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

Percentage Accurate: 95.3% → 98.0%

Time: 18.6s

Alternatives: 25

Speedup: 0.5×

• 36.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 73.7%

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

4. Final simplification 98.5%

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

Alternative 2: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 73.7%

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

4. Final simplification 98.4%

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

Alternative 3: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-306}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+30}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+133} \lor \neg \left(y \leq 4.5 \cdot 10^{+170}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -6e+45)
     t_1
     (if (<= y -6.6e-49)
       (* t (- b a))
       (if (<= y 2e-306)
         (+ x (+ z a))
         (if (<= y 5e+30)
           (- x (* t a))
           (if (or (<= y 2.5e+133) (not (<= y 4.5e+170)))
             t_1
             (* a (- 1.0 t)))))))))

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 <= -6e+45) {
		tmp = t_1;
	} else if (y <= -6.6e-49) {
		tmp = t * (b - a);
	} else if (y <= 2e-306) {
		tmp = x + (z + a);
	} else if (y <= 5e+30) {
		tmp = x - (t * a);
	} else if ((y <= 2.5e+133) || !(y <= 4.5e+170)) {
		tmp = t_1;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-6d+45)) then
        tmp = t_1
    else if (y <= (-6.6d-49)) then
        tmp = t * (b - a)
    else if (y <= 2d-306) then
        tmp = x + (z + a)
    else if (y <= 5d+30) then
        tmp = x - (t * a)
    else if ((y <= 2.5d+133) .or. (.not. (y <= 4.5d+170))) then
        tmp = t_1
    else
        tmp = a * (1.0d0 - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -6e+45) {
		tmp = t_1;
	} else if (y <= -6.6e-49) {
		tmp = t * (b - a);
	} else if (y <= 2e-306) {
		tmp = x + (z + a);
	} else if (y <= 5e+30) {
		tmp = x - (t * a);
	} else if ((y <= 2.5e+133) || !(y <= 4.5e+170)) {
		tmp = t_1;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -6e+45:
		tmp = t_1
	elif y <= -6.6e-49:
		tmp = t * (b - a)
	elif y <= 2e-306:
		tmp = x + (z + a)
	elif y <= 5e+30:
		tmp = x - (t * a)
	elif (y <= 2.5e+133) or not (y <= 4.5e+170):
		tmp = t_1
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -6e+45)
		tmp = t_1;
	elseif (y <= -6.6e-49)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 2e-306)
		tmp = Float64(x + Float64(z + a));
	elseif (y <= 5e+30)
		tmp = Float64(x - Float64(t * a));
	elseif ((y <= 2.5e+133) || !(y <= 4.5e+170))
		tmp = t_1;
	else
		tmp = Float64(a * Float64(1.0 - t));
	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 <= -6e+45)
		tmp = t_1;
	elseif (y <= -6.6e-49)
		tmp = t * (b - a);
	elseif (y <= 2e-306)
		tmp = x + (z + a);
	elseif (y <= 5e+30)
		tmp = x - (t * a);
	elseif ((y <= 2.5e+133) || ~((y <= 4.5e+170)))
		tmp = t_1;
	else
		tmp = a * (1.0 - t);
	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, -6e+45], t$95$1, If[LessEqual[y, -6.6e-49], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-306], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+30], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.5e+133], N[Not[LessEqual[y, 4.5e+170]], $MachinePrecision]], t$95$1, N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.00000000000000021e45 or 4.9999999999999998e30 < y < 2.4999999999999998e133 or 4.50000000000000022e170 < y

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf 72.2%

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

   if -6.00000000000000021e45 < y < -6.6e-49

   1. Initial program 95.6%

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

   3. Taylor expanded in t around inf 50.4%

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

   if -6.6e-49 < y < 2.00000000000000006e-306

   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 y around 0 97.9%

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

   4. Taylor expanded in t around inf 91.2%

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

   5. Taylor expanded in t around 0 58.5%

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

      1. sub-neg 58.5%

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

      2. +-commutative 58.5%

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

      3. distribute-neg-in 58.5%

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

      4. mul-1-neg 58.5%

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

      5. remove-double-neg 58.5%

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

      6. mul-1-neg 58.5%

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

      7. remove-double-neg 58.5%

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

   7. Simplified 58.5%

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

   if 2.00000000000000006e-306 < y < 4.9999999999999998e30

   1. Initial program 92.8%

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

   3. Taylor expanded in b around 0 73.9%

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

   4. Taylor expanded in t around inf 55.6%

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

      1. *-commutative 55.6%

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

   6. Simplified 55.6%

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

   if 2.4999999999999998e133 < y < 4.50000000000000022e170

   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 a around inf 78.8%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-306}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+30}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+133} \lor \neg \left(y \leq 4.5 \cdot 10^{+170}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-104}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -3e+177)
     t_2
     (if (<= t -7.2e+53)
       t_1
       (if (<= t -5.9e+32)
         t_2
         (if (<= t 4.8e-277)
           t_1
           (if (<= t 1.32e-104)
             (+ x (+ z a))
             (if (<= t 1.75e+23) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3e+177) {
		tmp = t_2;
	} else if (t <= -7.2e+53) {
		tmp = t_1;
	} else if (t <= -5.9e+32) {
		tmp = t_2;
	} else if (t <= 4.8e-277) {
		tmp = t_1;
	} else if (t <= 1.32e-104) {
		tmp = x + (z + a);
	} else if (t <= 1.75e+23) {
		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 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-3d+177)) then
        tmp = t_2
    else if (t <= (-7.2d+53)) then
        tmp = t_1
    else if (t <= (-5.9d+32)) then
        tmp = t_2
    else if (t <= 4.8d-277) then
        tmp = t_1
    else if (t <= 1.32d-104) then
        tmp = x + (z + a)
    else if (t <= 1.75d+23) 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 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3e+177) {
		tmp = t_2;
	} else if (t <= -7.2e+53) {
		tmp = t_1;
	} else if (t <= -5.9e+32) {
		tmp = t_2;
	} else if (t <= 4.8e-277) {
		tmp = t_1;
	} else if (t <= 1.32e-104) {
		tmp = x + (z + a);
	} else if (t <= 1.75e+23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -3e+177:
		tmp = t_2
	elif t <= -7.2e+53:
		tmp = t_1
	elif t <= -5.9e+32:
		tmp = t_2
	elif t <= 4.8e-277:
		tmp = t_1
	elif t <= 1.32e-104:
		tmp = x + (z + a)
	elif t <= 1.75e+23:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3e+177)
		tmp = t_2;
	elseif (t <= -7.2e+53)
		tmp = t_1;
	elseif (t <= -5.9e+32)
		tmp = t_2;
	elseif (t <= 4.8e-277)
		tmp = t_1;
	elseif (t <= 1.32e-104)
		tmp = Float64(x + Float64(z + a));
	elseif (t <= 1.75e+23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -3e+177)
		tmp = t_2;
	elseif (t <= -7.2e+53)
		tmp = t_1;
	elseif (t <= -5.9e+32)
		tmp = t_2;
	elseif (t <= 4.8e-277)
		tmp = t_1;
	elseif (t <= 1.32e-104)
		tmp = x + (z + a);
	elseif (t <= 1.75e+23)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+177], t$95$2, If[LessEqual[t, -7.2e+53], t$95$1, If[LessEqual[t, -5.9e+32], t$95$2, If[LessEqual[t, 4.8e-277], t$95$1, If[LessEqual[t, 1.32e-104], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+23], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3e177 or -7.2e53 < t < -5.89999999999999965e32 or 1.7500000000000001e23 < t

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf 76.0%

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

   if -3e177 < t < -7.2e53 or -5.89999999999999965e32 < t < 4.8e-277 or 1.3199999999999999e-104 < t < 1.7500000000000001e23

   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 y around inf 54.1%

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

   if 4.8e-277 < t < 1.3199999999999999e-104

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in t around inf 55.6%

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

   5. Taylor expanded in t around 0 55.7%

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

      1. sub-neg 55.7%

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

      2. +-commutative 55.7%

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

      3. distribute-neg-in 55.7%

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

      4. mul-1-neg 55.7%

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

      5. remove-double-neg 55.7%

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

      6. mul-1-neg 55.7%

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

      7. remove-double-neg 55.7%

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

   7. Simplified 55.7%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-104}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-232}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+21}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -3e+177)
     t_2
     (if (<= t -6e+54)
       t_1
       (if (<= t -2.15e+30)
         t_2
         (if (<= t 1.45e-278)
           t_1
           (if (<= t 8.6e-232)
             (+ x (+ z a))
             (if (<= t 7.2e+21) (- x (* y z)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3e+177) {
		tmp = t_2;
	} else if (t <= -6e+54) {
		tmp = t_1;
	} else if (t <= -2.15e+30) {
		tmp = t_2;
	} else if (t <= 1.45e-278) {
		tmp = t_1;
	} else if (t <= 8.6e-232) {
		tmp = x + (z + a);
	} else if (t <= 7.2e+21) {
		tmp = x - (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 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-3d+177)) then
        tmp = t_2
    else if (t <= (-6d+54)) then
        tmp = t_1
    else if (t <= (-2.15d+30)) then
        tmp = t_2
    else if (t <= 1.45d-278) then
        tmp = t_1
    else if (t <= 8.6d-232) then
        tmp = x + (z + a)
    else if (t <= 7.2d+21) then
        tmp = x - (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 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3e+177) {
		tmp = t_2;
	} else if (t <= -6e+54) {
		tmp = t_1;
	} else if (t <= -2.15e+30) {
		tmp = t_2;
	} else if (t <= 1.45e-278) {
		tmp = t_1;
	} else if (t <= 8.6e-232) {
		tmp = x + (z + a);
	} else if (t <= 7.2e+21) {
		tmp = x - (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -3e+177:
		tmp = t_2
	elif t <= -6e+54:
		tmp = t_1
	elif t <= -2.15e+30:
		tmp = t_2
	elif t <= 1.45e-278:
		tmp = t_1
	elif t <= 8.6e-232:
		tmp = x + (z + a)
	elif t <= 7.2e+21:
		tmp = x - (y * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3e+177)
		tmp = t_2;
	elseif (t <= -6e+54)
		tmp = t_1;
	elseif (t <= -2.15e+30)
		tmp = t_2;
	elseif (t <= 1.45e-278)
		tmp = t_1;
	elseif (t <= 8.6e-232)
		tmp = Float64(x + Float64(z + a));
	elseif (t <= 7.2e+21)
		tmp = Float64(x - Float64(y * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -3e+177)
		tmp = t_2;
	elseif (t <= -6e+54)
		tmp = t_1;
	elseif (t <= -2.15e+30)
		tmp = t_2;
	elseif (t <= 1.45e-278)
		tmp = t_1;
	elseif (t <= 8.6e-232)
		tmp = x + (z + a);
	elseif (t <= 7.2e+21)
		tmp = x - (y * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+177], t$95$2, If[LessEqual[t, -6e+54], t$95$1, If[LessEqual[t, -2.15e+30], t$95$2, If[LessEqual[t, 1.45e-278], t$95$1, If[LessEqual[t, 8.6e-232], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+21], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3e177 or -5.9999999999999998e54 < t < -2.15e30 or 7.2e21 < t

   1. Initial program 91.8%

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

   3. Taylor expanded in t around inf 75.3%

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

   if -3e177 < t < -5.9999999999999998e54 or -2.15e30 < t < 1.45e-278

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 53.8%

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

   if 1.45e-278 < t < 8.5999999999999994e-232

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in t around inf 67.5%

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

   5. Taylor expanded in t around 0 67.5%

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

      1. sub-neg 67.5%

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

      2. +-commutative 67.5%

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

      3. distribute-neg-in 67.5%

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

      4. mul-1-neg 67.5%

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

      5. remove-double-neg 67.5%

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

      6. mul-1-neg 67.5%

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

      7. remove-double-neg 67.5%

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

   7. Simplified 67.5%

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

   if 8.5999999999999994e-232 < t < 7.2e21

   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 74.8%

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

   4. Taylor expanded in y around inf 58.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-232}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+21}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y + -1\right) \cdot z\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-99}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ y -1.0) z))) (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -6.6e+32)
     t_2
     (if (<= b 9e-279)
       t_1
       (if (<= b 1.5e-99)
         (- x (* (+ t -1.0) a))
         (if (<= b 8.4e+24) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -6.6e+32) {
		tmp = t_2;
	} else if (b <= 9e-279) {
		tmp = t_1;
	} else if (b <= 1.5e-99) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 8.4e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((y + (-1.0d0)) * z)
    t_2 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-6.6d+32)) then
        tmp = t_2
    else if (b <= 9d-279) then
        tmp = t_1
    else if (b <= 1.5d-99) then
        tmp = x - ((t + (-1.0d0)) * a)
    else if (b <= 8.4d+24) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -6.6e+32) {
		tmp = t_2;
	} else if (b <= 9e-279) {
		tmp = t_1;
	} else if (b <= 1.5e-99) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 8.4e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((y + -1.0) * z)
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -6.6e+32:
		tmp = t_2
	elif b <= 9e-279:
		tmp = t_1
	elif b <= 1.5e-99:
		tmp = x - ((t + -1.0) * a)
	elif b <= 8.4e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y + -1.0) * z))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -6.6e+32)
		tmp = t_2;
	elseif (b <= 9e-279)
		tmp = t_1;
	elseif (b <= 1.5e-99)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	elseif (b <= 8.4e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((y + -1.0) * z);
	t_2 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -6.6e+32)
		tmp = t_2;
	elseif (b <= 9e-279)
		tmp = t_1;
	elseif (b <= 1.5e-99)
		tmp = x - ((t + -1.0) * a);
	elseif (b <= 8.4e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.6e+32], t$95$2, If[LessEqual[b, 9e-279], t$95$1, If[LessEqual[b, 1.5e-99], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.4e+24], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.60000000000000039e32 or 8.4000000000000005e24 < b

   1. Initial program 86.7%

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

   3. Taylor expanded in a around 0 80.0%

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

   4. Taylor expanded in z around 0 75.2%

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

   if -6.60000000000000039e32 < b < 8.99999999999999991e-279 or 1.50000000000000003e-99 < b < 8.4000000000000005e24

   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 89.6%

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

   4. Taylor expanded in a around 0 67.0%

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

   if 8.99999999999999991e-279 < b < 1.50000000000000003e-99

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in a around inf 75.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+32}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-279}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-99}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+24}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y + -1\right) \cdot z\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-99}:\\ \;\;\;\;x + \left(z - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ y -1.0) z))) (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.2e+36)
     t_2
     (if (<= b 2.3e-275)
       t_1
       (if (<= b 4e-99)
         (+ x (- z (* (+ t -1.0) a)))
         (if (<= b 7.2e+25) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.2e+36) {
		tmp = t_2;
	} else if (b <= 2.3e-275) {
		tmp = t_1;
	} else if (b <= 4e-99) {
		tmp = x + (z - ((t + -1.0) * a));
	} else if (b <= 7.2e+25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((y + (-1.0d0)) * z)
    t_2 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-1.2d+36)) then
        tmp = t_2
    else if (b <= 2.3d-275) then
        tmp = t_1
    else if (b <= 4d-99) then
        tmp = x + (z - ((t + (-1.0d0)) * a))
    else if (b <= 7.2d+25) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.2e+36) {
		tmp = t_2;
	} else if (b <= 2.3e-275) {
		tmp = t_1;
	} else if (b <= 4e-99) {
		tmp = x + (z - ((t + -1.0) * a));
	} else if (b <= 7.2e+25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((y + -1.0) * z)
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -1.2e+36:
		tmp = t_2
	elif b <= 2.3e-275:
		tmp = t_1
	elif b <= 4e-99:
		tmp = x + (z - ((t + -1.0) * a))
	elif b <= 7.2e+25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y + -1.0) * z))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.2e+36)
		tmp = t_2;
	elseif (b <= 2.3e-275)
		tmp = t_1;
	elseif (b <= 4e-99)
		tmp = Float64(x + Float64(z - Float64(Float64(t + -1.0) * a)));
	elseif (b <= 7.2e+25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((y + -1.0) * z);
	t_2 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -1.2e+36)
		tmp = t_2;
	elseif (b <= 2.3e-275)
		tmp = t_1;
	elseif (b <= 4e-99)
		tmp = x + (z - ((t + -1.0) * a));
	elseif (b <= 7.2e+25)
		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[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e+36], t$95$2, If[LessEqual[b, 2.3e-275], t$95$1, If[LessEqual[b, 4e-99], N[(x + N[(z - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e+25], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.19999999999999996e36 or 7.20000000000000031e25 < b

   1. Initial program 86.7%

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

   3. Taylor expanded in a around 0 80.0%

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

   4. Taylor expanded in z around 0 75.2%

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

   if -1.19999999999999996e36 < b < 2.2999999999999999e-275 or 4.0000000000000001e-99 < b < 7.20000000000000031e25

   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 89.6%

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

   4. Taylor expanded in a around 0 67.0%

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

   if 2.2999999999999999e-275 < b < 4.0000000000000001e-99

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in y around 0 80.6%

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

      1. +-commutative 80.6%

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

      2. sub-neg 80.6%

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

      3. metadata-eval 80.6%

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

      4. mul-1-neg 80.6%

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

      5. unsub-neg 80.6%

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

   6. Simplified 80.6%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+36}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-275}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-99}:\\ \;\;\;\;x + \left(z - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+25}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(\left(y + -1\right) \cdot z - a\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-104}:\\ \;\;\;\;x + \left(z - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (- (* (+ y -1.0) z) a))) (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.25e+40)
     t_2
     (if (<= b 1.05e-278)
       t_1
       (if (<= b 1.6e-104)
         (+ x (- z (* (+ t -1.0) a)))
         (if (<= b 8.2e+46) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (((y + -1.0) * z) - a);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.25e+40) {
		tmp = t_2;
	} else if (b <= 1.05e-278) {
		tmp = t_1;
	} else if (b <= 1.6e-104) {
		tmp = x + (z - ((t + -1.0) * a));
	} else if (b <= 8.2e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (((y + (-1.0d0)) * z) - a)
    t_2 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-1.25d+40)) then
        tmp = t_2
    else if (b <= 1.05d-278) then
        tmp = t_1
    else if (b <= 1.6d-104) then
        tmp = x + (z - ((t + (-1.0d0)) * a))
    else if (b <= 8.2d+46) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (((y + -1.0) * z) - a);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.25e+40) {
		tmp = t_2;
	} else if (b <= 1.05e-278) {
		tmp = t_1;
	} else if (b <= 1.6e-104) {
		tmp = x + (z - ((t + -1.0) * a));
	} else if (b <= 8.2e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (((y + -1.0) * z) - a)
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -1.25e+40:
		tmp = t_2
	elif b <= 1.05e-278:
		tmp = t_1
	elif b <= 1.6e-104:
		tmp = x + (z - ((t + -1.0) * a))
	elif b <= 8.2e+46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(Float64(y + -1.0) * z) - a))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.25e+40)
		tmp = t_2;
	elseif (b <= 1.05e-278)
		tmp = t_1;
	elseif (b <= 1.6e-104)
		tmp = Float64(x + Float64(z - Float64(Float64(t + -1.0) * a)));
	elseif (b <= 8.2e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (((y + -1.0) * z) - a);
	t_2 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -1.25e+40)
		tmp = t_2;
	elseif (b <= 1.05e-278)
		tmp = t_1;
	elseif (b <= 1.6e-104)
		tmp = x + (z - ((t + -1.0) * a));
	elseif (b <= 8.2e+46)
		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[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+40], t$95$2, If[LessEqual[b, 1.05e-278], t$95$1, If[LessEqual[b, 1.6e-104], N[(x + N[(z - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+46], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25000000000000001e40 or 8.19999999999999999e46 < b

   1. Initial program 86.1%

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

   3. Taylor expanded in a around 0 82.6%

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

   4. Taylor expanded in z around 0 77.6%

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

   if -1.25000000000000001e40 < b < 1.05000000000000007e-278 or 1.59999999999999994e-104 < b < 8.19999999999999999e46

   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 89.3%

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

   4. Taylor expanded in t around 0 73.9%

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

      1. +-commutative 73.9%

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

      2. sub-neg 73.9%

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

      3. metadata-eval 73.9%

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

      4. mul-1-neg 73.9%

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

      5. unsub-neg 73.9%

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

   6. Simplified 73.9%

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

   if 1.05000000000000007e-278 < b < 1.59999999999999994e-104

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in y around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. sub-neg 80.2%

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

      3. metadata-eval 80.2%

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

      4. mul-1-neg 80.2%

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

      5. unsub-neg 80.2%

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

   6. Simplified 80.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+40}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-278}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - a\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-104}:\\ \;\;\;\;x + \left(z - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+46}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-106}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -4.5e+35)
     t_2
     (if (<= b 1.45e-273)
       t_1
       (if (<= b 7.4e-106) (- x (* t a)) (if (<= b 1.2e+26) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -4.5e+35) {
		tmp = t_2;
	} else if (b <= 1.45e-273) {
		tmp = t_1;
	} else if (b <= 7.4e-106) {
		tmp = x - (t * a);
	} else if (b <= 1.2e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-4.5d+35)) then
        tmp = t_2
    else if (b <= 1.45d-273) then
        tmp = t_1
    else if (b <= 7.4d-106) then
        tmp = x - (t * a)
    else if (b <= 1.2d+26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -4.5e+35) {
		tmp = t_2;
	} else if (b <= 1.45e-273) {
		tmp = t_1;
	} else if (b <= 7.4e-106) {
		tmp = x - (t * a);
	} else if (b <= 1.2e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -4.5e+35:
		tmp = t_2
	elif b <= 1.45e-273:
		tmp = t_1
	elif b <= 7.4e-106:
		tmp = x - (t * a)
	elif b <= 1.2e+26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -4.5e+35)
		tmp = t_2;
	elseif (b <= 1.45e-273)
		tmp = t_1;
	elseif (b <= 7.4e-106)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 1.2e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -4.5e+35)
		tmp = t_2;
	elseif (b <= 1.45e-273)
		tmp = t_1;
	elseif (b <= 7.4e-106)
		tmp = x - (t * a);
	elseif (b <= 1.2e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4.5e+35], t$95$2, If[LessEqual[b, 1.45e-273], t$95$1, If[LessEqual[b, 7.4e-106], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e+26], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.4999999999999997e35 or 1.20000000000000002e26 < b

   1. Initial program 86.7%

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

   3. Taylor expanded in b around inf 69.1%

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

   if -4.4999999999999997e35 < b < 1.44999999999999993e-273 or 7.39999999999999959e-106 < b < 1.20000000000000002e26

   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 89.7%

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

   4. Taylor expanded in y around inf 57.6%

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

   if 1.44999999999999993e-273 < b < 7.39999999999999959e-106

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in t around inf 65.6%

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

      1. *-commutative 65.6%

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

   6. Simplified 65.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-273}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-106}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+26}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-99}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -1.8e+30)
     t_2
     (if (<= b 2.9e-277)
       t_1
       (if (<= b 1.9e-99)
         (- x (* (+ t -1.0) a))
         (if (<= b 4.4e+24) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.8e+30) {
		tmp = t_2;
	} else if (b <= 2.9e-277) {
		tmp = t_1;
	} else if (b <= 1.9e-99) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 4.4e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-1.8d+30)) then
        tmp = t_2
    else if (b <= 2.9d-277) then
        tmp = t_1
    else if (b <= 1.9d-99) then
        tmp = x - ((t + (-1.0d0)) * a)
    else if (b <= 4.4d+24) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.8e+30) {
		tmp = t_2;
	} else if (b <= 2.9e-277) {
		tmp = t_1;
	} else if (b <= 1.9e-99) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 4.4e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1.8e+30:
		tmp = t_2
	elif b <= 2.9e-277:
		tmp = t_1
	elif b <= 1.9e-99:
		tmp = x - ((t + -1.0) * a)
	elif b <= 4.4e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.8e+30)
		tmp = t_2;
	elseif (b <= 2.9e-277)
		tmp = t_1;
	elseif (b <= 1.9e-99)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	elseif (b <= 4.4e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.8e+30)
		tmp = t_2;
	elseif (b <= 2.9e-277)
		tmp = t_1;
	elseif (b <= 1.9e-99)
		tmp = x - ((t + -1.0) * a);
	elseif (b <= 4.4e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.8e+30], t$95$2, If[LessEqual[b, 2.9e-277], t$95$1, If[LessEqual[b, 1.9e-99], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e+24], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8000000000000001e30 or 4.40000000000000003e24 < b

   1. Initial program 86.7%

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

   3. Taylor expanded in b around inf 69.1%

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

   if -1.8000000000000001e30 < b < 2.89999999999999977e-277 or 1.8999999999999998e-99 < b < 4.40000000000000003e24

   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 89.6%

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

   4. Taylor expanded in y around inf 58.2%

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

   if 2.89999999999999977e-277 < b < 1.8999999999999998e-99

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in a around inf 75.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+30}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-277}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-99}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+24}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y + -1\right) \cdot z\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-99}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ y -1.0) z))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -1.65e+114)
     t_2
     (if (<= b 2.7e-275)
       t_1
       (if (<= b 3.5e-99)
         (- x (* (+ t -1.0) a))
         (if (<= b 2.4e+24) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.65e+114) {
		tmp = t_2;
	} else if (b <= 2.7e-275) {
		tmp = t_1;
	} else if (b <= 3.5e-99) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 2.4e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((y + (-1.0d0)) * z)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-1.65d+114)) then
        tmp = t_2
    else if (b <= 2.7d-275) then
        tmp = t_1
    else if (b <= 3.5d-99) then
        tmp = x - ((t + (-1.0d0)) * a)
    else if (b <= 2.4d+24) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.65e+114) {
		tmp = t_2;
	} else if (b <= 2.7e-275) {
		tmp = t_1;
	} else if (b <= 3.5e-99) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 2.4e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((y + -1.0) * z)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1.65e+114:
		tmp = t_2
	elif b <= 2.7e-275:
		tmp = t_1
	elif b <= 3.5e-99:
		tmp = x - ((t + -1.0) * a)
	elif b <= 2.4e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y + -1.0) * z))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.65e+114)
		tmp = t_2;
	elseif (b <= 2.7e-275)
		tmp = t_1;
	elseif (b <= 3.5e-99)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	elseif (b <= 2.4e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((y + -1.0) * z);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.65e+114)
		tmp = t_2;
	elseif (b <= 2.7e-275)
		tmp = t_1;
	elseif (b <= 3.5e-99)
		tmp = x - ((t + -1.0) * a);
	elseif (b <= 2.4e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.65e+114], t$95$2, If[LessEqual[b, 2.7e-275], t$95$1, If[LessEqual[b, 3.5e-99], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e+24], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.65e114 or 2.4000000000000001e24 < b

   1. Initial program 86.6%

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

   3. Taylor expanded in b around inf 74.0%

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

   if -1.65e114 < b < 2.69999999999999993e-275 or 3.4999999999999999e-99 < b < 2.4000000000000001e24

   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 85.7%

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

   4. Taylor expanded in a around 0 64.7%

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

   if 2.69999999999999993e-275 < b < 3.4999999999999999e-99

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in a around inf 75.9%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+114}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-275}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-99}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+177} \lor \neg \left(t \leq -3.7 \cdot 10^{+56} \lor \neg \left(t \leq -1.65 \cdot 10^{+31}\right) \land t \leq 1.85 \cdot 10^{+23}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3e+177)
         (not
          (or (<= t -3.7e+56) (and (not (<= t -1.65e+31)) (<= t 1.85e+23)))))
   (* t (- b a))
   (* y (- b z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e+177) || !((t <= -3.7e+56) || (!(t <= -1.65e+31) && (t <= 1.85e+23)))) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3d+177)) .or. (.not. (t <= (-3.7d+56)) .or. (.not. (t <= (-1.65d+31))) .and. (t <= 1.85d+23))) then
        tmp = t * (b - a)
    else
        tmp = y * (b - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e+177) || !((t <= -3.7e+56) || (!(t <= -1.65e+31) && (t <= 1.85e+23)))) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3e+177) or not ((t <= -3.7e+56) or (not (t <= -1.65e+31) and (t <= 1.85e+23))):
		tmp = t * (b - a)
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3e+177) || !((t <= -3.7e+56) || (!(t <= -1.65e+31) && (t <= 1.85e+23))))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3e+177) || ~(((t <= -3.7e+56) || (~((t <= -1.65e+31)) && (t <= 1.85e+23)))))
		tmp = t * (b - a);
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3e+177], N[Not[Or[LessEqual[t, -3.7e+56], And[N[Not[LessEqual[t, -1.65e+31]], $MachinePrecision], LessEqual[t, 1.85e+23]]]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e177 or -3.69999999999999997e56 < t < -1.64999999999999996e31 or 1.85000000000000006e23 < t

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf 76.0%

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

   if -3e177 < t < -3.69999999999999997e56 or -1.64999999999999996e31 < t < 1.85000000000000006e23

   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 y around inf 49.8%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+177} \lor \neg \left(t \leq -3.7 \cdot 10^{+56} \lor \neg \left(t \leq -1.65 \cdot 10^{+31}\right) \land t \leq 1.85 \cdot 10^{+23}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* y (- z))))
   (if (<= z -6.5e+34)
     t_2
     (if (<= z -4.8e-49)
       t_1
       (if (<= z -4.3e-259) x (if (<= z 1.1e+150) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = y * -z;
	double tmp;
	if (z <= -6.5e+34) {
		tmp = t_2;
	} else if (z <= -4.8e-49) {
		tmp = t_1;
	} else if (z <= -4.3e-259) {
		tmp = x;
	} else if (z <= 1.1e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = y * -z
    if (z <= (-6.5d+34)) then
        tmp = t_2
    else if (z <= (-4.8d-49)) then
        tmp = t_1
    else if (z <= (-4.3d-259)) then
        tmp = x
    else if (z <= 1.1d+150) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = y * -z;
	double tmp;
	if (z <= -6.5e+34) {
		tmp = t_2;
	} else if (z <= -4.8e-49) {
		tmp = t_1;
	} else if (z <= -4.3e-259) {
		tmp = x;
	} else if (z <= 1.1e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = y * -z
	tmp = 0
	if z <= -6.5e+34:
		tmp = t_2
	elif z <= -4.8e-49:
		tmp = t_1
	elif z <= -4.3e-259:
		tmp = x
	elif z <= 1.1e+150:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -6.5e+34)
		tmp = t_2;
	elseif (z <= -4.8e-49)
		tmp = t_1;
	elseif (z <= -4.3e-259)
		tmp = x;
	elseif (z <= 1.1e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = y * -z;
	tmp = 0.0;
	if (z <= -6.5e+34)
		tmp = t_2;
	elseif (z <= -4.8e-49)
		tmp = t_1;
	elseif (z <= -4.3e-259)
		tmp = x;
	elseif (z <= 1.1e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -6.5e+34], t$95$2, If[LessEqual[z, -4.8e-49], t$95$1, If[LessEqual[z, -4.3e-259], x, If[LessEqual[z, 1.1e+150], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.50000000000000017e34 or 1.1e150 < z

   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 z around inf 60.5%

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

   4. Taylor expanded in y around inf 49.1%

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

      1. mul-1-neg 49.1%

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

      2. distribute-rgt-neg-in 49.1%

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

   6. Simplified 49.1%

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

   if -6.50000000000000017e34 < z < -4.79999999999999985e-49 or -4.3000000000000001e-259 < z < 1.1e150

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf 45.9%

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

   if -4.79999999999999985e-49 < z < -4.3000000000000001e-259

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 36.8%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-49}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+25}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -2e+114)
     t_1
     (if (<= b 2.9e+25)
       (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))
       (+ t_1 (* a (- 1.0 t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2e+114) {
		tmp = t_1;
	} else if (b <= 2.9e+25) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else {
		tmp = t_1 + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-2d+114)) then
        tmp = t_1
    else if (b <= 2.9d+25) then
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    else
        tmp = t_1 + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2e+114) {
		tmp = t_1;
	} else if (b <= 2.9e+25) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else {
		tmp = t_1 + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -2e+114:
		tmp = t_1
	elif b <= 2.9e+25:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	else:
		tmp = t_1 + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -2e+114)
		tmp = t_1;
	elseif (b <= 2.9e+25)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	else
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -2e+114)
		tmp = t_1;
	elseif (b <= 2.9e+25)
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	else
		tmp = t_1 + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+114], t$95$1, If[LessEqual[b, 2.9e+25], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2e114

   1. Initial program 78.9%

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

   3. Taylor expanded in a around 0 78.5%

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

   4. Taylor expanded in z around 0 85.0%

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

   if -2e114 < b < 2.8999999999999999e25

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0 89.8%

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

   if 2.8999999999999999e25 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 86.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+114}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+25}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+39}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+25}:\\ \;\;\;\;x + \left(t_1 - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -2.2e+39)
     (+ t_2 t_1)
     (if (<= b 2.55e+25)
       (+ x (- t_1 (* (+ t -1.0) a)))
       (+ t_2 (* a (- 1.0 t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.2e+39) {
		tmp = t_2 + t_1;
	} else if (b <= 2.55e+25) {
		tmp = x + (t_1 - ((t + -1.0) * a));
	} else {
		tmp = t_2 + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-2.2d+39)) then
        tmp = t_2 + t_1
    else if (b <= 2.55d+25) then
        tmp = x + (t_1 - ((t + (-1.0d0)) * a))
    else
        tmp = t_2 + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.2e+39) {
		tmp = t_2 + t_1;
	} else if (b <= 2.55e+25) {
		tmp = x + (t_1 - ((t + -1.0) * a));
	} else {
		tmp = t_2 + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -2.2e+39:
		tmp = t_2 + t_1
	elif b <= 2.55e+25:
		tmp = x + (t_1 - ((t + -1.0) * a))
	else:
		tmp = t_2 + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -2.2e+39)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 2.55e+25)
		tmp = Float64(x + Float64(t_1 - Float64(Float64(t + -1.0) * a)));
	else
		tmp = Float64(t_2 + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -2.2e+39)
		tmp = t_2 + t_1;
	elseif (b <= 2.55e+25)
		tmp = x + (t_1 - ((t + -1.0) * a));
	else
		tmp = t_2 + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+39], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 2.55e+25], N[(x + N[(t$95$1 - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2000000000000001e39

   1. Initial program 81.1%

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

   3. Taylor expanded in a around 0 81.0%

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

   if -2.2000000000000001e39 < b < 2.5500000000000002e25

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 93.0%

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

   if 2.5500000000000002e25 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 86.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+39}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+25}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+39}:\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+26}:\\ \;\;\;\;\left(x - y \cdot z\right) - \left(\left(t + -1\right) \cdot a - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -7.4e+39)
     (+ t_1 (* z (- 1.0 y)))
     (if (<= b 1.85e+26)
       (- (- x (* y z)) (- (* (+ t -1.0) a) z))
       (+ t_1 (* a (- 1.0 t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -7.4e+39) {
		tmp = t_1 + (z * (1.0 - y));
	} else if (b <= 1.85e+26) {
		tmp = (x - (y * z)) - (((t + -1.0) * a) - z);
	} else {
		tmp = t_1 + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-7.4d+39)) then
        tmp = t_1 + (z * (1.0d0 - y))
    else if (b <= 1.85d+26) then
        tmp = (x - (y * z)) - (((t + (-1.0d0)) * a) - z)
    else
        tmp = t_1 + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -7.4e+39) {
		tmp = t_1 + (z * (1.0 - y));
	} else if (b <= 1.85e+26) {
		tmp = (x - (y * z)) - (((t + -1.0) * a) - z);
	} else {
		tmp = t_1 + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -7.4e+39:
		tmp = t_1 + (z * (1.0 - y))
	elif b <= 1.85e+26:
		tmp = (x - (y * z)) - (((t + -1.0) * a) - z)
	else:
		tmp = t_1 + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -7.4e+39)
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	elseif (b <= 1.85e+26)
		tmp = Float64(Float64(x - Float64(y * z)) - Float64(Float64(Float64(t + -1.0) * a) - z));
	else
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -7.4e+39)
		tmp = t_1 + (z * (1.0 - y));
	elseif (b <= 1.85e+26)
		tmp = (x - (y * z)) - (((t + -1.0) * a) - z);
	else
		tmp = t_1 + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e+39], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e+26], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.40000000000000025e39

   1. Initial program 81.1%

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

   3. Taylor expanded in a around 0 81.0%

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

   if -7.40000000000000025e39 < b < 1.84999999999999994e26

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in b around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   6. Simplified 93.0%

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

   if 1.84999999999999994e26 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 86.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+39}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+26}:\\ \;\;\;\;\left(x - y \cdot z\right) - \left(\left(t + -1\right) \cdot a - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 27.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+119}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-111}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= b -3.4e+119)
     (* t b)
     (if (<= b 1.1e-138)
       t_1
       (if (<= b 5.7e-111) (+ x z) (if (<= b 1.55e+23) t_1 (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (b <= -3.4e+119) {
		tmp = t * b;
	} else if (b <= 1.1e-138) {
		tmp = t_1;
	} else if (b <= 5.7e-111) {
		tmp = x + z;
	} else if (b <= 1.55e+23) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (b <= (-3.4d+119)) then
        tmp = t * b
    else if (b <= 1.1d-138) then
        tmp = t_1
    else if (b <= 5.7d-111) then
        tmp = x + z
    else if (b <= 1.55d+23) then
        tmp = t_1
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (b <= -3.4e+119) {
		tmp = t * b;
	} else if (b <= 1.1e-138) {
		tmp = t_1;
	} else if (b <= 5.7e-111) {
		tmp = x + z;
	} else if (b <= 1.55e+23) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if b <= -3.4e+119:
		tmp = t * b
	elif b <= 1.1e-138:
		tmp = t_1
	elif b <= 5.7e-111:
		tmp = x + z
	elif b <= 1.55e+23:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (b <= -3.4e+119)
		tmp = Float64(t * b);
	elseif (b <= 1.1e-138)
		tmp = t_1;
	elseif (b <= 5.7e-111)
		tmp = Float64(x + z);
	elseif (b <= 1.55e+23)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (b <= -3.4e+119)
		tmp = t * b;
	elseif (b <= 1.1e-138)
		tmp = t_1;
	elseif (b <= 5.7e-111)
		tmp = x + z;
	elseif (b <= 1.55e+23)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[b, -3.4e+119], N[(t * b), $MachinePrecision], If[LessEqual[b, 1.1e-138], t$95$1, If[LessEqual[b, 5.7e-111], N[(x + z), $MachinePrecision], If[LessEqual[b, 1.55e+23], t$95$1, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.40000000000000013e119 or 1.54999999999999985e23 < b

   1. Initial program 87.4%

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

   3. Taylor expanded in a around 0 79.8%

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

   4. Taylor expanded in t around inf 40.1%

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

   if -3.40000000000000013e119 < b < 1.0999999999999999e-138 or 5.7e-111 < b < 1.54999999999999985e23

   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 z around inf 42.8%

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

   4. Taylor expanded in y around inf 35.6%

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

      1. mul-1-neg 35.6%

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

      2. distribute-rgt-neg-in 35.6%

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

   6. Simplified 35.6%

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

   if 1.0999999999999999e-138 < b < 5.7e-111

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in a around 0 40.1%

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

   5. Taylor expanded in y around 0 39.5%

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

      1. sub-neg 39.5%

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

      2. mul-1-neg 39.5%

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

      3. remove-double-neg 39.5%

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

      4. +-commutative 39.5%

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

   7. Simplified 39.5%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+119}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-111}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 26.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-260}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))) (t_2 (* y (- z))))
   (if (<= z -6e+34)
     t_2
     (if (<= z -2.2e-46)
       t_1
       (if (<= z -5e-260) x (if (<= z 1.1e+150) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double t_2 = y * -z;
	double tmp;
	if (z <= -6e+34) {
		tmp = t_2;
	} else if (z <= -2.2e-46) {
		tmp = t_1;
	} else if (z <= -5e-260) {
		tmp = x;
	} else if (z <= 1.1e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * -a
    t_2 = y * -z
    if (z <= (-6d+34)) then
        tmp = t_2
    else if (z <= (-2.2d-46)) then
        tmp = t_1
    else if (z <= (-5d-260)) then
        tmp = x
    else if (z <= 1.1d+150) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double t_2 = y * -z;
	double tmp;
	if (z <= -6e+34) {
		tmp = t_2;
	} else if (z <= -2.2e-46) {
		tmp = t_1;
	} else if (z <= -5e-260) {
		tmp = x;
	} else if (z <= 1.1e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	t_2 = y * -z
	tmp = 0
	if z <= -6e+34:
		tmp = t_2
	elif z <= -2.2e-46:
		tmp = t_1
	elif z <= -5e-260:
		tmp = x
	elif z <= 1.1e+150:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	t_2 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -6e+34)
		tmp = t_2;
	elseif (z <= -2.2e-46)
		tmp = t_1;
	elseif (z <= -5e-260)
		tmp = x;
	elseif (z <= 1.1e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	t_2 = y * -z;
	tmp = 0.0;
	if (z <= -6e+34)
		tmp = t_2;
	elseif (z <= -2.2e-46)
		tmp = t_1;
	elseif (z <= -5e-260)
		tmp = x;
	elseif (z <= 1.1e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -6e+34], t$95$2, If[LessEqual[z, -2.2e-46], t$95$1, If[LessEqual[z, -5e-260], x, If[LessEqual[z, 1.1e+150], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.00000000000000037e34 or 1.1e150 < z

   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 z around inf 60.5%

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

   4. Taylor expanded in y around inf 49.1%

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

      1. mul-1-neg 49.1%

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

      2. distribute-rgt-neg-in 49.1%

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

   6. Simplified 49.1%

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

   if -6.00000000000000037e34 < z < -2.2000000000000001e-46 or -5.0000000000000003e-260 < z < 1.1e150

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf 45.9%

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

   4. Taylor expanded in t around inf 35.4%

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

      1. associate-*r* 35.4%

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

      2. mul-1-neg 35.4%

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

   6. Simplified 35.4%

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

   if -2.2000000000000001e-46 < z < -5.0000000000000003e-260

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 36.8%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-260}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+114} \lor \neg \left(b \leq 4.6 \cdot 10^{+47}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.9e+114) (not (<= b 4.6e+47)))
   (+ x (* (- (+ y t) 2.0) b))
   (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+114) || !(b <= 4.6e+47)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.9d+114)) .or. (.not. (b <= 4.6d+47))) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+114) || !(b <= 4.6e+47)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.9e+114) or not (b <= 4.6e+47):
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.9e+114) || !(b <= 4.6e+47))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.9e+114) || ~((b <= 4.6e+47)))
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.9e+114], N[Not[LessEqual[b, 4.6e+47]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.9e114 or 4.5999999999999997e47 < b

   1. Initial program 86.0%

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

   3. Taylor expanded in a around 0 81.9%

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

   4. Taylor expanded in z around 0 81.2%

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

   if -1.9e114 < b < 4.5999999999999997e47

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0 89.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+114} \lor \neg \left(b \leq 4.6 \cdot 10^{+47}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 46.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.3e+19)
     t_1
     (if (<= t -1.55e-251)
       (* y (- z))
       (if (<= t 4.1e+22) (* b (- y 2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.3e+19) {
		tmp = t_1;
	} else if (t <= -1.55e-251) {
		tmp = y * -z;
	} else if (t <= 4.1e+22) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-4.3d+19)) then
        tmp = t_1
    else if (t <= (-1.55d-251)) then
        tmp = y * -z
    else if (t <= 4.1d+22) then
        tmp = b * (y - 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.3e+19) {
		tmp = t_1;
	} else if (t <= -1.55e-251) {
		tmp = y * -z;
	} else if (t <= 4.1e+22) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.3e+19:
		tmp = t_1
	elif t <= -1.55e-251:
		tmp = y * -z
	elif t <= 4.1e+22:
		tmp = b * (y - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.3e+19)
		tmp = t_1;
	elseif (t <= -1.55e-251)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 4.1e+22)
		tmp = Float64(b * Float64(y - 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.3e+19)
		tmp = t_1;
	elseif (t <= -1.55e-251)
		tmp = y * -z;
	elseif (t <= 4.1e+22)
		tmp = b * (y - 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e+19], t$95$1, If[LessEqual[t, -1.55e-251], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 4.1e+22], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3e19 or 4.09999999999999979e22 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf 68.3%

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

   if -4.3e19 < t < -1.55000000000000001e-251

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf 54.0%

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

   4. Taylor expanded in y around inf 41.5%

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

      1. mul-1-neg 41.5%

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

      2. distribute-rgt-neg-in 41.5%

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

   6. Simplified 41.5%

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

   if -1.55000000000000001e-251 < t < 4.09999999999999979e22

   1. Initial program 98.7%

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

   3. Taylor expanded in b around inf 32.2%

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

   4. Taylor expanded in t around 0 32.2%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 23.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-227}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+232}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.4e+110)
   x
   (if (<= x 1.55e-227) (* y b) (if (<= x 2.35e+232) (* t b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.4e+110) {
		tmp = x;
	} else if (x <= 1.55e-227) {
		tmp = y * b;
	} else if (x <= 2.35e+232) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.4d+110)) then
        tmp = x
    else if (x <= 1.55d-227) then
        tmp = y * b
    else if (x <= 2.35d+232) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.4e+110) {
		tmp = x;
	} else if (x <= 1.55e-227) {
		tmp = y * b;
	} else if (x <= 2.35e+232) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.4e+110:
		tmp = x
	elif x <= 1.55e-227:
		tmp = y * b
	elif x <= 2.35e+232:
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.4e+110)
		tmp = x;
	elseif (x <= 1.55e-227)
		tmp = Float64(y * b);
	elseif (x <= 2.35e+232)
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.4e+110)
		tmp = x;
	elseif (x <= 1.55e-227)
		tmp = y * b;
	elseif (x <= 2.35e+232)
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.4e+110], x, If[LessEqual[x, 1.55e-227], N[(y * b), $MachinePrecision], If[LessEqual[x, 2.35e+232], N[(t * b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.40000000000000012e110 or 2.34999999999999996e232 < x

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf 52.7%

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

   if -2.40000000000000012e110 < x < 1.5499999999999999e-227

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 42.1%

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

   4. Taylor expanded in b around inf 23.3%

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

   if 1.5499999999999999e-227 < x < 2.34999999999999996e232

   1. Initial program 92.4%

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

   3. Taylor expanded in a around 0 79.0%

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

   4. Taylor expanded in t around inf 28.0%

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

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-227}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+232}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 26.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+35} \lor \neg \left(b \leq 1.9 \cdot 10^{+25}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.1e+35) (not (<= b 1.9e+25))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.1e+35) || !(b <= 1.9e+25)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.1d+35)) .or. (.not. (b <= 1.9d+25))) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.1e+35) || !(b <= 1.9e+25)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.1e+35) or not (b <= 1.9e+25):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.1e+35) || !(b <= 1.9e+25))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.1e+35) || ~((b <= 1.9e+25)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.1e+35], N[Not[LessEqual[b, 1.9e+25]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -3.09999999999999987e35 or 1.9e25 < b

   1. Initial program 86.7%

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

   3. Taylor expanded in a around 0 80.0%

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

   4. Taylor expanded in t around inf 37.7%

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

   if -3.09999999999999987e35 < b < 1.9e25

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 19.9%

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

4. Final simplification 27.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+35} \lor \neg \left(b \leq 1.9 \cdot 10^{+25}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 33.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+114} \lor \neg \left(b \leq 4.1 \cdot 10^{+23}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.7e+114) (not (<= b 4.1e+23))) (* t b) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.7e+114) || !(b <= 4.1e+23)) {
		tmp = t * 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 ((b <= (-1.7d+114)) .or. (.not. (b <= 4.1d+23))) then
        tmp = t * 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 ((b <= -1.7e+114) || !(b <= 4.1e+23)) {
		tmp = t * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.7e+114) or not (b <= 4.1e+23):
		tmp = t * b
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.7e+114) || !(b <= 4.1e+23))
		tmp = Float64(t * 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 ((b <= -1.7e+114) || ~((b <= 4.1e+23)))
		tmp = t * b;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.7e+114], N[Not[LessEqual[b, 4.1e+23]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7e114 or 4.09999999999999996e23 < b

   1. Initial program 86.6%

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

   3. Taylor expanded in a around 0 79.6%

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

   4. Taylor expanded in t around inf 40.3%

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

   if -1.7e114 < b < 4.09999999999999996e23

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0 89.8%

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

   4. Taylor expanded in a around 0 57.7%

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

   5. Taylor expanded in y around 0 27.1%

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

      1. sub-neg 27.1%

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

      2. mul-1-neg 27.1%

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

      3. remove-double-neg 27.1%

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

      4. +-commutative 27.1%

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

   7. Simplified 27.1%

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

4. Final simplification 32.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+114} \lor \neg \left(b \leq 4.1 \cdot 10^{+23}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 20.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+53}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.4e+114) x (if (<= x 9.5e+53) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.4e+114) {
		tmp = x;
	} else if (x <= 9.5e+53) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.4d+114)) then
        tmp = x
    else if (x <= 9.5d+53) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.4e+114) {
		tmp = x;
	} else if (x <= 9.5e+53) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.4e+114:
		tmp = x
	elif x <= 9.5e+53:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.4e+114)
		tmp = x;
	elseif (x <= 9.5e+53)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.4e+114)
		tmp = x;
	elseif (x <= 9.5e+53)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.4e+114], x, If[LessEqual[x, 9.5e+53], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4000000000000001e114 or 9.5000000000000006e53 < x

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 39.4%

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

   if -4.4000000000000001e114 < x < 9.5000000000000006e53

   1. Initial program 94.8%

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

   3. Taylor expanded in a around inf 36.5%

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

   4. Taylor expanded in t around 0 10.9%

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

4. Final simplification 20.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+53}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 11.0% 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 94.1%

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

3. Taylor expanded in a around inf 31.1%

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

4. Taylor expanded in t around 0 8.9%

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

5. Final simplification 8.9%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024023 
(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)))