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

Percentage Accurate: 94.9% → 97.2%

Time: 15.4s

Alternatives: 25

Speedup: 0.5×

• 36.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

   1. +-commutative 93.7%

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

   2. fma-define 96.9%

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

   3. associate--l+ 96.9%

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

   4. sub-neg 96.9%

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

   5. metadata-eval 96.9%

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

   6. sub-neg 96.9%

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

   7. associate-+l- 96.9%

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

   8. fmm-def 97.7%

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

   9. sub-neg 97.7%

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

   10. metadata-eval 97.7%

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

   11. remove-double-neg 97.7%

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

   12. sub-neg 97.7%

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

   13. metadata-eval 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 2: 80.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + \left(z \cdot \left(1 - y\right) + t\_1\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+161}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+124}:\\ \;\;\;\;x + \left(z + t\_1\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{+74}:\\ \;\;\;\;x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+19}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+112}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + t\right) + -2 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (+ x (+ (* z (- 1.0 y)) t_1))))
   (if (<= b -3.1e+161)
     t_2
     (if (<= b -4e+124)
       (+ x (+ z t_1))
       (if (<= b -3.5e+110)
         (* y (- b z))
         (if (<= b -4.3e+74)
           (+ x (- a (* b (- 2.0 y))))
           (if (<= b 4.6e+19)
             t_3
             (if (<= b 3.6e+40)
               t_2
               (if (<= b 1.75e+112) t_3 (+ (* b (+ y t)) (* -2.0 b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + ((z * (1.0 - y)) + t_1);
	double tmp;
	if (b <= -3.1e+161) {
		tmp = t_2;
	} else if (b <= -4e+124) {
		tmp = x + (z + t_1);
	} else if (b <= -3.5e+110) {
		tmp = y * (b - z);
	} else if (b <= -4.3e+74) {
		tmp = x + (a - (b * (2.0 - y)));
	} else if (b <= 4.6e+19) {
		tmp = t_3;
	} else if (b <= 3.6e+40) {
		tmp = t_2;
	} else if (b <= 1.75e+112) {
		tmp = t_3;
	} else {
		tmp = (b * (y + t)) + (-2.0 * 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x + ((z * (1.0d0 - y)) + t_1)
    if (b <= (-3.1d+161)) then
        tmp = t_2
    else if (b <= (-4d+124)) then
        tmp = x + (z + t_1)
    else if (b <= (-3.5d+110)) then
        tmp = y * (b - z)
    else if (b <= (-4.3d+74)) then
        tmp = x + (a - (b * (2.0d0 - y)))
    else if (b <= 4.6d+19) then
        tmp = t_3
    else if (b <= 3.6d+40) then
        tmp = t_2
    else if (b <= 1.75d+112) then
        tmp = t_3
    else
        tmp = (b * (y + t)) + ((-2.0d0) * 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 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + ((z * (1.0 - y)) + t_1);
	double tmp;
	if (b <= -3.1e+161) {
		tmp = t_2;
	} else if (b <= -4e+124) {
		tmp = x + (z + t_1);
	} else if (b <= -3.5e+110) {
		tmp = y * (b - z);
	} else if (b <= -4.3e+74) {
		tmp = x + (a - (b * (2.0 - y)));
	} else if (b <= 4.6e+19) {
		tmp = t_3;
	} else if (b <= 3.6e+40) {
		tmp = t_2;
	} else if (b <= 1.75e+112) {
		tmp = t_3;
	} else {
		tmp = (b * (y + t)) + (-2.0 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * ((y + t) - 2.0)
	t_3 = x + ((z * (1.0 - y)) + t_1)
	tmp = 0
	if b <= -3.1e+161:
		tmp = t_2
	elif b <= -4e+124:
		tmp = x + (z + t_1)
	elif b <= -3.5e+110:
		tmp = y * (b - z)
	elif b <= -4.3e+74:
		tmp = x + (a - (b * (2.0 - y)))
	elif b <= 4.6e+19:
		tmp = t_3
	elif b <= 3.6e+40:
		tmp = t_2
	elif b <= 1.75e+112:
		tmp = t_3
	else:
		tmp = (b * (y + t)) + (-2.0 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1))
	tmp = 0.0
	if (b <= -3.1e+161)
		tmp = t_2;
	elseif (b <= -4e+124)
		tmp = Float64(x + Float64(z + t_1));
	elseif (b <= -3.5e+110)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= -4.3e+74)
		tmp = Float64(x + Float64(a - Float64(b * Float64(2.0 - y))));
	elseif (b <= 4.6e+19)
		tmp = t_3;
	elseif (b <= 3.6e+40)
		tmp = t_2;
	elseif (b <= 1.75e+112)
		tmp = t_3;
	else
		tmp = Float64(Float64(b * Float64(y + t)) + Float64(-2.0 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * ((y + t) - 2.0);
	t_3 = x + ((z * (1.0 - y)) + t_1);
	tmp = 0.0;
	if (b <= -3.1e+161)
		tmp = t_2;
	elseif (b <= -4e+124)
		tmp = x + (z + t_1);
	elseif (b <= -3.5e+110)
		tmp = y * (b - z);
	elseif (b <= -4.3e+74)
		tmp = x + (a - (b * (2.0 - y)));
	elseif (b <= 4.6e+19)
		tmp = t_3;
	elseif (b <= 3.6e+40)
		tmp = t_2;
	elseif (b <= 1.75e+112)
		tmp = t_3;
	else
		tmp = (b * (y + t)) + (-2.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+161], t$95$2, If[LessEqual[b, -4e+124], N[(x + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e+110], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.3e+74], N[(x + N[(a - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.6e+19], t$95$3, If[LessEqual[b, 3.6e+40], t$95$2, If[LessEqual[b, 1.75e+112], t$95$3, N[(N[(b * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.10000000000000007e161 or 4.6e19 < b < 3.59999999999999996e40

   1. Initial program 90.6%

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

   3. Taylor expanded in b around inf 93.6%

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

   if -3.10000000000000007e161 < b < -3.99999999999999979e124

   1. Initial program 77.8%

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

   3. Taylor expanded in b around 0 68.1%

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

   4. Taylor expanded in y around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. sub-neg 78.6%

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

      3. metadata-eval 78.6%

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

      4. mul-1-neg 78.6%

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

      5. unsub-neg 78.6%

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

   6. Simplified 78.6%

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

   if -3.99999999999999979e124 < b < -3.4999999999999999e110

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -3.4999999999999999e110 < b < -4.30000000000000001e74

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. mul-1-neg 100.0%

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

      8. sub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

   if -4.30000000000000001e74 < b < 4.6e19 or 3.59999999999999996e40 < b < 1.74999999999999998e112

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0 90.3%

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

   if 1.74999999999999998e112 < b

   1. Initial program 90.0%

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

   3. Taylor expanded in b around inf 83.1%

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

      1. sub-neg 83.1%

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

      2. metadata-eval 83.1%

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

      3. distribute-rgt-in 83.1%

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

      4. +-commutative 83.1%

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

      5. *-commutative 83.1%

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

   5. Applied egg-rr 83.1%

      \[\leadsto \color{blue}{\left(y + t\right) \cdot b + b \cdot -2} \]
3. Recombined 6 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+124}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{+74}:\\ \;\;\;\;x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+19}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+112}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + t\right) + -2 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -5.7 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-9}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-279}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-225}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (+ x (* a (- 1.0 t)))))
   (if (<= b -5.7e+165)
     t_2
     (if (<= b -1.45e+106)
       t_1
       (if (<= b -2.6e-9)
         t_3
         (if (<= b -4.5e-188)
           t_1
           (if (<= b -1.8e-279)
             t_3
             (if (<= b 3e-305)
               t_1
               (if (<= b 1.3e-225) t_3 (if (<= b 4e+19) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -5.7e+165) {
		tmp = t_2;
	} else if (b <= -1.45e+106) {
		tmp = t_1;
	} else if (b <= -2.6e-9) {
		tmp = t_3;
	} else if (b <= -4.5e-188) {
		tmp = t_1;
	} else if (b <= -1.8e-279) {
		tmp = t_3;
	} else if (b <= 3e-305) {
		tmp = t_1;
	} else if (b <= 1.3e-225) {
		tmp = t_3;
	} else if (b <= 4e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x + (a * (1.0d0 - t))
    if (b <= (-5.7d+165)) then
        tmp = t_2
    else if (b <= (-1.45d+106)) then
        tmp = t_1
    else if (b <= (-2.6d-9)) then
        tmp = t_3
    else if (b <= (-4.5d-188)) then
        tmp = t_1
    else if (b <= (-1.8d-279)) then
        tmp = t_3
    else if (b <= 3d-305) then
        tmp = t_1
    else if (b <= 1.3d-225) then
        tmp = t_3
    else if (b <= 4d+19) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -5.7e+165) {
		tmp = t_2;
	} else if (b <= -1.45e+106) {
		tmp = t_1;
	} else if (b <= -2.6e-9) {
		tmp = t_3;
	} else if (b <= -4.5e-188) {
		tmp = t_1;
	} else if (b <= -1.8e-279) {
		tmp = t_3;
	} else if (b <= 3e-305) {
		tmp = t_1;
	} else if (b <= 1.3e-225) {
		tmp = t_3;
	} else if (b <= 4e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = b * ((y + t) - 2.0)
	t_3 = x + (a * (1.0 - t))
	tmp = 0
	if b <= -5.7e+165:
		tmp = t_2
	elif b <= -1.45e+106:
		tmp = t_1
	elif b <= -2.6e-9:
		tmp = t_3
	elif b <= -4.5e-188:
		tmp = t_1
	elif b <= -1.8e-279:
		tmp = t_3
	elif b <= 3e-305:
		tmp = t_1
	elif b <= 1.3e-225:
		tmp = t_3
	elif b <= 4e+19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (b <= -5.7e+165)
		tmp = t_2;
	elseif (b <= -1.45e+106)
		tmp = t_1;
	elseif (b <= -2.6e-9)
		tmp = t_3;
	elseif (b <= -4.5e-188)
		tmp = t_1;
	elseif (b <= -1.8e-279)
		tmp = t_3;
	elseif (b <= 3e-305)
		tmp = t_1;
	elseif (b <= 1.3e-225)
		tmp = t_3;
	elseif (b <= 4e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = b * ((y + t) - 2.0);
	t_3 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (b <= -5.7e+165)
		tmp = t_2;
	elseif (b <= -1.45e+106)
		tmp = t_1;
	elseif (b <= -2.6e-9)
		tmp = t_3;
	elseif (b <= -4.5e-188)
		tmp = t_1;
	elseif (b <= -1.8e-279)
		tmp = t_3;
	elseif (b <= 3e-305)
		tmp = t_1;
	elseif (b <= 1.3e-225)
		tmp = t_3;
	elseif (b <= 4e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.7e+165], t$95$2, If[LessEqual[b, -1.45e+106], t$95$1, If[LessEqual[b, -2.6e-9], t$95$3, If[LessEqual[b, -4.5e-188], t$95$1, If[LessEqual[b, -1.8e-279], t$95$3, If[LessEqual[b, 3e-305], t$95$1, If[LessEqual[b, 1.3e-225], t$95$3, If[LessEqual[b, 4e+19], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.70000000000000027e165 or 4e19 < b

   1. Initial program 90.8%

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

   3. Taylor expanded in b around inf 78.4%

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

   if -5.70000000000000027e165 < b < -1.4500000000000001e106 or -2.6000000000000001e-9 < b < -4.49999999999999993e-188 or -1.7999999999999998e-279 < b < 3.0000000000000001e-305 or 1.30000000000000007e-225 < b < 4e19

   1. Initial program 96.3%

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

   3. Taylor expanded in b around 0 89.0%

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

   4. Taylor expanded in a around 0 72.1%

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

   if -1.4500000000000001e106 < b < -2.6000000000000001e-9 or -4.49999999999999993e-188 < b < -1.7999999999999998e-279 or 3.0000000000000001e-305 < b < 1.30000000000000007e-225

   1. Initial program 94.0%

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

   3. Taylor expanded in b around 0 86.3%

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

   4. Taylor expanded in a around inf 66.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.7 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+106}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-9}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-188}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-279}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-305}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-225}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+19}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 57.4%

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

4. Final simplification 97.3%

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

Alternative 5: 51.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -0.00175:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-89}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-263}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+98}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -7.5e+60)
     t_2
     (if (<= t -0.00175)
       t_1
       (if (<= t -5.5e-89)
         (+ x a)
         (if (<= t -3.4e-192)
           t_1
           (if (<= t -8.8e-263)
             (+ x a)
             (if (<= t 7.8e+17)
               t_1
               (if (<= t 2.3e+98) (- x (* t a)) 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 <= -7.5e+60) {
		tmp = t_2;
	} else if (t <= -0.00175) {
		tmp = t_1;
	} else if (t <= -5.5e-89) {
		tmp = x + a;
	} else if (t <= -3.4e-192) {
		tmp = t_1;
	} else if (t <= -8.8e-263) {
		tmp = x + a;
	} else if (t <= 7.8e+17) {
		tmp = t_1;
	} else if (t <= 2.3e+98) {
		tmp = x - (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-7.5d+60)) then
        tmp = t_2
    else if (t <= (-0.00175d0)) then
        tmp = t_1
    else if (t <= (-5.5d-89)) then
        tmp = x + a
    else if (t <= (-3.4d-192)) then
        tmp = t_1
    else if (t <= (-8.8d-263)) then
        tmp = x + a
    else if (t <= 7.8d+17) then
        tmp = t_1
    else if (t <= 2.3d+98) then
        tmp = x - (t * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.5e+60) {
		tmp = t_2;
	} else if (t <= -0.00175) {
		tmp = t_1;
	} else if (t <= -5.5e-89) {
		tmp = x + a;
	} else if (t <= -3.4e-192) {
		tmp = t_1;
	} else if (t <= -8.8e-263) {
		tmp = x + a;
	} else if (t <= 7.8e+17) {
		tmp = t_1;
	} else if (t <= 2.3e+98) {
		tmp = x - (t * a);
	} 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 <= -7.5e+60:
		tmp = t_2
	elif t <= -0.00175:
		tmp = t_1
	elif t <= -5.5e-89:
		tmp = x + a
	elif t <= -3.4e-192:
		tmp = t_1
	elif t <= -8.8e-263:
		tmp = x + a
	elif t <= 7.8e+17:
		tmp = t_1
	elif t <= 2.3e+98:
		tmp = x - (t * a)
	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 <= -7.5e+60)
		tmp = t_2;
	elseif (t <= -0.00175)
		tmp = t_1;
	elseif (t <= -5.5e-89)
		tmp = Float64(x + a);
	elseif (t <= -3.4e-192)
		tmp = t_1;
	elseif (t <= -8.8e-263)
		tmp = Float64(x + a);
	elseif (t <= 7.8e+17)
		tmp = t_1;
	elseif (t <= 2.3e+98)
		tmp = Float64(x - Float64(t * a));
	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 <= -7.5e+60)
		tmp = t_2;
	elseif (t <= -0.00175)
		tmp = t_1;
	elseif (t <= -5.5e-89)
		tmp = x + a;
	elseif (t <= -3.4e-192)
		tmp = t_1;
	elseif (t <= -8.8e-263)
		tmp = x + a;
	elseif (t <= 7.8e+17)
		tmp = t_1;
	elseif (t <= 2.3e+98)
		tmp = x - (t * a);
	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, -7.5e+60], t$95$2, If[LessEqual[t, -0.00175], t$95$1, If[LessEqual[t, -5.5e-89], N[(x + a), $MachinePrecision], If[LessEqual[t, -3.4e-192], t$95$1, If[LessEqual[t, -8.8e-263], N[(x + a), $MachinePrecision], If[LessEqual[t, 7.8e+17], t$95$1, If[LessEqual[t, 2.3e+98], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.5e60 or 2.30000000000000013e98 < t

   1. Initial program 87.5%

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

   3. Taylor expanded in t around inf 73.3%

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

   if -7.5e60 < t < -0.00175000000000000004 or -5.50000000000000012e-89 < t < -3.40000000000000002e-192 or -8.8000000000000001e-263 < t < 7.8e17

   1. Initial program 95.7%

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

   3. Taylor expanded in y around inf 54.0%

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

   if -0.00175000000000000004 < t < -5.50000000000000012e-89 or -3.40000000000000002e-192 < t < -8.8000000000000001e-263

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in t around 0 99.5%

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

      1. associate--l+ 99.5%

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

      2. sub-neg 99.5%

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

      3. metadata-eval 99.5%

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

      4. +-commutative 99.5%

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

      5. sub-neg 99.5%

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

      6. metadata-eval 99.5%

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

      7. mul-1-neg 99.5%

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

      8. sub-neg 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in a around inf 53.6%

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

   if 7.8e17 < t < 2.30000000000000013e98

   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 b around 0 77.3%

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

   4. Taylor expanded in t around inf 77.3%

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

      1. *-commutative 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in t around inf 66.2%

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

      1. *-commutative 66.2%

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

   9. Simplified 66.2%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -0.00175:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-89}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-192}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-263}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+98}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.9 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -505:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-191}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-262}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+98}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -4.6e+61)
     t_2
     (if (<= t -6.9e+33)
       t_1
       (if (<= t -505.0)
         t_2
         (if (<= t -1e-191)
           (- x (* y z))
           (if (<= t -2.1e-262)
             (+ x a)
             (if (<= t 2e+19) t_1 (if (<= t 1.8e+98) (- x (* t a)) 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 <= -4.6e+61) {
		tmp = t_2;
	} else if (t <= -6.9e+33) {
		tmp = t_1;
	} else if (t <= -505.0) {
		tmp = t_2;
	} else if (t <= -1e-191) {
		tmp = x - (y * z);
	} else if (t <= -2.1e-262) {
		tmp = x + a;
	} else if (t <= 2e+19) {
		tmp = t_1;
	} else if (t <= 1.8e+98) {
		tmp = x - (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-4.6d+61)) then
        tmp = t_2
    else if (t <= (-6.9d+33)) then
        tmp = t_1
    else if (t <= (-505.0d0)) then
        tmp = t_2
    else if (t <= (-1d-191)) then
        tmp = x - (y * z)
    else if (t <= (-2.1d-262)) then
        tmp = x + a
    else if (t <= 2d+19) then
        tmp = t_1
    else if (t <= 1.8d+98) then
        tmp = x - (t * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.6e+61) {
		tmp = t_2;
	} else if (t <= -6.9e+33) {
		tmp = t_1;
	} else if (t <= -505.0) {
		tmp = t_2;
	} else if (t <= -1e-191) {
		tmp = x - (y * z);
	} else if (t <= -2.1e-262) {
		tmp = x + a;
	} else if (t <= 2e+19) {
		tmp = t_1;
	} else if (t <= 1.8e+98) {
		tmp = x - (t * a);
	} 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 <= -4.6e+61:
		tmp = t_2
	elif t <= -6.9e+33:
		tmp = t_1
	elif t <= -505.0:
		tmp = t_2
	elif t <= -1e-191:
		tmp = x - (y * z)
	elif t <= -2.1e-262:
		tmp = x + a
	elif t <= 2e+19:
		tmp = t_1
	elif t <= 1.8e+98:
		tmp = x - (t * a)
	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 <= -4.6e+61)
		tmp = t_2;
	elseif (t <= -6.9e+33)
		tmp = t_1;
	elseif (t <= -505.0)
		tmp = t_2;
	elseif (t <= -1e-191)
		tmp = Float64(x - Float64(y * z));
	elseif (t <= -2.1e-262)
		tmp = Float64(x + a);
	elseif (t <= 2e+19)
		tmp = t_1;
	elseif (t <= 1.8e+98)
		tmp = Float64(x - Float64(t * a));
	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 <= -4.6e+61)
		tmp = t_2;
	elseif (t <= -6.9e+33)
		tmp = t_1;
	elseif (t <= -505.0)
		tmp = t_2;
	elseif (t <= -1e-191)
		tmp = x - (y * z);
	elseif (t <= -2.1e-262)
		tmp = x + a;
	elseif (t <= 2e+19)
		tmp = t_1;
	elseif (t <= 1.8e+98)
		tmp = x - (t * a);
	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, -4.6e+61], t$95$2, If[LessEqual[t, -6.9e+33], t$95$1, If[LessEqual[t, -505.0], t$95$2, If[LessEqual[t, -1e-191], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.1e-262], N[(x + a), $MachinePrecision], If[LessEqual[t, 2e+19], t$95$1, If[LessEqual[t, 1.8e+98], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.5999999999999999e61 or -6.8999999999999995e33 < t < -505 or 1.7999999999999999e98 < t

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf 73.1%

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

   if -4.5999999999999999e61 < t < -6.8999999999999995e33 or -2.1e-262 < t < 2e19

   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 53.6%

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

   if -505 < t < -1e-191

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0 69.2%

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

   4. Taylor expanded in y around inf 54.2%

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

   if -1e-191 < t < -2.1e-262

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. mul-1-neg 100.0%

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

      8. sub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around inf 57.7%

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

   if 2e19 < t < 1.7999999999999999e98

   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 b around 0 77.3%

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

   4. Taylor expanded in t around inf 77.3%

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

      1. *-commutative 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in t around inf 66.2%

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

      1. *-commutative 66.2%

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

   9. Simplified 66.2%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -6.9 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -505:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-191}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-262}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+98}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -345:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-263}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-56}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2800:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+51}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -345.0)
     t_1
     (if (<= t -8.5e-263)
       (+ x a)
       (if (<= t -7e-305)
         (* z (- y))
         (if (<= t 5.8e-56)
           (+ x a)
           (if (<= t 2800.0) (* y b) (if (<= t 2.65e+51) (+ x a) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -345.0) {
		tmp = t_1;
	} else if (t <= -8.5e-263) {
		tmp = x + a;
	} else if (t <= -7e-305) {
		tmp = z * -y;
	} else if (t <= 5.8e-56) {
		tmp = x + a;
	} else if (t <= 2800.0) {
		tmp = y * b;
	} else if (t <= 2.65e+51) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-345.0d0)) then
        tmp = t_1
    else if (t <= (-8.5d-263)) then
        tmp = x + a
    else if (t <= (-7d-305)) then
        tmp = z * -y
    else if (t <= 5.8d-56) then
        tmp = x + a
    else if (t <= 2800.0d0) then
        tmp = y * b
    else if (t <= 2.65d+51) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -345.0) {
		tmp = t_1;
	} else if (t <= -8.5e-263) {
		tmp = x + a;
	} else if (t <= -7e-305) {
		tmp = z * -y;
	} else if (t <= 5.8e-56) {
		tmp = x + a;
	} else if (t <= 2800.0) {
		tmp = y * b;
	} else if (t <= 2.65e+51) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -345.0:
		tmp = t_1
	elif t <= -8.5e-263:
		tmp = x + a
	elif t <= -7e-305:
		tmp = z * -y
	elif t <= 5.8e-56:
		tmp = x + a
	elif t <= 2800.0:
		tmp = y * b
	elif t <= 2.65e+51:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -345.0)
		tmp = t_1;
	elseif (t <= -8.5e-263)
		tmp = Float64(x + a);
	elseif (t <= -7e-305)
		tmp = Float64(z * Float64(-y));
	elseif (t <= 5.8e-56)
		tmp = Float64(x + a);
	elseif (t <= 2800.0)
		tmp = Float64(y * b);
	elseif (t <= 2.65e+51)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -345.0)
		tmp = t_1;
	elseif (t <= -8.5e-263)
		tmp = x + a;
	elseif (t <= -7e-305)
		tmp = z * -y;
	elseif (t <= 5.8e-56)
		tmp = x + a;
	elseif (t <= 2800.0)
		tmp = y * b;
	elseif (t <= 2.65e+51)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -345.0], t$95$1, If[LessEqual[t, -8.5e-263], N[(x + a), $MachinePrecision], If[LessEqual[t, -7e-305], N[(z * (-y)), $MachinePrecision], If[LessEqual[t, 5.8e-56], N[(x + a), $MachinePrecision], If[LessEqual[t, 2800.0], N[(y * b), $MachinePrecision], If[LessEqual[t, 2.65e+51], N[(x + a), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -345 or 2.6499999999999998e51 < t

   1. Initial program 89.1%

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

   3. Taylor expanded in t around inf 64.8%

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

   if -345 < t < -8.49999999999999975e-263 or -6.9999999999999996e-305 < t < 5.79999999999999982e-56 or 2800 < t < 2.6499999999999998e51

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0 97.6%

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

   4. Taylor expanded in t around 0 96.7%

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

      1. associate--l+ 96.7%

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

      2. sub-neg 96.7%

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

      3. metadata-eval 96.7%

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

      4. +-commutative 96.7%

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

      5. sub-neg 96.7%

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

      6. metadata-eval 96.7%

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

      7. mul-1-neg 96.7%

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

      8. sub-neg 96.7%

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

   6. Simplified 96.7%

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

   7. Taylor expanded in a around inf 41.7%

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

   if -8.49999999999999975e-263 < t < -6.9999999999999996e-305

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 77.2%

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

   4. Taylor expanded in y around inf 62.2%

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

   5. Taylor expanded in x around 0 59.7%

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

      1. associate-*r* 59.7%

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

      2. neg-mul-1 59.7%

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

   7. Simplified 59.7%

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

   if 5.79999999999999982e-56 < t < 2800

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf 67.1%

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

   4. Taylor expanded in b around inf 44.6%

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

      1. *-commutative 44.6%

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

   6. Simplified 44.6%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -345:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-263}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-56}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2800:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+51}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -0.00024:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-93}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-262}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -3.6e+60)
     t_2
     (if (<= t -0.00024)
       t_1
       (if (<= t -2.4e-93)
         (+ x a)
         (if (<= t -1.6e-193)
           t_1
           (if (<= t -1.9e-262) (+ x a) (if (<= t 1.15e+37) 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 <= -3.6e+60) {
		tmp = t_2;
	} else if (t <= -0.00024) {
		tmp = t_1;
	} else if (t <= -2.4e-93) {
		tmp = x + a;
	} else if (t <= -1.6e-193) {
		tmp = t_1;
	} else if (t <= -1.9e-262) {
		tmp = x + a;
	} else if (t <= 1.15e+37) {
		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 <= (-3.6d+60)) then
        tmp = t_2
    else if (t <= (-0.00024d0)) then
        tmp = t_1
    else if (t <= (-2.4d-93)) then
        tmp = x + a
    else if (t <= (-1.6d-193)) then
        tmp = t_1
    else if (t <= (-1.9d-262)) then
        tmp = x + a
    else if (t <= 1.15d+37) 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 <= -3.6e+60) {
		tmp = t_2;
	} else if (t <= -0.00024) {
		tmp = t_1;
	} else if (t <= -2.4e-93) {
		tmp = x + a;
	} else if (t <= -1.6e-193) {
		tmp = t_1;
	} else if (t <= -1.9e-262) {
		tmp = x + a;
	} else if (t <= 1.15e+37) {
		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 <= -3.6e+60:
		tmp = t_2
	elif t <= -0.00024:
		tmp = t_1
	elif t <= -2.4e-93:
		tmp = x + a
	elif t <= -1.6e-193:
		tmp = t_1
	elif t <= -1.9e-262:
		tmp = x + a
	elif t <= 1.15e+37:
		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 <= -3.6e+60)
		tmp = t_2;
	elseif (t <= -0.00024)
		tmp = t_1;
	elseif (t <= -2.4e-93)
		tmp = Float64(x + a);
	elseif (t <= -1.6e-193)
		tmp = t_1;
	elseif (t <= -1.9e-262)
		tmp = Float64(x + a);
	elseif (t <= 1.15e+37)
		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 <= -3.6e+60)
		tmp = t_2;
	elseif (t <= -0.00024)
		tmp = t_1;
	elseif (t <= -2.4e-93)
		tmp = x + a;
	elseif (t <= -1.6e-193)
		tmp = t_1;
	elseif (t <= -1.9e-262)
		tmp = x + a;
	elseif (t <= 1.15e+37)
		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, -3.6e+60], t$95$2, If[LessEqual[t, -0.00024], t$95$1, If[LessEqual[t, -2.4e-93], N[(x + a), $MachinePrecision], If[LessEqual[t, -1.6e-193], t$95$1, If[LessEqual[t, -1.9e-262], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.15e+37], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999968e60 or 1.15000000000000001e37 < t

   1. Initial program 88.4%

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

   3. Taylor expanded in t around inf 67.3%

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

   if -3.59999999999999968e60 < t < -2.40000000000000006e-4 or -2.4000000000000001e-93 < t < -1.60000000000000003e-193 or -1.9000000000000001e-262 < t < 1.15000000000000001e37

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf 53.2%

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

   if -2.40000000000000006e-4 < t < -2.4000000000000001e-93 or -1.60000000000000003e-193 < t < -1.9000000000000001e-262

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in t around 0 99.5%

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

      1. associate--l+ 99.5%

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

      2. sub-neg 99.5%

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

      3. metadata-eval 99.5%

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

      4. +-commutative 99.5%

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

      5. sub-neg 99.5%

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

      6. metadata-eval 99.5%

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

      7. mul-1-neg 99.5%

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

      8. sub-neg 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in a around inf 53.6%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -0.00024:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-93}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-262}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - b \cdot \left(2 - y\right)\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-8}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-40}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- a (* b (- 2.0 y))))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -5e+165)
     t_2
     (if (<= b -6.6e+63)
       t_1
       (if (<= b -2.7e-8)
         (+ x (* a (- 1.0 t)))
         (if (<= b 2.3e-40)
           (- x (* z (+ y -1.0)))
           (if (<= b 4e+138) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (b * (2.0 - y)));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -5e+165) {
		tmp = t_2;
	} else if (b <= -6.6e+63) {
		tmp = t_1;
	} else if (b <= -2.7e-8) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.3e-40) {
		tmp = x - (z * (y + -1.0));
	} else if (b <= 4e+138) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a - (b * (2.0d0 - y)))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-5d+165)) then
        tmp = t_2
    else if (b <= (-6.6d+63)) then
        tmp = t_1
    else if (b <= (-2.7d-8)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 2.3d-40) then
        tmp = x - (z * (y + (-1.0d0)))
    else if (b <= 4d+138) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (b * (2.0 - y)));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -5e+165) {
		tmp = t_2;
	} else if (b <= -6.6e+63) {
		tmp = t_1;
	} else if (b <= -2.7e-8) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.3e-40) {
		tmp = x - (z * (y + -1.0));
	} else if (b <= 4e+138) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a - (b * (2.0 - y)))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -5e+165:
		tmp = t_2
	elif b <= -6.6e+63:
		tmp = t_1
	elif b <= -2.7e-8:
		tmp = x + (a * (1.0 - t))
	elif b <= 2.3e-40:
		tmp = x - (z * (y + -1.0))
	elif b <= 4e+138:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a - Float64(b * Float64(2.0 - y))))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -5e+165)
		tmp = t_2;
	elseif (b <= -6.6e+63)
		tmp = t_1;
	elseif (b <= -2.7e-8)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 2.3e-40)
		tmp = Float64(x - Float64(z * Float64(y + -1.0)));
	elseif (b <= 4e+138)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a - (b * (2.0 - y)));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -5e+165)
		tmp = t_2;
	elseif (b <= -6.6e+63)
		tmp = t_1;
	elseif (b <= -2.7e-8)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 2.3e-40)
		tmp = x - (z * (y + -1.0));
	elseif (b <= 4e+138)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+165], t$95$2, If[LessEqual[b, -6.6e+63], t$95$1, If[LessEqual[b, -2.7e-8], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-40], N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+138], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.9999999999999997e165 or 4.0000000000000001e138 < b

   1. Initial program 88.2%

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

   3. Taylor expanded in b around inf 88.7%

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

   if -4.9999999999999997e165 < b < -6.6000000000000003e63 or 2.3e-40 < b < 4.0000000000000001e138

   1. Initial program 92.3%

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

   3. Taylor expanded in t around 0 92.3%

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

   4. Taylor expanded in t around 0 83.6%

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

      1. associate--l+ 83.6%

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

      2. sub-neg 83.6%

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

      3. metadata-eval 83.6%

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

      4. +-commutative 83.6%

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

      5. sub-neg 83.6%

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

      6. metadata-eval 83.6%

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

      7. mul-1-neg 83.6%

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

      8. sub-neg 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in z around 0 66.4%

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

   if -6.6000000000000003e63 < b < -2.70000000000000002e-8

   1. Initial program 62.5%

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

   3. Taylor expanded in b around 0 75.0%

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

   4. Taylor expanded in a around inf 75.3%

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

   if -2.70000000000000002e-8 < b < 2.3e-40

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 95.6%

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

   4. Taylor expanded in a around 0 66.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+63}:\\ \;\;\;\;x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-8}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-40}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+138}:\\ \;\;\;\;x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-8}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-40}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + t\right) + -2 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- a (* b (- 2.0 y))))))
   (if (<= b -5e+165)
     (* b (- (+ y t) 2.0))
     (if (<= b -7.8e+60)
       t_1
       (if (<= b -4.8e-8)
         (+ x (* a (- 1.0 t)))
         (if (<= b 2.15e-40)
           (- x (* z (+ y -1.0)))
           (if (<= b 4.2e+138) t_1 (+ (* b (+ y t)) (* -2.0 b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (b * (2.0 - y)));
	double tmp;
	if (b <= -5e+165) {
		tmp = b * ((y + t) - 2.0);
	} else if (b <= -7.8e+60) {
		tmp = t_1;
	} else if (b <= -4.8e-8) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.15e-40) {
		tmp = x - (z * (y + -1.0));
	} else if (b <= 4.2e+138) {
		tmp = t_1;
	} else {
		tmp = (b * (y + t)) + (-2.0 * 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 = x + (a - (b * (2.0d0 - y)))
    if (b <= (-5d+165)) then
        tmp = b * ((y + t) - 2.0d0)
    else if (b <= (-7.8d+60)) then
        tmp = t_1
    else if (b <= (-4.8d-8)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 2.15d-40) then
        tmp = x - (z * (y + (-1.0d0)))
    else if (b <= 4.2d+138) then
        tmp = t_1
    else
        tmp = (b * (y + t)) + ((-2.0d0) * 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 = x + (a - (b * (2.0 - y)));
	double tmp;
	if (b <= -5e+165) {
		tmp = b * ((y + t) - 2.0);
	} else if (b <= -7.8e+60) {
		tmp = t_1;
	} else if (b <= -4.8e-8) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.15e-40) {
		tmp = x - (z * (y + -1.0));
	} else if (b <= 4.2e+138) {
		tmp = t_1;
	} else {
		tmp = (b * (y + t)) + (-2.0 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a - (b * (2.0 - y)))
	tmp = 0
	if b <= -5e+165:
		tmp = b * ((y + t) - 2.0)
	elif b <= -7.8e+60:
		tmp = t_1
	elif b <= -4.8e-8:
		tmp = x + (a * (1.0 - t))
	elif b <= 2.15e-40:
		tmp = x - (z * (y + -1.0))
	elif b <= 4.2e+138:
		tmp = t_1
	else:
		tmp = (b * (y + t)) + (-2.0 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a - Float64(b * Float64(2.0 - y))))
	tmp = 0.0
	if (b <= -5e+165)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	elseif (b <= -7.8e+60)
		tmp = t_1;
	elseif (b <= -4.8e-8)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 2.15e-40)
		tmp = Float64(x - Float64(z * Float64(y + -1.0)));
	elseif (b <= 4.2e+138)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * Float64(y + t)) + Float64(-2.0 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a - (b * (2.0 - y)));
	tmp = 0.0;
	if (b <= -5e+165)
		tmp = b * ((y + t) - 2.0);
	elseif (b <= -7.8e+60)
		tmp = t_1;
	elseif (b <= -4.8e-8)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 2.15e-40)
		tmp = x - (z * (y + -1.0));
	elseif (b <= 4.2e+138)
		tmp = t_1;
	else
		tmp = (b * (y + t)) + (-2.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+165], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.8e+60], t$95$1, If[LessEqual[b, -4.8e-8], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e-40], N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+138], t$95$1, N[(N[(b * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.9999999999999997e165

   1. Initial program 88.0%

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

   3. Taylor expanded in b around inf 91.7%

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

   if -4.9999999999999997e165 < b < -7.8000000000000006e60 or 2.1500000000000001e-40 < b < 4.20000000000000014e138

   1. Initial program 92.3%

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

   3. Taylor expanded in t around 0 92.3%

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

   4. Taylor expanded in t around 0 83.6%

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

      1. associate--l+ 83.6%

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

      2. sub-neg 83.6%

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

      3. metadata-eval 83.6%

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

      4. +-commutative 83.6%

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

      5. sub-neg 83.6%

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

      6. metadata-eval 83.6%

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

      7. mul-1-neg 83.6%

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

      8. sub-neg 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in z around 0 66.4%

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

   if -7.8000000000000006e60 < b < -4.79999999999999997e-8

   1. Initial program 62.5%

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

   3. Taylor expanded in b around 0 75.0%

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

   4. Taylor expanded in a around inf 75.3%

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

   if -4.79999999999999997e-8 < b < 2.1500000000000001e-40

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 95.6%

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

   4. Taylor expanded in a around 0 66.5%

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

   if 4.20000000000000014e138 < b

   1. Initial program 88.3%

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

   3. Taylor expanded in b around inf 86.9%

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

      1. sub-neg 86.9%

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

      2. metadata-eval 86.9%

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

      3. distribute-rgt-in 86.9%

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

      4. +-commutative 86.9%

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

      5. *-commutative 86.9%

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

   5. Applied egg-rr 86.9%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{+60}:\\ \;\;\;\;x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-8}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-40}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+138}:\\ \;\;\;\;x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + t\right) + -2 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{+133}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-40}:\\ \;\;\;\;x - \left(z \cdot \left(y + -1\right) + t \cdot a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + t\right) + -2 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- a (* b (- 2.0 y))))))
   (if (<= b -3.1e+161)
     (* b (- (+ y t) 2.0))
     (if (<= b -2.15e+133)
       (+ x (+ z (* a (- 1.0 t))))
       (if (<= b -2.2e+58)
         t_1
         (if (<= b 2.3e-40)
           (- x (+ (* z (+ y -1.0)) (* t a)))
           (if (<= b 8.5e+138) t_1 (+ (* b (+ y t)) (* -2.0 b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (b * (2.0 - y)));
	double tmp;
	if (b <= -3.1e+161) {
		tmp = b * ((y + t) - 2.0);
	} else if (b <= -2.15e+133) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (b <= -2.2e+58) {
		tmp = t_1;
	} else if (b <= 2.3e-40) {
		tmp = x - ((z * (y + -1.0)) + (t * a));
	} else if (b <= 8.5e+138) {
		tmp = t_1;
	} else {
		tmp = (b * (y + t)) + (-2.0 * 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 = x + (a - (b * (2.0d0 - y)))
    if (b <= (-3.1d+161)) then
        tmp = b * ((y + t) - 2.0d0)
    else if (b <= (-2.15d+133)) then
        tmp = x + (z + (a * (1.0d0 - t)))
    else if (b <= (-2.2d+58)) then
        tmp = t_1
    else if (b <= 2.3d-40) then
        tmp = x - ((z * (y + (-1.0d0))) + (t * a))
    else if (b <= 8.5d+138) then
        tmp = t_1
    else
        tmp = (b * (y + t)) + ((-2.0d0) * 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 = x + (a - (b * (2.0 - y)));
	double tmp;
	if (b <= -3.1e+161) {
		tmp = b * ((y + t) - 2.0);
	} else if (b <= -2.15e+133) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (b <= -2.2e+58) {
		tmp = t_1;
	} else if (b <= 2.3e-40) {
		tmp = x - ((z * (y + -1.0)) + (t * a));
	} else if (b <= 8.5e+138) {
		tmp = t_1;
	} else {
		tmp = (b * (y + t)) + (-2.0 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a - (b * (2.0 - y)))
	tmp = 0
	if b <= -3.1e+161:
		tmp = b * ((y + t) - 2.0)
	elif b <= -2.15e+133:
		tmp = x + (z + (a * (1.0 - t)))
	elif b <= -2.2e+58:
		tmp = t_1
	elif b <= 2.3e-40:
		tmp = x - ((z * (y + -1.0)) + (t * a))
	elif b <= 8.5e+138:
		tmp = t_1
	else:
		tmp = (b * (y + t)) + (-2.0 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a - Float64(b * Float64(2.0 - y))))
	tmp = 0.0
	if (b <= -3.1e+161)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	elseif (b <= -2.15e+133)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	elseif (b <= -2.2e+58)
		tmp = t_1;
	elseif (b <= 2.3e-40)
		tmp = Float64(x - Float64(Float64(z * Float64(y + -1.0)) + Float64(t * a)));
	elseif (b <= 8.5e+138)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * Float64(y + t)) + Float64(-2.0 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a - (b * (2.0 - y)));
	tmp = 0.0;
	if (b <= -3.1e+161)
		tmp = b * ((y + t) - 2.0);
	elseif (b <= -2.15e+133)
		tmp = x + (z + (a * (1.0 - t)));
	elseif (b <= -2.2e+58)
		tmp = t_1;
	elseif (b <= 2.3e-40)
		tmp = x - ((z * (y + -1.0)) + (t * a));
	elseif (b <= 8.5e+138)
		tmp = t_1;
	else
		tmp = (b * (y + t)) + (-2.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+161], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.15e+133], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.2e+58], t$95$1, If[LessEqual[b, 2.3e-40], N[(x - N[(N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+138], t$95$1, N[(N[(b * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.10000000000000007e161

   1. Initial program 88.5%

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

   3. Taylor expanded in b around inf 92.1%

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

   if -3.10000000000000007e161 < b < -2.14999999999999997e133

   1. Initial program 71.4%

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

   3. Taylor expanded in b around 0 72.5%

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

   4. Taylor expanded in y around 0 86.8%

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

      1. +-commutative 86.8%

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

      2. sub-neg 86.8%

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

      3. metadata-eval 86.8%

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

      4. mul-1-neg 86.8%

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

      5. unsub-neg 86.8%

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

   6. Simplified 86.8%

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

   if -2.14999999999999997e133 < b < -2.2000000000000001e58 or 2.3e-40 < b < 8.5000000000000006e138

   1. Initial program 93.1%

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

   3. Taylor expanded in t around 0 91.4%

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

   4. Taylor expanded in t around 0 84.9%

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

      1. associate--l+ 84.9%

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

      2. sub-neg 84.9%

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

      3. metadata-eval 84.9%

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

      4. +-commutative 84.9%

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

      5. sub-neg 84.9%

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

      6. metadata-eval 84.9%

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

      7. mul-1-neg 84.9%

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

      8. sub-neg 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in z around 0 68.4%

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

   if -2.2000000000000001e58 < b < 2.3e-40

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0 95.1%

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

   4. Taylor expanded in t around inf 80.4%

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

      1. *-commutative 80.4%

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

   6. Simplified 80.4%

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

   if 8.5000000000000006e138 < b

   1. Initial program 88.3%

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

   3. Taylor expanded in b around inf 86.9%

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

      1. sub-neg 86.9%

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

      2. metadata-eval 86.9%

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

      3. distribute-rgt-in 86.9%

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

      4. +-commutative 86.9%

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

      5. *-commutative 86.9%

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

   5. Applied egg-rr 86.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{+133}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{+58}:\\ \;\;\;\;x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-40}:\\ \;\;\;\;x - \left(z \cdot \left(y + -1\right) + t \cdot a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+138}:\\ \;\;\;\;x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + t\right) + -2 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x - y \cdot z\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-188}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+19}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (- x (* y z))))
   (if (<= b -7.2e+89)
     t_2
     (if (<= b -7.8e-15)
       t_1
       (if (<= b -6e-188)
         t_3
         (if (<= b 3.9e-249) t_1 (if (<= b 5.3e+19) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x - (y * z);
	double tmp;
	if (b <= -7.2e+89) {
		tmp = t_2;
	} else if (b <= -7.8e-15) {
		tmp = t_1;
	} else if (b <= -6e-188) {
		tmp = t_3;
	} else if (b <= 3.9e-249) {
		tmp = t_1;
	} else if (b <= 5.3e+19) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x - (y * z)
    if (b <= (-7.2d+89)) then
        tmp = t_2
    else if (b <= (-7.8d-15)) then
        tmp = t_1
    else if (b <= (-6d-188)) then
        tmp = t_3
    else if (b <= 3.9d-249) then
        tmp = t_1
    else if (b <= 5.3d+19) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x - (y * z);
	double tmp;
	if (b <= -7.2e+89) {
		tmp = t_2;
	} else if (b <= -7.8e-15) {
		tmp = t_1;
	} else if (b <= -6e-188) {
		tmp = t_3;
	} else if (b <= 3.9e-249) {
		tmp = t_1;
	} else if (b <= 5.3e+19) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = b * ((y + t) - 2.0)
	t_3 = x - (y * z)
	tmp = 0
	if b <= -7.2e+89:
		tmp = t_2
	elif b <= -7.8e-15:
		tmp = t_1
	elif b <= -6e-188:
		tmp = t_3
	elif b <= 3.9e-249:
		tmp = t_1
	elif b <= 5.3e+19:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (b <= -7.2e+89)
		tmp = t_2;
	elseif (b <= -7.8e-15)
		tmp = t_1;
	elseif (b <= -6e-188)
		tmp = t_3;
	elseif (b <= 3.9e-249)
		tmp = t_1;
	elseif (b <= 5.3e+19)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	t_3 = x - (y * z);
	tmp = 0.0;
	if (b <= -7.2e+89)
		tmp = t_2;
	elseif (b <= -7.8e-15)
		tmp = t_1;
	elseif (b <= -6e-188)
		tmp = t_3;
	elseif (b <= 3.9e-249)
		tmp = t_1;
	elseif (b <= 5.3e+19)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+89], t$95$2, If[LessEqual[b, -7.8e-15], t$95$1, If[LessEqual[b, -6e-188], t$95$3, If[LessEqual[b, 3.9e-249], t$95$1, If[LessEqual[b, 5.3e+19], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.2e89 or 5.3e19 < b

   1. Initial program 89.0%

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

   3. Taylor expanded in b around inf 73.0%

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

   if -7.2e89 < b < -7.80000000000000053e-15 or -6.00000000000000033e-188 < b < 3.8999999999999999e-249

   1. Initial program 93.6%

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

   3. Taylor expanded in b around 0 91.7%

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

   4. Taylor expanded in a around inf 64.7%

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

   if -7.80000000000000053e-15 < b < -6.00000000000000033e-188 or 3.8999999999999999e-249 < b < 5.3e19

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 92.3%

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

   4. Taylor expanded in y around inf 63.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+89}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-15}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-188}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-249}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+19}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-21}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+60}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))))
   (if (<= y -8.8e+15)
     t_1
     (if (<= y -4.8e-21)
       (+ x a)
       (if (<= y 9.5e-218)
         (* b (- t 2.0))
         (if (<= y 4.2e+60) (+ x a) (if (<= y 7.6e+169) t_1 (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -8.8e+15) {
		tmp = t_1;
	} else if (y <= -4.8e-21) {
		tmp = x + a;
	} else if (y <= 9.5e-218) {
		tmp = b * (t - 2.0);
	} else if (y <= 4.2e+60) {
		tmp = x + a;
	} else if (y <= 7.6e+169) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -y
    if (y <= (-8.8d+15)) then
        tmp = t_1
    else if (y <= (-4.8d-21)) then
        tmp = x + a
    else if (y <= 9.5d-218) then
        tmp = b * (t - 2.0d0)
    else if (y <= 4.2d+60) then
        tmp = x + a
    else if (y <= 7.6d+169) then
        tmp = t_1
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -8.8e+15) {
		tmp = t_1;
	} else if (y <= -4.8e-21) {
		tmp = x + a;
	} else if (y <= 9.5e-218) {
		tmp = b * (t - 2.0);
	} else if (y <= 4.2e+60) {
		tmp = x + a;
	} else if (y <= 7.6e+169) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * -y
	tmp = 0
	if y <= -8.8e+15:
		tmp = t_1
	elif y <= -4.8e-21:
		tmp = x + a
	elif y <= 9.5e-218:
		tmp = b * (t - 2.0)
	elif y <= 4.2e+60:
		tmp = x + a
	elif y <= 7.6e+169:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -8.8e+15)
		tmp = t_1;
	elseif (y <= -4.8e-21)
		tmp = Float64(x + a);
	elseif (y <= 9.5e-218)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 4.2e+60)
		tmp = Float64(x + a);
	elseif (y <= 7.6e+169)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * -y;
	tmp = 0.0;
	if (y <= -8.8e+15)
		tmp = t_1;
	elseif (y <= -4.8e-21)
		tmp = x + a;
	elseif (y <= 9.5e-218)
		tmp = b * (t - 2.0);
	elseif (y <= 4.2e+60)
		tmp = x + a;
	elseif (y <= 7.6e+169)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -8.8e+15], t$95$1, If[LessEqual[y, -4.8e-21], N[(x + a), $MachinePrecision], If[LessEqual[y, 9.5e-218], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+60], N[(x + a), $MachinePrecision], If[LessEqual[y, 7.6e+169], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.8e15 or 4.2000000000000002e60 < y < 7.59999999999999983e169

   1. Initial program 92.0%

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

   3. Taylor expanded in b around 0 71.2%

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

   4. Taylor expanded in y around inf 56.2%

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

   5. Taylor expanded in x around 0 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

   7. Simplified 50.9%

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

   if -8.8e15 < y < -4.7999999999999999e-21 or 9.49999999999999967e-218 < y < 4.2000000000000002e60

   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 0 97.1%

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

   4. Taylor expanded in t around 0 75.5%

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

      1. associate--l+ 75.5%

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

      2. sub-neg 75.5%

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

      3. metadata-eval 75.5%

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

      4. +-commutative 75.5%

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

      5. sub-neg 75.5%

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

      6. metadata-eval 75.5%

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

      7. mul-1-neg 75.5%

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

      8. sub-neg 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in a around inf 46.2%

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

   if -4.7999999999999999e-21 < y < 9.49999999999999967e-218

   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 b around inf 45.3%

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

   4. Taylor expanded in y around 0 45.3%

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

   if 7.59999999999999983e169 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 80.2%

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

   4. Taylor expanded in b around inf 57.4%

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

      1. *-commutative 57.4%

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

   6. Simplified 57.4%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-21}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+60}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-302}:\\ \;\;\;\;x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (* y (- b z))))
   (if (<= y -1.2e+48)
     t_2
     (if (<= y -1.05e-152)
       t_1
       (if (<= y -4.6e-302)
         (+ x (- a (* b (- 2.0 y))))
         (if (<= y 4.1e+60) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.2e+48) {
		tmp = t_2;
	} else if (y <= -1.05e-152) {
		tmp = t_1;
	} else if (y <= -4.6e-302) {
		tmp = x + (a - (b * (2.0 - y)));
	} else if (y <= 4.1e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z + (a * (1.0d0 - t)))
    t_2 = y * (b - z)
    if (y <= (-1.2d+48)) then
        tmp = t_2
    else if (y <= (-1.05d-152)) then
        tmp = t_1
    else if (y <= (-4.6d-302)) then
        tmp = x + (a - (b * (2.0d0 - y)))
    else if (y <= 4.1d+60) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.2e+48) {
		tmp = t_2;
	} else if (y <= -1.05e-152) {
		tmp = t_1;
	} else if (y <= -4.6e-302) {
		tmp = x + (a - (b * (2.0 - y)));
	} else if (y <= 4.1e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -1.2e+48:
		tmp = t_2
	elif y <= -1.05e-152:
		tmp = t_1
	elif y <= -4.6e-302:
		tmp = x + (a - (b * (2.0 - y)))
	elif y <= 4.1e+60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.2e+48)
		tmp = t_2;
	elseif (y <= -1.05e-152)
		tmp = t_1;
	elseif (y <= -4.6e-302)
		tmp = Float64(x + Float64(a - Float64(b * Float64(2.0 - y))));
	elseif (y <= 4.1e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a * (1.0 - t)));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.2e+48)
		tmp = t_2;
	elseif (y <= -1.05e-152)
		tmp = t_1;
	elseif (y <= -4.6e-302)
		tmp = x + (a - (b * (2.0 - y)));
	elseif (y <= 4.1e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+48], t$95$2, If[LessEqual[y, -1.05e-152], t$95$1, If[LessEqual[y, -4.6e-302], N[(x + N[(a - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+60], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2000000000000001e48 or 4.1e60 < y

   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 y around inf 76.2%

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

   if -1.2000000000000001e48 < y < -1.04999999999999999e-152 or -4.60000000000000004e-302 < y < 4.1e60

   1. Initial program 94.6%

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

   3. Taylor expanded in b around 0 71.0%

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

   4. Taylor expanded in y around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. sub-neg 68.5%

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

      3. metadata-eval 68.5%

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

      4. mul-1-neg 68.5%

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

      5. unsub-neg 68.5%

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

   6. Simplified 68.5%

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

   if -1.04999999999999999e-152 < y < -4.60000000000000004e-302

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in t around 0 78.4%

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

      1. associate--l+ 78.4%

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

      2. sub-neg 78.4%

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

      3. metadata-eval 78.4%

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

      4. +-commutative 78.4%

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

      5. sub-neg 78.4%

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

      6. metadata-eval 78.4%

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

      7. mul-1-neg 78.4%

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

      8. sub-neg 78.4%

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

   6. Simplified 78.4%

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

   7. Taylor expanded in z around 0 71.3%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-152}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-302}:\\ \;\;\;\;x + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+60}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -4.9 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.45 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -4.9e+52)
     t_2
     (if (<= b 6.5e-303)
       t_1
       (if (<= b 7.5e-250) (* a (- 1.0 t)) (if (<= b 3.45e+19) 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 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.9e+52) {
		tmp = t_2;
	} else if (b <= 6.5e-303) {
		tmp = t_1;
	} else if (b <= 7.5e-250) {
		tmp = a * (1.0 - t);
	} else if (b <= 3.45e+19) {
		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 = b * ((y + t) - 2.0d0)
    if (b <= (-4.9d+52)) then
        tmp = t_2
    else if (b <= 6.5d-303) then
        tmp = t_1
    else if (b <= 7.5d-250) then
        tmp = a * (1.0d0 - t)
    else if (b <= 3.45d+19) 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 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.9e+52) {
		tmp = t_2;
	} else if (b <= 6.5e-303) {
		tmp = t_1;
	} else if (b <= 7.5e-250) {
		tmp = a * (1.0 - t);
	} else if (b <= 3.45e+19) {
		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 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -4.9e+52:
		tmp = t_2
	elif b <= 6.5e-303:
		tmp = t_1
	elif b <= 7.5e-250:
		tmp = a * (1.0 - t)
	elif b <= 3.45e+19:
		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(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -4.9e+52)
		tmp = t_2;
	elseif (b <= 6.5e-303)
		tmp = t_1;
	elseif (b <= 7.5e-250)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 3.45e+19)
		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 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -4.9e+52)
		tmp = t_2;
	elseif (b <= 6.5e-303)
		tmp = t_1;
	elseif (b <= 7.5e-250)
		tmp = a * (1.0 - t);
	elseif (b <= 3.45e+19)
		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[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.9e+52], t$95$2, If[LessEqual[b, 6.5e-303], t$95$1, If[LessEqual[b, 7.5e-250], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.45e+19], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.89999999999999997e52 or 3.45e19 < b

   1. Initial program 88.6%

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

   3. Taylor expanded in b around inf 72.5%

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

   if -4.89999999999999997e52 < b < 6.50000000000000028e-303 or 7.50000000000000009e-250 < b < 3.45e19

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0 92.8%

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

   4. Taylor expanded in y around inf 57.4%

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

   if 6.50000000000000028e-303 < b < 7.50000000000000009e-250

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 87.8%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.9 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-303}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.45 \cdot 10^{+19}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+85} \lor \neg \left(t \leq 1.22 \cdot 10^{+131}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(b \cdot \left(y + -2\right) + \left(a - z \cdot \left(y + -1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9.5e+85) (not (<= t 1.22e+131)))
   (* t (- b a))
   (+ x (+ (* b (+ y -2.0)) (- a (* z (+ y -1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.5e+85) || !(t <= 1.22e+131)) {
		tmp = t * (b - a);
	} else {
		tmp = x + ((b * (y + -2.0)) + (a - (z * (y + -1.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-9.5d+85)) .or. (.not. (t <= 1.22d+131))) then
        tmp = t * (b - a)
    else
        tmp = x + ((b * (y + (-2.0d0))) + (a - (z * (y + (-1.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.5e+85) || !(t <= 1.22e+131)) {
		tmp = t * (b - a);
	} else {
		tmp = x + ((b * (y + -2.0)) + (a - (z * (y + -1.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9.5e+85) or not (t <= 1.22e+131):
		tmp = t * (b - a)
	else:
		tmp = x + ((b * (y + -2.0)) + (a - (z * (y + -1.0))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9.5e+85) || !(t <= 1.22e+131))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + Float64(Float64(b * Float64(y + -2.0)) + Float64(a - Float64(z * Float64(y + -1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9.5e+85) || ~((t <= 1.22e+131)))
		tmp = t * (b - a);
	else
		tmp = x + ((b * (y + -2.0)) + (a - (z * (y + -1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9.5e+85], N[Not[LessEqual[t, 1.22e+131]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + N[(a - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.49999999999999945e85 or 1.22e131 < t

   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 t around inf 78.5%

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

   if -9.49999999999999945e85 < t < 1.22e131

   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 t around 0 96.7%

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

   4. Taylor expanded in t around 0 91.8%

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

      1. associate--l+ 91.8%

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

      2. sub-neg 91.8%

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

      3. metadata-eval 91.8%

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

      4. +-commutative 91.8%

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

      5. sub-neg 91.8%

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

      6. metadata-eval 91.8%

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

      7. mul-1-neg 91.8%

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

      8. sub-neg 91.8%

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

   6. Simplified 91.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+85} \lor \neg \left(t \leq 1.22 \cdot 10^{+131}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(b \cdot \left(y + -2\right) + \left(a - z \cdot \left(y + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+51} \lor \neg \left(t \leq 10000000000000\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(b \cdot \left(y + -2\right) + \left(a - z \cdot \left(y + -1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.25e+51) (not (<= t 10000000000000.0)))
   (+ (- x (* b (- 2.0 (+ y t)))) (* a (- 1.0 t)))
   (+ x (+ (* b (+ y -2.0)) (- a (* z (+ y -1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.25e+51) || !(t <= 10000000000000.0)) {
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	} else {
		tmp = x + ((b * (y + -2.0)) + (a - (z * (y + -1.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.25d+51)) .or. (.not. (t <= 10000000000000.0d0))) then
        tmp = (x - (b * (2.0d0 - (y + t)))) + (a * (1.0d0 - t))
    else
        tmp = x + ((b * (y + (-2.0d0))) + (a - (z * (y + (-1.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.25e+51) || !(t <= 10000000000000.0)) {
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	} else {
		tmp = x + ((b * (y + -2.0)) + (a - (z * (y + -1.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.25e+51) or not (t <= 10000000000000.0):
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t))
	else:
		tmp = x + ((b * (y + -2.0)) + (a - (z * (y + -1.0))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.25e+51) || !(t <= 10000000000000.0))
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x + Float64(Float64(b * Float64(y + -2.0)) + Float64(a - Float64(z * Float64(y + -1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.25e+51) || ~((t <= 10000000000000.0)))
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	else
		tmp = x + ((b * (y + -2.0)) + (a - (z * (y + -1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.25e+51], N[Not[LessEqual[t, 10000000000000.0]], $MachinePrecision]], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + N[(a - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25e51 or 1e13 < t

   1. Initial program 89.1%

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

   3. Taylor expanded in z around 0 81.8%

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

   if -1.25e51 < t < 1e13

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0 96.8%

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

   4. Taylor expanded in t around 0 95.3%

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

      1. associate--l+ 95.3%

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

      2. sub-neg 95.3%

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

      3. metadata-eval 95.3%

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

      4. +-commutative 95.3%

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

      5. sub-neg 95.3%

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

      6. metadata-eval 95.3%

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

      7. mul-1-neg 95.3%

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

      8. sub-neg 95.3%

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

   6. Simplified 95.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+51} \lor \neg \left(t \leq 10000000000000\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(b \cdot \left(y + -2\right) + \left(a - z \cdot \left(y + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1.85 \cdot 10^{+58}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-60}:\\ \;\;\;\;x + \left(t\_3 + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (- x (* b (- 2.0 (+ y t)))))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -1.85e+58)
     (+ t_2 t_1)
     (if (<= b 2.35e-60) (+ x (+ t_3 t_1)) (+ t_2 t_3)))))

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 = x - (b * (2.0 - (y + t)));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.85e+58) {
		tmp = t_2 + t_1;
	} else if (b <= 2.35e-60) {
		tmp = x + (t_3 + t_1);
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x - (b * (2.0d0 - (y + t)))
    t_3 = z * (1.0d0 - y)
    if (b <= (-1.85d+58)) then
        tmp = t_2 + t_1
    else if (b <= 2.35d-60) then
        tmp = x + (t_3 + t_1)
    else
        tmp = t_2 + t_3
    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 = x - (b * (2.0 - (y + t)));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.85e+58) {
		tmp = t_2 + t_1;
	} else if (b <= 2.35e-60) {
		tmp = x + (t_3 + t_1);
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x - (b * (2.0 - (y + t)))
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -1.85e+58:
		tmp = t_2 + t_1
	elif b <= 2.35e-60:
		tmp = x + (t_3 + t_1)
	else:
		tmp = t_2 + t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -1.85e+58)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 2.35e-60)
		tmp = Float64(x + Float64(t_3 + t_1));
	else
		tmp = Float64(t_2 + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x - (b * (2.0 - (y + t)));
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -1.85e+58)
		tmp = t_2 + t_1;
	elseif (b <= 2.35e-60)
		tmp = x + (t_3 + t_1);
	else
		tmp = t_2 + t_3;
	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[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.85e+58], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 2.35e-60], N[(x + N[(t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8500000000000001e58

   1. Initial program 83.3%

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

   3. Taylor expanded in z around 0 86.0%

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

   if -1.8500000000000001e58 < b < 2.35e-60

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0 94.8%

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

   if 2.35e-60 < b

   1. Initial program 93.4%

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

   3. Taylor expanded in a around 0 87.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+58}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-60}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -505:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5600000:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -505.0)
   (* t b)
   (if (<= t 7e-184) x (if (<= t 5600000.0) z (if (<= t 1.8e+98) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -505.0) {
		tmp = t * b;
	} else if (t <= 7e-184) {
		tmp = x;
	} else if (t <= 5600000.0) {
		tmp = z;
	} else if (t <= 1.8e+98) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-505.0d0)) then
        tmp = t * b
    else if (t <= 7d-184) then
        tmp = x
    else if (t <= 5600000.0d0) then
        tmp = z
    else if (t <= 1.8d+98) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -505.0) {
		tmp = t * b;
	} else if (t <= 7e-184) {
		tmp = x;
	} else if (t <= 5600000.0) {
		tmp = z;
	} else if (t <= 1.8e+98) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -505.0:
		tmp = t * b
	elif t <= 7e-184:
		tmp = x
	elif t <= 5600000.0:
		tmp = z
	elif t <= 1.8e+98:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -505.0)
		tmp = Float64(t * b);
	elseif (t <= 7e-184)
		tmp = x;
	elseif (t <= 5600000.0)
		tmp = z;
	elseif (t <= 1.8e+98)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -505.0)
		tmp = t * b;
	elseif (t <= 7e-184)
		tmp = x;
	elseif (t <= 5600000.0)
		tmp = z;
	elseif (t <= 1.8e+98)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -505.0], N[(t * b), $MachinePrecision], If[LessEqual[t, 7e-184], x, If[LessEqual[t, 5600000.0], z, If[LessEqual[t, 1.8e+98], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -505 or 1.7999999999999999e98 < t

   1. Initial program 88.8%

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

   3. Taylor expanded in b around inf 55.4%

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

   4. Taylor expanded in t around inf 45.6%

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

   if -505 < t < 6.99999999999999962e-184 or 5.6e6 < t < 1.7999999999999999e98

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf 25.0%

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

   if 6.99999999999999962e-184 < t < 5.6e6

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf 47.0%

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

   4. Taylor expanded in y around 0 18.5%

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

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -505:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5600000:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+60}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))))
   (if (<= y -8e+16)
     t_1
     (if (<= y 4.1e+60) (+ x a) (if (<= y 2.75e+170) t_1 (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -8e+16) {
		tmp = t_1;
	} else if (y <= 4.1e+60) {
		tmp = x + a;
	} else if (y <= 2.75e+170) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -y
    if (y <= (-8d+16)) then
        tmp = t_1
    else if (y <= 4.1d+60) then
        tmp = x + a
    else if (y <= 2.75d+170) then
        tmp = t_1
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -8e+16) {
		tmp = t_1;
	} else if (y <= 4.1e+60) {
		tmp = x + a;
	} else if (y <= 2.75e+170) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * -y
	tmp = 0
	if y <= -8e+16:
		tmp = t_1
	elif y <= 4.1e+60:
		tmp = x + a
	elif y <= 2.75e+170:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -8e+16)
		tmp = t_1;
	elseif (y <= 4.1e+60)
		tmp = Float64(x + a);
	elseif (y <= 2.75e+170)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * -y;
	tmp = 0.0;
	if (y <= -8e+16)
		tmp = t_1;
	elseif (y <= 4.1e+60)
		tmp = x + a;
	elseif (y <= 2.75e+170)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -8e+16], t$95$1, If[LessEqual[y, 4.1e+60], N[(x + a), $MachinePrecision], If[LessEqual[y, 2.75e+170], t$95$1, N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8e16 or 4.1e60 < y < 2.7499999999999999e170

   1. Initial program 92.0%

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

   3. Taylor expanded in b around 0 71.2%

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

   4. Taylor expanded in y around inf 56.2%

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

   5. Taylor expanded in x around 0 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

   7. Simplified 50.9%

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

   if -8e16 < y < 4.1e60

   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 0 98.5%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate--l+ 71.0%

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

      2. sub-neg 71.0%

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

      3. metadata-eval 71.0%

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

      4. +-commutative 71.0%

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

      5. sub-neg 71.0%

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

      6. metadata-eval 71.0%

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

      7. mul-1-neg 71.0%

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

      8. sub-neg 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in a around inf 40.1%

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

   if 2.7499999999999999e170 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 80.2%

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

   4. Taylor expanded in b around inf 57.4%

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

      1. *-commutative 57.4%

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

   6. Simplified 57.4%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+60}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+170}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 63.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+15} \lor \neg \left(y \leq 4.1 \cdot 10^{+60}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + \left(z + -2 \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.5e+15) (not (<= y 4.1e+60)))
   (* y (- b z))
   (+ x (+ a (+ z (* -2.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.5e+15) || !(y <= 4.1e+60)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (a + (z + (-2.0 * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.5d+15)) .or. (.not. (y <= 4.1d+60))) then
        tmp = y * (b - z)
    else
        tmp = x + (a + (z + ((-2.0d0) * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.5e+15) || !(y <= 4.1e+60)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (a + (z + (-2.0 * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.5e+15) or not (y <= 4.1e+60):
		tmp = y * (b - z)
	else:
		tmp = x + (a + (z + (-2.0 * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.5e+15) || !(y <= 4.1e+60))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x + Float64(a + Float64(z + Float64(-2.0 * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.5e+15) || ~((y <= 4.1e+60)))
		tmp = y * (b - z);
	else
		tmp = x + (a + (z + (-2.0 * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.5e+15], N[Not[LessEqual[y, 4.1e+60]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(a + N[(z + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e15 or 4.1e60 < y

   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 y around inf 75.2%

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

   if -6.5e15 < y < 4.1e60

   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 0 98.5%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate--l+ 71.0%

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

      2. sub-neg 71.0%

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

      3. metadata-eval 71.0%

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

      4. +-commutative 71.0%

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

      5. sub-neg 71.0%

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

      6. metadata-eval 71.0%

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

      7. mul-1-neg 71.0%

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

      8. sub-neg 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 66.7%

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

      1. neg-mul-1 66.7%

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

      2. associate--l+ 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+15} \lor \neg \left(y \leq 4.1 \cdot 10^{+60}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + \left(z + -2 \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 26.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+14}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.2e+84)
   (* t b)
   (if (<= t 2.55e+14) (* y b) (if (<= t 1.8e+98) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e+84) {
		tmp = t * b;
	} else if (t <= 2.55e+14) {
		tmp = y * b;
	} else if (t <= 1.8e+98) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.2d+84)) then
        tmp = t * b
    else if (t <= 2.55d+14) then
        tmp = y * b
    else if (t <= 1.8d+98) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e+84) {
		tmp = t * b;
	} else if (t <= 2.55e+14) {
		tmp = y * b;
	} else if (t <= 1.8e+98) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.2e+84:
		tmp = t * b
	elif t <= 2.55e+14:
		tmp = y * b
	elif t <= 1.8e+98:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.2e+84)
		tmp = Float64(t * b);
	elseif (t <= 2.55e+14)
		tmp = Float64(y * b);
	elseif (t <= 1.8e+98)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.2e+84)
		tmp = t * b;
	elseif (t <= 2.55e+14)
		tmp = y * b;
	elseif (t <= 1.8e+98)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.2e+84], N[(t * b), $MachinePrecision], If[LessEqual[t, 2.55e+14], N[(y * b), $MachinePrecision], If[LessEqual[t, 1.8e+98], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2e84 or 1.7999999999999999e98 < t

   1. Initial program 87.0%

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

   3. Taylor expanded in b around inf 55.9%

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

   4. Taylor expanded in t around inf 50.7%

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

   if -1.2e84 < t < 2.55e14

   1. Initial program 96.9%

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

   3. Taylor expanded in y around inf 46.7%

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

   4. Taylor expanded in b around inf 21.1%

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

      1. *-commutative 21.1%

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

   6. Simplified 21.1%

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

   if 2.55e14 < t < 1.7999999999999999e98

   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 x around inf 42.4%

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

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+14}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 32.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+89}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.66 \cdot 10^{+139}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.4e+89) (* y b) (if (<= b 1.66e+139) (+ x a) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.4e+89) {
		tmp = y * b;
	} else if (b <= 1.66e+139) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.4d+89)) then
        tmp = y * b
    else if (b <= 1.66d+139) then
        tmp = x + a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.4e+89) {
		tmp = y * b;
	} else if (b <= 1.66e+139) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.4e+89:
		tmp = y * b
	elif b <= 1.66e+139:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.4e+89)
		tmp = Float64(y * b);
	elseif (b <= 1.66e+139)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.4e+89)
		tmp = y * b;
	elseif (b <= 1.66e+139)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.4e+89], N[(y * b), $MachinePrecision], If[LessEqual[b, 1.66e+139], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.4e89

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf 46.7%

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

   4. Taylor expanded in b around inf 41.8%

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

      1. *-commutative 41.8%

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

   6. Simplified 41.8%

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

   if -5.4e89 < b < 1.66e139

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0 98.2%

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

   4. Taylor expanded in t around 0 81.5%

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

      1. associate--l+ 81.5%

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

      2. sub-neg 81.5%

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

      3. metadata-eval 81.5%

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

      4. +-commutative 81.5%

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

      5. sub-neg 81.5%

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

      6. metadata-eval 81.5%

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

      7. mul-1-neg 81.5%

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

      8. sub-neg 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in a around inf 36.2%

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

   if 1.66e139 < b

   1. Initial program 88.3%

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

   3. Taylor expanded in b around inf 86.9%

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

   4. Taylor expanded in t around inf 44.4%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+89}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.66 \cdot 10^{+139}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 20.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+134}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.7e+134) z (if (<= z 1.72e+170) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.7e+134) {
		tmp = z;
	} else if (z <= 1.72e+170) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.7d+134)) then
        tmp = z
    else if (z <= 1.72d+170) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.7e+134) {
		tmp = z;
	} else if (z <= 1.72e+170) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.7e+134:
		tmp = z
	elif z <= 1.72e+170:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.7e+134)
		tmp = z;
	elseif (z <= 1.72e+170)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.7e+134)
		tmp = z;
	elseif (z <= 1.72e+170)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.7e+134], z, If[LessEqual[z, 1.72e+170], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e134 or 1.7200000000000001e170 < z

   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 z around inf 68.7%

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

   4. Taylor expanded in y around 0 24.7%

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

   if -2.7e134 < z < 1.7200000000000001e170

   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 x around inf 21.5%

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

4. Final simplification 22.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+134}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 15.4% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

3. Taylor expanded in x around inf 16.8%

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

4. Final simplification 16.8%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024115 
(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)))