 1.06e+68)))
		tmp = y * b;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.2e+19], N[Not[LessEqual[y, 1.06e+68]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e19 or 1.06e68 < y

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 67.6%

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

   4. Taylor expanded in b around inf 34.6%

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

   if -4.2e19 < y < 1.06e68

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0 71.6%

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

   4. Taylor expanded in a around 0 35.9%

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

   5. Taylor expanded in y around 0 31.5%

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

      1. cancel-sign-sub-inv 31.5%

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

      2. metadata-eval 31.5%

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

      3. *-lft-identity 31.5%

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

   7. Simplified 31.5%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+19} \lor \neg \left(y \leq 1.06 \cdot 10^{+68}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 24.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+137}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.4e+100) x (if (<= x 1.7e+137) (* y b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.4e+100) {
		tmp = x;
	} else if (x <= 1.7e+137) {
		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 (x <= (-3.4d+100)) then
        tmp = x
    else if (x <= 1.7d+137) 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 (x <= -3.4e+100) {
		tmp = x;
	} else if (x <= 1.7e+137) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.4e+100:
		tmp = x
	elif x <= 1.7e+137:
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.4e+100)
		tmp = x;
	elseif (x <= 1.7e+137)
		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 (x <= -3.4e+100)
		tmp = x;
	elseif (x <= 1.7e+137)
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.4e+100], x, If[LessEqual[x, 1.7e+137], N[(y * b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.39999999999999994e100 or 1.69999999999999993e137 < x

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf 39.6%

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

   if -3.39999999999999994e100 < x < 1.69999999999999993e137

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 36.8%

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

   4. Taylor expanded in b around inf 20.3%

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

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+137}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 20.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+197}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.6e+197) a (if (<= a 1.4e+140) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.6e+197) {
		tmp = a;
	} else if (a <= 1.4e+140) {
		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 <= (-6.6d+197)) then
        tmp = a
    else if (a <= 1.4d+140) 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 <= -6.6e+197) {
		tmp = a;
	} else if (a <= 1.4e+140) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.6e+197:
		tmp = a
	elif a <= 1.4e+140:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.6e+197)
		tmp = a;
	elseif (a <= 1.4e+140)
		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 <= -6.6e+197)
		tmp = a;
	elseif (a <= 1.4e+140)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.6e+197], a, If[LessEqual[a, 1.4e+140], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5999999999999993e197 or 1.39999999999999991e140 < a

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf 71.9%

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

   4. Taylor expanded in t around 0 25.0%

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

   if -6.5999999999999993e197 < a < 1.39999999999999991e140

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 19.5%

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

Alternative 22: 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 94.5%

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

3. Taylor expanded in a around inf 31.3%

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

4. Taylor expanded in t around 0 9.5%

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

Reproduce

herbie shell --seed 2024094 
(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)))