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

Percentage Accurate: 95.3% → 97.6%

Time: 20.5s

Alternatives: 22

Speedup: 0.5×

• 37.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0)))
        (t_2 (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) t_1)))
   (if (<= t_2 INFINITY) t_2 (+ x t_1))))

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + t_1;
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	t_2 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + t_1
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = x + t_1
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	t_2 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + t_1;
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around 0 33.3%

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

   3. Taylor expanded in z around 0 66.7%

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

4. Final simplification 98.8%

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

Alternative 2: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-def 97.2%

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

   3. associate--l+ 97.2%

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

   4. sub-neg 97.2%

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

   5. metadata-eval 97.2%

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

   6. sub-neg 97.2%

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

   7. associate-+l- 97.2%

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

   8. fma-neg 97.2%

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

   9. sub-neg 97.2%

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

   10. metadata-eval 97.2%

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

   11. remove-double-neg 97.2%

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

   12. sub-neg 97.2%

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

   13. metadata-eval 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 3: 58.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := x + \left(a - t \cdot a\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1.36 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-205}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1.82 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-269}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.35 \cdot 10^{-186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-85} \lor \neg \left(b \leq 1.46 \cdot 10^{+40}\right) \land b \leq 6 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0))))
        (t_2 (+ x (- a (* t a))))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -1.36e+75)
     t_1
     (if (<= b -4.7e-92)
       t_2
       (if (<= b -4.2e-205)
         (- x (* y z))
         (if (<= b -1.82e-234)
           t_2
           (if (<= b -2.5e-269)
             t_3
             (if (<= b 3.35e-186)
               t_2
               (if (or (<= b 1.26e-85)
                       (and (not (<= b 1.46e+40)) (<= b 6e+85)))
                 t_3
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double t_2 = x + (a - (t * a));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.36e+75) {
		tmp = t_1;
	} else if (b <= -4.7e-92) {
		tmp = t_2;
	} else if (b <= -4.2e-205) {
		tmp = x - (y * z);
	} else if (b <= -1.82e-234) {
		tmp = t_2;
	} else if (b <= -2.5e-269) {
		tmp = t_3;
	} else if (b <= 3.35e-186) {
		tmp = t_2;
	} else if ((b <= 1.26e-85) || (!(b <= 1.46e+40) && (b <= 6e+85))) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    t_2 = x + (a - (t * a))
    t_3 = z * (1.0d0 - y)
    if (b <= (-1.36d+75)) then
        tmp = t_1
    else if (b <= (-4.7d-92)) then
        tmp = t_2
    else if (b <= (-4.2d-205)) then
        tmp = x - (y * z)
    else if (b <= (-1.82d-234)) then
        tmp = t_2
    else if (b <= (-2.5d-269)) then
        tmp = t_3
    else if (b <= 3.35d-186) then
        tmp = t_2
    else if ((b <= 1.26d-85) .or. (.not. (b <= 1.46d+40)) .and. (b <= 6d+85)) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double t_2 = x + (a - (t * a));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.36e+75) {
		tmp = t_1;
	} else if (b <= -4.7e-92) {
		tmp = t_2;
	} else if (b <= -4.2e-205) {
		tmp = x - (y * z);
	} else if (b <= -1.82e-234) {
		tmp = t_2;
	} else if (b <= -2.5e-269) {
		tmp = t_3;
	} else if (b <= 3.35e-186) {
		tmp = t_2;
	} else if ((b <= 1.26e-85) || (!(b <= 1.46e+40) && (b <= 6e+85))) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	t_2 = x + (a - (t * a))
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -1.36e+75:
		tmp = t_1
	elif b <= -4.7e-92:
		tmp = t_2
	elif b <= -4.2e-205:
		tmp = x - (y * z)
	elif b <= -1.82e-234:
		tmp = t_2
	elif b <= -2.5e-269:
		tmp = t_3
	elif b <= 3.35e-186:
		tmp = t_2
	elif (b <= 1.26e-85) or (not (b <= 1.46e+40) and (b <= 6e+85)):
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_2 = Float64(x + Float64(a - Float64(t * a)))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -1.36e+75)
		tmp = t_1;
	elseif (b <= -4.7e-92)
		tmp = t_2;
	elseif (b <= -4.2e-205)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= -1.82e-234)
		tmp = t_2;
	elseif (b <= -2.5e-269)
		tmp = t_3;
	elseif (b <= 3.35e-186)
		tmp = t_2;
	elseif ((b <= 1.26e-85) || (!(b <= 1.46e+40) && (b <= 6e+85)))
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	t_2 = x + (a - (t * a));
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -1.36e+75)
		tmp = t_1;
	elseif (b <= -4.7e-92)
		tmp = t_2;
	elseif (b <= -4.2e-205)
		tmp = x - (y * z);
	elseif (b <= -1.82e-234)
		tmp = t_2;
	elseif (b <= -2.5e-269)
		tmp = t_3;
	elseif (b <= 3.35e-186)
		tmp = t_2;
	elseif ((b <= 1.26e-85) || (~((b <= 1.46e+40)) && (b <= 6e+85)))
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.36e+75], t$95$1, If[LessEqual[b, -4.7e-92], t$95$2, If[LessEqual[b, -4.2e-205], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.82e-234], t$95$2, If[LessEqual[b, -2.5e-269], t$95$3, If[LessEqual[b, 3.35e-186], t$95$2, If[Or[LessEqual[b, 1.26e-85], And[N[Not[LessEqual[b, 1.46e+40]], $MachinePrecision], LessEqual[b, 6e+85]]], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.36e75 or 1.26e-85 < b < 1.46e40 or 6.0000000000000001e85 < b

   1. Initial program 92.9%

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

   2. Taylor expanded in a around 0 87.1%

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

   3. Taylor expanded in z around 0 82.1%

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

   if -1.36e75 < b < -4.69999999999999993e-92 or -4.19999999999999965e-205 < b < -1.8200000000000001e-234 or -2.49999999999999989e-269 < b < 3.35000000000000017e-186

   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. Taylor expanded in b around 0 91.2%

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

   3. Taylor expanded in a around inf 70.6%

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

      1. sub-neg 70.6%

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

      2. metadata-eval 70.6%

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

      3. distribute-rgt-in 70.6%

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

      4. *-commutative 70.6%

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

      5. neg-mul-1 70.6%

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

      6. unsub-neg 70.6%

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

   5. Simplified 70.6%

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

   if -4.69999999999999993e-92 < b < -4.19999999999999965e-205

   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. Taylor expanded in b around 0 93.4%

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

   3. Taylor expanded in y around inf 63.3%

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

   if -1.8200000000000001e-234 < b < -2.49999999999999989e-269 or 3.35000000000000017e-186 < b < 1.26e-85 or 1.46e40 < b < 6.0000000000000001e85

   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. Taylor expanded in z around inf 68.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.36 \cdot 10^{+75}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-92}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-205}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1.82 \cdot 10^{-234}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-269}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.35 \cdot 10^{-186}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-85} \lor \neg \left(b \leq 1.46 \cdot 10^{+40}\right) \land b \leq 6 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 4: 50.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_4 := t \cdot \left(b - a\right)\\ \mathbf{if}\;b \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -0.0095:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-53}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-248}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-7}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z)))
        (t_2 (* z (- 1.0 y)))
        (t_3 (* b (- (+ y t) 2.0)))
        (t_4 (* t (- b a))))
   (if (<= b -2.9e+123)
     t_3
     (if (<= b -0.0095)
       t_1
       (if (<= b -7e-53)
         t_4
         (if (<= b -2e-90)
           (* a (- 1.0 t))
           (if (<= b 2.8e-306)
             t_1
             (if (<= b 1.8e-248)
               (- x (* t a))
               (if (<= b 1.65e-85)
                 t_2
                 (if (<= b 4e-7) t_4 (if (<= b 1.8e+87) t_2 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = z * (1.0 - y);
	double t_3 = b * ((y + t) - 2.0);
	double t_4 = t * (b - a);
	double tmp;
	if (b <= -2.9e+123) {
		tmp = t_3;
	} else if (b <= -0.0095) {
		tmp = t_1;
	} else if (b <= -7e-53) {
		tmp = t_4;
	} else if (b <= -2e-90) {
		tmp = a * (1.0 - t);
	} else if (b <= 2.8e-306) {
		tmp = t_1;
	} else if (b <= 1.8e-248) {
		tmp = x - (t * a);
	} else if (b <= 1.65e-85) {
		tmp = t_2;
	} else if (b <= 4e-7) {
		tmp = t_4;
	} else if (b <= 1.8e+87) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_4
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = z * (1.0d0 - y)
    t_3 = b * ((y + t) - 2.0d0)
    t_4 = t * (b - a)
    if (b <= (-2.9d+123)) then
        tmp = t_3
    else if (b <= (-0.0095d0)) then
        tmp = t_1
    else if (b <= (-7d-53)) then
        tmp = t_4
    else if (b <= (-2d-90)) then
        tmp = a * (1.0d0 - t)
    else if (b <= 2.8d-306) then
        tmp = t_1
    else if (b <= 1.8d-248) then
        tmp = x - (t * a)
    else if (b <= 1.65d-85) then
        tmp = t_2
    else if (b <= 4d-7) then
        tmp = t_4
    else if (b <= 1.8d+87) then
        tmp = t_2
    else
        tmp = 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 = x - (y * z);
	double t_2 = z * (1.0 - y);
	double t_3 = b * ((y + t) - 2.0);
	double t_4 = t * (b - a);
	double tmp;
	if (b <= -2.9e+123) {
		tmp = t_3;
	} else if (b <= -0.0095) {
		tmp = t_1;
	} else if (b <= -7e-53) {
		tmp = t_4;
	} else if (b <= -2e-90) {
		tmp = a * (1.0 - t);
	} else if (b <= 2.8e-306) {
		tmp = t_1;
	} else if (b <= 1.8e-248) {
		tmp = x - (t * a);
	} else if (b <= 1.65e-85) {
		tmp = t_2;
	} else if (b <= 4e-7) {
		tmp = t_4;
	} else if (b <= 1.8e+87) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = z * (1.0 - y)
	t_3 = b * ((y + t) - 2.0)
	t_4 = t * (b - a)
	tmp = 0
	if b <= -2.9e+123:
		tmp = t_3
	elif b <= -0.0095:
		tmp = t_1
	elif b <= -7e-53:
		tmp = t_4
	elif b <= -2e-90:
		tmp = a * (1.0 - t)
	elif b <= 2.8e-306:
		tmp = t_1
	elif b <= 1.8e-248:
		tmp = x - (t * a)
	elif b <= 1.65e-85:
		tmp = t_2
	elif b <= 4e-7:
		tmp = t_4
	elif b <= 1.8e+87:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(z * Float64(1.0 - y))
	t_3 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_4 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (b <= -2.9e+123)
		tmp = t_3;
	elseif (b <= -0.0095)
		tmp = t_1;
	elseif (b <= -7e-53)
		tmp = t_4;
	elseif (b <= -2e-90)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 2.8e-306)
		tmp = t_1;
	elseif (b <= 1.8e-248)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 1.65e-85)
		tmp = t_2;
	elseif (b <= 4e-7)
		tmp = t_4;
	elseif (b <= 1.8e+87)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = z * (1.0 - y);
	t_3 = b * ((y + t) - 2.0);
	t_4 = t * (b - a);
	tmp = 0.0;
	if (b <= -2.9e+123)
		tmp = t_3;
	elseif (b <= -0.0095)
		tmp = t_1;
	elseif (b <= -7e-53)
		tmp = t_4;
	elseif (b <= -2e-90)
		tmp = a * (1.0 - t);
	elseif (b <= 2.8e-306)
		tmp = t_1;
	elseif (b <= 1.8e-248)
		tmp = x - (t * a);
	elseif (b <= 1.65e-85)
		tmp = t_2;
	elseif (b <= 4e-7)
		tmp = t_4;
	elseif (b <= 1.8e+87)
		tmp = t_2;
	else
		tmp = t_3;
	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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.9e+123], t$95$3, If[LessEqual[b, -0.0095], t$95$1, If[LessEqual[b, -7e-53], t$95$4, If[LessEqual[b, -2e-90], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-306], t$95$1, If[LessEqual[b, 1.8e-248], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e-85], t$95$2, If[LessEqual[b, 4e-7], t$95$4, If[LessEqual[b, 1.8e+87], t$95$2, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.9000000000000001e123 or 1.79999999999999997e87 < b

   1. Initial program 90.7%

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

   2. Taylor expanded in b around inf 80.6%

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

   if -2.9000000000000001e123 < b < -0.00949999999999999976 or -1.99999999999999999e-90 < b < 2.8000000000000001e-306

   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. Taylor expanded in b around 0 90.5%

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

   3. Taylor expanded in y around inf 61.2%

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

   if -0.00949999999999999976 < b < -6.99999999999999987e-53 or 1.64999999999999986e-85 < b < 3.9999999999999998e-7

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 59.2%

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

   if -6.99999999999999987e-53 < b < -1.99999999999999999e-90

   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. Taylor expanded in a around inf 61.6%

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

   if 2.8000000000000001e-306 < b < 1.79999999999999992e-248

   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. Taylor expanded in b around 0 100.0%

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

   3. Taylor expanded in t around inf 69.9%

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

   if 1.79999999999999992e-248 < b < 1.64999999999999986e-85 or 3.9999999999999998e-7 < b < 1.79999999999999997e87

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf 56.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -0.0095:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-306}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-248}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 5: 55.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - t \cdot a\right)\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-204}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.35 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+44}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- a (* t a))))
        (t_2 (* z (- 1.0 y)))
        (t_3 (* b (- (+ y t) 2.0))))
   (if (<= b -1.4e+103)
     t_3
     (if (<= b -3.4e-91)
       t_1
       (if (<= b -3.1e-204)
         (- x (* y z))
         (if (<= b -5.3e-236)
           t_1
           (if (<= b -5.2e-274)
             t_2
             (if (<= b 3.35e-186)
               t_1
               (if (<= b 5e-81)
                 t_2
                 (if (<= b 5.8e+44)
                   (+ x (* b (- t 2.0)))
                   (if (<= b 6e+85) t_2 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (t * a));
	double t_2 = z * (1.0 - y);
	double t_3 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.4e+103) {
		tmp = t_3;
	} else if (b <= -3.4e-91) {
		tmp = t_1;
	} else if (b <= -3.1e-204) {
		tmp = x - (y * z);
	} else if (b <= -5.3e-236) {
		tmp = t_1;
	} else if (b <= -5.2e-274) {
		tmp = t_2;
	} else if (b <= 3.35e-186) {
		tmp = t_1;
	} else if (b <= 5e-81) {
		tmp = t_2;
	} else if (b <= 5.8e+44) {
		tmp = x + (b * (t - 2.0));
	} else if (b <= 6e+85) {
		tmp = t_2;
	} else {
		tmp = 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 = x + (a - (t * a))
    t_2 = z * (1.0d0 - y)
    t_3 = b * ((y + t) - 2.0d0)
    if (b <= (-1.4d+103)) then
        tmp = t_3
    else if (b <= (-3.4d-91)) then
        tmp = t_1
    else if (b <= (-3.1d-204)) then
        tmp = x - (y * z)
    else if (b <= (-5.3d-236)) then
        tmp = t_1
    else if (b <= (-5.2d-274)) then
        tmp = t_2
    else if (b <= 3.35d-186) then
        tmp = t_1
    else if (b <= 5d-81) then
        tmp = t_2
    else if (b <= 5.8d+44) then
        tmp = x + (b * (t - 2.0d0))
    else if (b <= 6d+85) then
        tmp = t_2
    else
        tmp = 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 = x + (a - (t * a));
	double t_2 = z * (1.0 - y);
	double t_3 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.4e+103) {
		tmp = t_3;
	} else if (b <= -3.4e-91) {
		tmp = t_1;
	} else if (b <= -3.1e-204) {
		tmp = x - (y * z);
	} else if (b <= -5.3e-236) {
		tmp = t_1;
	} else if (b <= -5.2e-274) {
		tmp = t_2;
	} else if (b <= 3.35e-186) {
		tmp = t_1;
	} else if (b <= 5e-81) {
		tmp = t_2;
	} else if (b <= 5.8e+44) {
		tmp = x + (b * (t - 2.0));
	} else if (b <= 6e+85) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a - (t * a))
	t_2 = z * (1.0 - y)
	t_3 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.4e+103:
		tmp = t_3
	elif b <= -3.4e-91:
		tmp = t_1
	elif b <= -3.1e-204:
		tmp = x - (y * z)
	elif b <= -5.3e-236:
		tmp = t_1
	elif b <= -5.2e-274:
		tmp = t_2
	elif b <= 3.35e-186:
		tmp = t_1
	elif b <= 5e-81:
		tmp = t_2
	elif b <= 5.8e+44:
		tmp = x + (b * (t - 2.0))
	elif b <= 6e+85:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a - Float64(t * a)))
	t_2 = Float64(z * Float64(1.0 - y))
	t_3 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.4e+103)
		tmp = t_3;
	elseif (b <= -3.4e-91)
		tmp = t_1;
	elseif (b <= -3.1e-204)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= -5.3e-236)
		tmp = t_1;
	elseif (b <= -5.2e-274)
		tmp = t_2;
	elseif (b <= 3.35e-186)
		tmp = t_1;
	elseif (b <= 5e-81)
		tmp = t_2;
	elseif (b <= 5.8e+44)
		tmp = Float64(x + Float64(b * Float64(t - 2.0)));
	elseif (b <= 6e+85)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a - (t * a));
	t_2 = z * (1.0 - y);
	t_3 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.4e+103)
		tmp = t_3;
	elseif (b <= -3.4e-91)
		tmp = t_1;
	elseif (b <= -3.1e-204)
		tmp = x - (y * z);
	elseif (b <= -5.3e-236)
		tmp = t_1;
	elseif (b <= -5.2e-274)
		tmp = t_2;
	elseif (b <= 3.35e-186)
		tmp = t_1;
	elseif (b <= 5e-81)
		tmp = t_2;
	elseif (b <= 5.8e+44)
		tmp = x + (b * (t - 2.0));
	elseif (b <= 6e+85)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+103], t$95$3, If[LessEqual[b, -3.4e-91], t$95$1, If[LessEqual[b, -3.1e-204], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.3e-236], t$95$1, If[LessEqual[b, -5.2e-274], t$95$2, If[LessEqual[b, 3.35e-186], t$95$1, If[LessEqual[b, 5e-81], t$95$2, If[LessEqual[b, 5.8e+44], N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+85], t$95$2, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.40000000000000004e103 or 6.0000000000000001e85 < b

   1. Initial program 91.1%

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

   2. Taylor expanded in b around inf 79.2%

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

   if -1.40000000000000004e103 < b < -3.40000000000000027e-91 or -3.0999999999999999e-204 < b < -5.3000000000000002e-236 or -5.2e-274 < b < 3.35000000000000017e-186

   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. Taylor expanded in b around 0 90.5%

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

   3. Taylor expanded in a around inf 71.3%

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

      1. sub-neg 71.3%

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

      2. metadata-eval 71.3%

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

      3. distribute-rgt-in 71.3%

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

      4. *-commutative 71.3%

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

      5. neg-mul-1 71.3%

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

      6. unsub-neg 71.3%

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

   5. Simplified 71.3%

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

   if -3.40000000000000027e-91 < b < -3.0999999999999999e-204

   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. Taylor expanded in b around 0 93.4%

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

   3. Taylor expanded in y around inf 63.3%

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

   if -5.3000000000000002e-236 < b < -5.2e-274 or 3.35000000000000017e-186 < b < 4.99999999999999981e-81 or 5.8000000000000004e44 < b < 6.0000000000000001e85

   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. Taylor expanded in z around inf 70.0%

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

   if 4.99999999999999981e-81 < b < 5.8000000000000004e44

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 70.7%

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

   3. Taylor expanded in z around 0 55.8%

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

   4. Taylor expanded in y around 0 50.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-204}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-236}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-274}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.35 \cdot 10^{-186}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+44}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 6: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + \left(a - t \cdot a\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.72 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (- a (* t a))))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -1.72e+75)
     t_2
     (if (<= b 4.9e-53)
       t_1
       (if (<= b 5.5e+34)
         t_2
         (if (<= b 3.2e+56)
           t_1
           (if (<= b 1.2e+91)
             (* y (- b z))
             (if (<= b 1.15e+104) (* a (- 1.0 t)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a - (t * a)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.72e+75) {
		tmp = t_2;
	} else if (b <= 4.9e-53) {
		tmp = t_1;
	} else if (b <= 5.5e+34) {
		tmp = t_2;
	} else if (b <= 3.2e+56) {
		tmp = t_1;
	} else if (b <= 1.2e+91) {
		tmp = y * (b - z);
	} else if (b <= 1.15e+104) {
		tmp = a * (1.0 - t);
	} 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 - (t * a)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-1.72d+75)) then
        tmp = t_2
    else if (b <= 4.9d-53) then
        tmp = t_1
    else if (b <= 5.5d+34) then
        tmp = t_2
    else if (b <= 3.2d+56) then
        tmp = t_1
    else if (b <= 1.2d+91) then
        tmp = y * (b - z)
    else if (b <= 1.15d+104) then
        tmp = a * (1.0d0 - t)
    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 - (t * a)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.72e+75) {
		tmp = t_2;
	} else if (b <= 4.9e-53) {
		tmp = t_1;
	} else if (b <= 5.5e+34) {
		tmp = t_2;
	} else if (b <= 3.2e+56) {
		tmp = t_1;
	} else if (b <= 1.2e+91) {
		tmp = y * (b - z);
	} else if (b <= 1.15e+104) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a - (t * a)))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -1.72e+75:
		tmp = t_2
	elif b <= 4.9e-53:
		tmp = t_1
	elif b <= 5.5e+34:
		tmp = t_2
	elif b <= 3.2e+56:
		tmp = t_1
	elif b <= 1.2e+91:
		tmp = y * (b - z)
	elif b <= 1.15e+104:
		tmp = a * (1.0 - t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a - Float64(t * a))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -1.72e+75)
		tmp = t_2;
	elseif (b <= 4.9e-53)
		tmp = t_1;
	elseif (b <= 5.5e+34)
		tmp = t_2;
	elseif (b <= 3.2e+56)
		tmp = t_1;
	elseif (b <= 1.2e+91)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 1.15e+104)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a - (t * a)));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -1.72e+75)
		tmp = t_2;
	elseif (b <= 4.9e-53)
		tmp = t_1;
	elseif (b <= 5.5e+34)
		tmp = t_2;
	elseif (b <= 3.2e+56)
		tmp = t_1;
	elseif (b <= 1.2e+91)
		tmp = y * (b - z);
	elseif (b <= 1.15e+104)
		tmp = a * (1.0 - t);
	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[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.72e+75], t$95$2, If[LessEqual[b, 4.9e-53], t$95$1, If[LessEqual[b, 5.5e+34], t$95$2, If[LessEqual[b, 3.2e+56], t$95$1, If[LessEqual[b, 1.2e+91], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+104], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.72e75 or 4.89999999999999963e-53 < b < 5.4999999999999996e34 or 1.14999999999999992e104 < b

   1. Initial program 93.3%

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

   2. Taylor expanded in a around 0 90.7%

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

   3. Taylor expanded in z around 0 85.2%

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

   if -1.72e75 < b < 4.89999999999999963e-53 or 5.4999999999999996e34 < b < 3.20000000000000003e56

   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. Taylor expanded in b around 0 93.9%

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

   3. Taylor expanded in y around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. sub-neg 70.2%

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

      3. metadata-eval 70.2%

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

      4. mul-1-neg 70.2%

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

      5. unsub-neg 70.2%

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

      6. distribute-rgt-in 70.2%

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

      7. *-commutative 70.2%

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

      8. neg-mul-1 70.2%

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

      9. unsub-neg 70.2%

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

   5. Simplified 70.2%

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

   if 3.20000000000000003e56 < b < 1.19999999999999991e91

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 78.3%

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

   if 1.19999999999999991e91 < b < 1.14999999999999992e104

   1. Initial program 75.0%

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

   2. Taylor expanded in a around inf 100.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{+75}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{-53}:\\ \;\;\;\;x + \left(z + \left(a - t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+34}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+56}:\\ \;\;\;\;x + \left(z + \left(a - t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 7: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-296}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-247}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= y -9e+25)
     t_1
     (if (<= y -1e-79)
       (* b (- t 2.0))
       (if (<= y -4.6e-255)
         (* a (- 1.0 t))
         (if (<= y -3.2e-289)
           t_2
           (if (<= y 9.5e-296)
             (* z (- 1.0 y))
             (if (<= y 1.42e-247)
               (- x (* t a))
               (if (<= y 3.7e+73) t_2 t_1)))))))))

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 (y <= -9e+25) {
		tmp = t_1;
	} else if (y <= -1e-79) {
		tmp = b * (t - 2.0);
	} else if (y <= -4.6e-255) {
		tmp = a * (1.0 - t);
	} else if (y <= -3.2e-289) {
		tmp = t_2;
	} else if (y <= 9.5e-296) {
		tmp = z * (1.0 - y);
	} else if (y <= 1.42e-247) {
		tmp = x - (t * a);
	} else if (y <= 3.7e+73) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (y <= (-9d+25)) then
        tmp = t_1
    else if (y <= (-1d-79)) then
        tmp = b * (t - 2.0d0)
    else if (y <= (-4.6d-255)) then
        tmp = a * (1.0d0 - t)
    else if (y <= (-3.2d-289)) then
        tmp = t_2
    else if (y <= 9.5d-296) then
        tmp = z * (1.0d0 - y)
    else if (y <= 1.42d-247) then
        tmp = x - (t * a)
    else if (y <= 3.7d+73) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (y <= -9e+25) {
		tmp = t_1;
	} else if (y <= -1e-79) {
		tmp = b * (t - 2.0);
	} else if (y <= -4.6e-255) {
		tmp = a * (1.0 - t);
	} else if (y <= -3.2e-289) {
		tmp = t_2;
	} else if (y <= 9.5e-296) {
		tmp = z * (1.0 - y);
	} else if (y <= 1.42e-247) {
		tmp = x - (t * a);
	} else if (y <= 3.7e+73) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if y <= -9e+25:
		tmp = t_1
	elif y <= -1e-79:
		tmp = b * (t - 2.0)
	elif y <= -4.6e-255:
		tmp = a * (1.0 - t)
	elif y <= -3.2e-289:
		tmp = t_2
	elif y <= 9.5e-296:
		tmp = z * (1.0 - y)
	elif y <= 1.42e-247:
		tmp = x - (t * a)
	elif y <= 3.7e+73:
		tmp = t_2
	else:
		tmp = t_1
	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 (y <= -9e+25)
		tmp = t_1;
	elseif (y <= -1e-79)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= -4.6e-255)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= -3.2e-289)
		tmp = t_2;
	elseif (y <= 9.5e-296)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= 1.42e-247)
		tmp = Float64(x - Float64(t * a));
	elseif (y <= 3.7e+73)
		tmp = t_2;
	else
		tmp = t_1;
	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 (y <= -9e+25)
		tmp = t_1;
	elseif (y <= -1e-79)
		tmp = b * (t - 2.0);
	elseif (y <= -4.6e-255)
		tmp = a * (1.0 - t);
	elseif (y <= -3.2e-289)
		tmp = t_2;
	elseif (y <= 9.5e-296)
		tmp = z * (1.0 - y);
	elseif (y <= 1.42e-247)
		tmp = x - (t * a);
	elseif (y <= 3.7e+73)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+25], t$95$1, If[LessEqual[y, -1e-79], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-255], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-289], t$95$2, If[LessEqual[y, 9.5e-296], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.42e-247], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+73], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -9.0000000000000006e25 or 3.69999999999999973e73 < y

   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. Taylor expanded in y around inf 71.4%

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

   if -9.0000000000000006e25 < y < -1e-79

   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. Taylor expanded in b around inf 56.3%

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

   3. Taylor expanded in y around 0 53.6%

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

   if -1e-79 < y < -4.5999999999999997e-255

   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. Taylor expanded in a around inf 44.8%

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

   if -4.5999999999999997e-255 < y < -3.2000000000000002e-289 or 1.42000000000000001e-247 < y < 3.69999999999999973e73

   1. Initial program 98.5%

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

   2. Taylor expanded in t around inf 46.4%

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

   if -3.2000000000000002e-289 < y < 9.50000000000000046e-296

   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. Taylor expanded in z around inf 72.9%

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

   if 9.50000000000000046e-296 < y < 1.42000000000000001e-247

   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. Taylor expanded in b around 0 88.6%

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

   3. Taylor expanded in t around inf 74.2%

      \[\leadsto x - \color{blue}{a \cdot t} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-289}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-296}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-247}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 8: 85.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{-50} \lor \neg \left(b \leq 2.5 \cdot 10^{-79}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_1 + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -2.2e-50) (not (<= b 2.5e-79)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (+ t_1 (* z (- 1.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -2.2e-50) || !(b <= 2.5e-79)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-2.2d-50)) .or. (.not. (b <= 2.5d-79))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -2.2e-50) || !(b <= 2.5e-79)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -2.2e-50) or not (b <= 2.5e-79):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + (t_1 + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -2.2e-50) || !(b <= 2.5e-79))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((b <= -2.2e-50) || ~((b <= 2.5e-79)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + (t_1 + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2.2e-50], N[Not[LessEqual[b, 2.5e-79]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1999999999999999e-50 or 2.5e-79 < b

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 83.9%

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

   if -2.1999999999999999e-50 < b < 2.5e-79

   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. Taylor expanded in b around 0 97.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{-50} \lor \neg \left(b \leq 2.5 \cdot 10^{-79}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 9: 85.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{-52}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-53}:\\ \;\;\;\;x + \left(t_1 + t_3\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -1.5e-52)
     (+ t_2 t_1)
     (if (<= b 2.3e-53) (+ x (+ t_1 t_3)) (+ 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 * ((y + t) - 2.0));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.5e-52) {
		tmp = t_2 + t_1;
	} else if (b <= 2.3e-53) {
		tmp = x + (t_1 + t_3);
	} 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 * ((y + t) - 2.0d0))
    t_3 = z * (1.0d0 - y)
    if (b <= (-1.5d-52)) then
        tmp = t_2 + t_1
    else if (b <= 2.3d-53) then
        tmp = x + (t_1 + t_3)
    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 * ((y + t) - 2.0));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.5e-52) {
		tmp = t_2 + t_1;
	} else if (b <= 2.3e-53) {
		tmp = x + (t_1 + t_3);
	} 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 * ((y + t) - 2.0))
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -1.5e-52:
		tmp = t_2 + t_1
	elif b <= 2.3e-53:
		tmp = x + (t_1 + t_3)
	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(Float64(y + t) - 2.0)))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -1.5e-52)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 2.3e-53)
		tmp = Float64(x + Float64(t_1 + t_3));
	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 * ((y + t) - 2.0));
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -1.5e-52)
		tmp = t_2 + t_1;
	elseif (b <= 2.3e-53)
		tmp = x + (t_1 + t_3);
	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[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.5e-52], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 2.3e-53], N[(x + N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.5e-52

   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. Taylor expanded in z around 0 88.7%

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

   if -1.5e-52 < b < 2.3000000000000001e-53

   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. Taylor expanded in b around 0 97.2%

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

   if 2.3000000000000001e-53 < b

   1. Initial program 92.0%

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

   2. Taylor expanded in a around 0 81.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-52}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-53}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 10: 48.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-234}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= y -1.15e+25)
     t_1
     (if (<= y -1.5e-87)
       (* b (- t 2.0))
       (if (<= y -5.6e-254)
         (* a (- 1.0 t))
         (if (<= y -7e-289)
           t_2
           (if (<= y 3.2e-234)
             (* z (- 1.0 y))
             (if (<= y 1.45e+75) t_2 t_1))))))))

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 (y <= -1.15e+25) {
		tmp = t_1;
	} else if (y <= -1.5e-87) {
		tmp = b * (t - 2.0);
	} else if (y <= -5.6e-254) {
		tmp = a * (1.0 - t);
	} else if (y <= -7e-289) {
		tmp = t_2;
	} else if (y <= 3.2e-234) {
		tmp = z * (1.0 - y);
	} else if (y <= 1.45e+75) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (y <= (-1.15d+25)) then
        tmp = t_1
    else if (y <= (-1.5d-87)) then
        tmp = b * (t - 2.0d0)
    else if (y <= (-5.6d-254)) then
        tmp = a * (1.0d0 - t)
    else if (y <= (-7d-289)) then
        tmp = t_2
    else if (y <= 3.2d-234) then
        tmp = z * (1.0d0 - y)
    else if (y <= 1.45d+75) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (y <= -1.15e+25) {
		tmp = t_1;
	} else if (y <= -1.5e-87) {
		tmp = b * (t - 2.0);
	} else if (y <= -5.6e-254) {
		tmp = a * (1.0 - t);
	} else if (y <= -7e-289) {
		tmp = t_2;
	} else if (y <= 3.2e-234) {
		tmp = z * (1.0 - y);
	} else if (y <= 1.45e+75) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if y <= -1.15e+25:
		tmp = t_1
	elif y <= -1.5e-87:
		tmp = b * (t - 2.0)
	elif y <= -5.6e-254:
		tmp = a * (1.0 - t)
	elif y <= -7e-289:
		tmp = t_2
	elif y <= 3.2e-234:
		tmp = z * (1.0 - y)
	elif y <= 1.45e+75:
		tmp = t_2
	else:
		tmp = t_1
	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 (y <= -1.15e+25)
		tmp = t_1;
	elseif (y <= -1.5e-87)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= -5.6e-254)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= -7e-289)
		tmp = t_2;
	elseif (y <= 3.2e-234)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= 1.45e+75)
		tmp = t_2;
	else
		tmp = t_1;
	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 (y <= -1.15e+25)
		tmp = t_1;
	elseif (y <= -1.5e-87)
		tmp = b * (t - 2.0);
	elseif (y <= -5.6e-254)
		tmp = a * (1.0 - t);
	elseif (y <= -7e-289)
		tmp = t_2;
	elseif (y <= 3.2e-234)
		tmp = z * (1.0 - y);
	elseif (y <= 1.45e+75)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+25], t$95$1, If[LessEqual[y, -1.5e-87], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.6e-254], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-289], t$95$2, If[LessEqual[y, 3.2e-234], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+75], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.1499999999999999e25 or 1.4499999999999999e75 < y

   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. Taylor expanded in y around inf 71.4%

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

   if -1.1499999999999999e25 < y < -1.50000000000000008e-87

   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. Taylor expanded in b around inf 56.3%

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

   3. Taylor expanded in y around 0 53.6%

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

   if -1.50000000000000008e-87 < y < -5.59999999999999966e-254

   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. Taylor expanded in a around inf 44.8%

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

   if -5.59999999999999966e-254 < y < -6.9999999999999999e-289 or 3.1999999999999999e-234 < y < 1.4499999999999999e75

   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. Taylor expanded in t around inf 47.0%

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

   if -6.9999999999999999e-289 < y < 3.1999999999999999e-234

   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. Taylor expanded in z around inf 46.0%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-289}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-234}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 11: 82.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+76} \lor \neg \left(b \leq 1.9 \cdot 10^{+129}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.2e+76) (not (<= b 1.9e+129)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.2e+76) || !(b <= 1.9e+129)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.2d+76)) .or. (.not. (b <= 1.9d+129))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.2e+76) || !(b <= 1.9e+129)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.2e+76) or not (b <= 1.9e+129):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.2e+76) || !(b <= 1.9e+129))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.2e+76) || ~((b <= 1.9e+129)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.2e+76], N[Not[LessEqual[b, 1.9e+129]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.19999999999999976e76 or 1.90000000000000003e129 < b

   1. Initial program 91.8%

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

   2. Taylor expanded in a around 0 91.8%

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

   3. Taylor expanded in z around 0 90.7%

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

   if -3.19999999999999976e76 < b < 1.90000000000000003e129

   1. Initial program 98.8%

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

   2. Taylor expanded in b around 0 86.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+76} \lor \neg \left(b \leq 1.9 \cdot 10^{+129}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 12: 39.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := b \cdot \left(t - 2\right)\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{-11}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.68 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* b (- t 2.0))) (t_3 (* a (- 1.0 t))))
   (if (<= a -2.85e-11)
     t_3
     (if (<= a -1.2e-159)
       t_1
       (if (<= a 1.4e-220)
         t_2
         (if (<= a 9.6e-37) t_1 (if (<= a 1.68e+72) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = b * (t - 2.0);
	double t_3 = a * (1.0 - t);
	double tmp;
	if (a <= -2.85e-11) {
		tmp = t_3;
	} else if (a <= -1.2e-159) {
		tmp = t_1;
	} else if (a <= 1.4e-220) {
		tmp = t_2;
	} else if (a <= 9.6e-37) {
		tmp = t_1;
	} else if (a <= 1.68e+72) {
		tmp = t_2;
	} else {
		tmp = 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 = b * (y - 2.0d0)
    t_2 = b * (t - 2.0d0)
    t_3 = a * (1.0d0 - t)
    if (a <= (-2.85d-11)) then
        tmp = t_3
    else if (a <= (-1.2d-159)) then
        tmp = t_1
    else if (a <= 1.4d-220) then
        tmp = t_2
    else if (a <= 9.6d-37) then
        tmp = t_1
    else if (a <= 1.68d+72) then
        tmp = t_2
    else
        tmp = 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 = b * (y - 2.0);
	double t_2 = b * (t - 2.0);
	double t_3 = a * (1.0 - t);
	double tmp;
	if (a <= -2.85e-11) {
		tmp = t_3;
	} else if (a <= -1.2e-159) {
		tmp = t_1;
	} else if (a <= 1.4e-220) {
		tmp = t_2;
	} else if (a <= 9.6e-37) {
		tmp = t_1;
	} else if (a <= 1.68e+72) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = b * (t - 2.0)
	t_3 = a * (1.0 - t)
	tmp = 0
	if a <= -2.85e-11:
		tmp = t_3
	elif a <= -1.2e-159:
		tmp = t_1
	elif a <= 1.4e-220:
		tmp = t_2
	elif a <= 9.6e-37:
		tmp = t_1
	elif a <= 1.68e+72:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(b * Float64(t - 2.0))
	t_3 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -2.85e-11)
		tmp = t_3;
	elseif (a <= -1.2e-159)
		tmp = t_1;
	elseif (a <= 1.4e-220)
		tmp = t_2;
	elseif (a <= 9.6e-37)
		tmp = t_1;
	elseif (a <= 1.68e+72)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = b * (t - 2.0);
	t_3 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -2.85e-11)
		tmp = t_3;
	elseif (a <= -1.2e-159)
		tmp = t_1;
	elseif (a <= 1.4e-220)
		tmp = t_2;
	elseif (a <= 9.6e-37)
		tmp = t_1;
	elseif (a <= 1.68e+72)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.85e-11], t$95$3, If[LessEqual[a, -1.2e-159], t$95$1, If[LessEqual[a, 1.4e-220], t$95$2, If[LessEqual[a, 9.6e-37], t$95$1, If[LessEqual[a, 1.68e+72], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.8499999999999999e-11 or 1.67999999999999991e72 < a

   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. Taylor expanded in a around inf 58.0%

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

   if -2.8499999999999999e-11 < a < -1.19999999999999999e-159 or 1.4e-220 < a < 9.59999999999999963e-37

   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. Taylor expanded in b around inf 45.1%

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

   3. Taylor expanded in t around 0 35.8%

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

   if -1.19999999999999999e-159 < a < 1.4e-220 or 9.59999999999999963e-37 < a < 1.67999999999999991e72

   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. Taylor expanded in b around inf 45.8%

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

   3. Taylor expanded in y around 0 34.9%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-159}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 1.68 \cdot 10^{+72}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 13: 55.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(t - 2\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-287}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- t 2.0)))) (t_2 (* y (- b z))))
   (if (<= y -1.7e+31)
     t_2
     (if (<= y -1.25e-228)
       t_1
       (if (<= y -5.8e-287) (* a (- 1.0 t)) (if (<= y 2.5e+87) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (t - 2.0));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.7e+31) {
		tmp = t_2;
	} else if (y <= -1.25e-228) {
		tmp = t_1;
	} else if (y <= -5.8e-287) {
		tmp = a * (1.0 - t);
	} else if (y <= 2.5e+87) {
		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 + (b * (t - 2.0d0))
    t_2 = y * (b - z)
    if (y <= (-1.7d+31)) then
        tmp = t_2
    else if (y <= (-1.25d-228)) then
        tmp = t_1
    else if (y <= (-5.8d-287)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 2.5d+87) 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 + (b * (t - 2.0));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.7e+31) {
		tmp = t_2;
	} else if (y <= -1.25e-228) {
		tmp = t_1;
	} else if (y <= -5.8e-287) {
		tmp = a * (1.0 - t);
	} else if (y <= 2.5e+87) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * (t - 2.0))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -1.7e+31:
		tmp = t_2
	elif y <= -1.25e-228:
		tmp = t_1
	elif y <= -5.8e-287:
		tmp = a * (1.0 - t)
	elif y <= 2.5e+87:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(t - 2.0)))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.7e+31)
		tmp = t_2;
	elseif (y <= -1.25e-228)
		tmp = t_1;
	elseif (y <= -5.8e-287)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 2.5e+87)
		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 + (b * (t - 2.0));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.7e+31)
		tmp = t_2;
	elseif (y <= -1.25e-228)
		tmp = t_1;
	elseif (y <= -5.8e-287)
		tmp = a * (1.0 - t);
	elseif (y <= 2.5e+87)
		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[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+31], t$95$2, If[LessEqual[y, -1.25e-228], t$95$1, If[LessEqual[y, -5.8e-287], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+87], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6999999999999999e31 or 2.4999999999999999e87 < y

   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. Taylor expanded in y around inf 73.0%

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

   if -1.6999999999999999e31 < y < -1.24999999999999993e-228 or -5.7999999999999996e-287 < y < 2.4999999999999999e87

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0 72.4%

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

   3. Taylor expanded in z around 0 53.3%

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

   4. Taylor expanded in y around 0 52.8%

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

   if -1.24999999999999993e-228 < y < -5.7999999999999996e-287

   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. Taylor expanded in a around inf 64.1%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-228}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-287}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+87}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 14: 47.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -1.45e+48)
     t_2
     (if (<= t 2.25e-269)
       t_1
       (if (<= t 1.55e-142) x (if (<= t 6000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.45e+48) {
		tmp = t_2;
	} else if (t <= 2.25e-269) {
		tmp = t_1;
	} else if (t <= 1.55e-142) {
		tmp = x;
	} else if (t <= 6000.0) {
		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 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-1.45d+48)) then
        tmp = t_2
    else if (t <= 2.25d-269) then
        tmp = t_1
    else if (t <= 1.55d-142) then
        tmp = x
    else if (t <= 6000.0d0) 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 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.45e+48) {
		tmp = t_2;
	} else if (t <= 2.25e-269) {
		tmp = t_1;
	} else if (t <= 1.55e-142) {
		tmp = x;
	} else if (t <= 6000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1.45e+48:
		tmp = t_2
	elif t <= 2.25e-269:
		tmp = t_1
	elif t <= 1.55e-142:
		tmp = x
	elif t <= 6000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.45e+48)
		tmp = t_2;
	elseif (t <= 2.25e-269)
		tmp = t_1;
	elseif (t <= 1.55e-142)
		tmp = x;
	elseif (t <= 6000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.45e+48)
		tmp = t_2;
	elseif (t <= 2.25e-269)
		tmp = t_1;
	elseif (t <= 1.55e-142)
		tmp = x;
	elseif (t <= 6000.0)
		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[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+48], t$95$2, If[LessEqual[t, 2.25e-269], t$95$1, If[LessEqual[t, 1.55e-142], x, If[LessEqual[t, 6000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4499999999999999e48 or 6e3 < t

   1. Initial program 94.4%

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

   2. Taylor expanded in t around inf 62.1%

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

   if -1.4499999999999999e48 < t < 2.2500000000000001e-269 or 1.55e-142 < t < 6e3

   1. Initial program 98.1%

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

   2. Taylor expanded in b around inf 32.8%

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

   3. Taylor expanded in t around 0 32.6%

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

   if 2.2500000000000001e-269 < t < 1.55e-142

   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. Taylor expanded in x around inf 41.1%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 15: 50.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -6.8e+25)
     t_1
     (if (<= y -6.8e-82)
       (* b (- t 2.0))
       (if (<= y -4.5e-254)
         (* a (- 1.0 t))
         (if (<= y 3.3e+73) (* t (- b a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -6.8e+25) {
		tmp = t_1;
	} else if (y <= -6.8e-82) {
		tmp = b * (t - 2.0);
	} else if (y <= -4.5e-254) {
		tmp = a * (1.0 - t);
	} else if (y <= 3.3e+73) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-6.8d+25)) then
        tmp = t_1
    else if (y <= (-6.8d-82)) then
        tmp = b * (t - 2.0d0)
    else if (y <= (-4.5d-254)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 3.3d+73) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -6.8e+25) {
		tmp = t_1;
	} else if (y <= -6.8e-82) {
		tmp = b * (t - 2.0);
	} else if (y <= -4.5e-254) {
		tmp = a * (1.0 - t);
	} else if (y <= 3.3e+73) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -6.8e+25:
		tmp = t_1
	elif y <= -6.8e-82:
		tmp = b * (t - 2.0)
	elif y <= -4.5e-254:
		tmp = a * (1.0 - t)
	elif y <= 3.3e+73:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -6.8e+25)
		tmp = t_1;
	elseif (y <= -6.8e-82)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= -4.5e-254)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 3.3e+73)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -6.8e+25)
		tmp = t_1;
	elseif (y <= -6.8e-82)
		tmp = b * (t - 2.0);
	elseif (y <= -4.5e-254)
		tmp = a * (1.0 - t);
	elseif (y <= 3.3e+73)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+25], t$95$1, If[LessEqual[y, -6.8e-82], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-254], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+73], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.79999999999999967e25 or 3.3000000000000003e73 < y

   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. Taylor expanded in y around inf 71.4%

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

   if -6.79999999999999967e25 < y < -6.7999999999999995e-82

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 56.3%

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

   3. Taylor expanded in y around 0 53.6%

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

   if -6.7999999999999995e-82 < y < -4.5e-254

   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. Taylor expanded in a around inf 44.8%

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

   if -4.5e-254 < y < 3.3000000000000003e73

   1. Initial program 98.7%

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

   2. Taylor expanded in t around inf 40.7%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 16: 28.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -1.52 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-140}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1700:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -1.52e-9) t_1 (if (<= t -9.5e-140) a (if (<= t 1700.0) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -1.52e-9) {
		tmp = t_1;
	} else if (t <= -9.5e-140) {
		tmp = a;
	} else if (t <= 1700.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-1.52d-9)) then
        tmp = t_1
    else if (t <= (-9.5d-140)) then
        tmp = a
    else if (t <= 1700.0d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -1.52e-9) {
		tmp = t_1;
	} else if (t <= -9.5e-140) {
		tmp = a;
	} else if (t <= 1700.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -1.52e-9:
		tmp = t_1
	elif t <= -9.5e-140:
		tmp = a
	elif t <= 1700.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -1.52e-9)
		tmp = t_1;
	elseif (t <= -9.5e-140)
		tmp = a;
	elseif (t <= 1700.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -1.52e-9)
		tmp = t_1;
	elseif (t <= -9.5e-140)
		tmp = a;
	elseif (t <= 1700.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -1.52e-9], t$95$1, If[LessEqual[t, -9.5e-140], a, If[LessEqual[t, 1700.0], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.51999999999999992e-9 or 1700 < t

   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. Taylor expanded in a around inf 36.9%

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

   3. Taylor expanded in t around inf 36.6%

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

      1. associate-*r* 36.6%

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

      2. neg-mul-1 36.6%

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

   5. Simplified 36.6%

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

   if -1.51999999999999992e-9 < t < -9.50000000000000019e-140

   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. Taylor expanded in a around inf 33.1%

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

   3. Taylor expanded in t around 0 32.8%

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

   if -9.50000000000000019e-140 < t < 1700

   1. Initial program 98.9%

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

   2. Taylor expanded in x around inf 26.5%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-140}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1700:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]

Alternative 17: 26.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+68}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-139}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5e+68)
   (* t b)
   (if (<= t -2e-139) a (if (<= t 2.35e+28) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5e+68) {
		tmp = t * b;
	} else if (t <= -2e-139) {
		tmp = a;
	} else if (t <= 2.35e+28) {
		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 <= (-5d+68)) then
        tmp = t * b
    else if (t <= (-2d-139)) then
        tmp = a
    else if (t <= 2.35d+28) 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 <= -5e+68) {
		tmp = t * b;
	} else if (t <= -2e-139) {
		tmp = a;
	} else if (t <= 2.35e+28) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5e+68:
		tmp = t * b
	elif t <= -2e-139:
		tmp = a
	elif t <= 2.35e+28:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5e+68)
		tmp = Float64(t * b);
	elseif (t <= -2e-139)
		tmp = a;
	elseif (t <= 2.35e+28)
		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 <= -5e+68)
		tmp = t * b;
	elseif (t <= -2e-139)
		tmp = a;
	elseif (t <= 2.35e+28)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5e+68], N[(t * b), $MachinePrecision], If[LessEqual[t, -2e-139], a, If[LessEqual[t, 2.35e+28], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000004e68 or 2.34999999999999983e28 < t

   1. Initial program 93.8%

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

      1. add-cube-cbrt 93.6%

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(\sqrt[3]{\left(t - 1\right) \cdot a} \cdot \sqrt[3]{\left(t - 1\right) \cdot a}\right) \cdot \sqrt[3]{\left(t - 1\right) \cdot a}}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. pow3 93.6%

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{{\left(\sqrt[3]{\left(t - 1\right) \cdot a}\right)}^{3}}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. sub-neg 93.6%

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - {\left(\sqrt[3]{\color{blue}{\left(t + \left(-1\right)\right)} \cdot a}\right)}^{3}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. metadata-eval 93.6%

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - {\left(\sqrt[3]{\left(t + \color{blue}{-1}\right) \cdot a}\right)}^{3}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   3. Applied egg-rr 93.6%

      \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{{\left(\sqrt[3]{\left(t + -1\right) \cdot a}\right)}^{3}}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   4. Taylor expanded in t around inf 35.3%

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

      1. *-commutative 35.3%

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

   6. Simplified 35.3%

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

   if -5.0000000000000004e68 < t < -2.00000000000000006e-139

   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. Taylor expanded in a around inf 33.5%

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

   3. Taylor expanded in t around 0 26.6%

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

   if -2.00000000000000006e-139 < t < 2.34999999999999983e28

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 24.8%

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

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+68}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-139}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 18: 40.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-9} \lor \neg \left(a \leq 8.4 \cdot 10^{+71}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.5e-9) (not (<= a 8.4e+71))) (* a (- 1.0 t)) (* b (- t 2.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.5e-9) || !(a <= 8.4e+71)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.5d-9)) .or. (.not. (a <= 8.4d+71))) then
        tmp = a * (1.0d0 - t)
    else
        tmp = b * (t - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.5e-9) || !(a <= 8.4e+71)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.5e-9) or not (a <= 8.4e+71):
		tmp = a * (1.0 - t)
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.5e-9) || !(a <= 8.4e+71))
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.5e-9) || ~((a <= 8.4e+71)))
		tmp = a * (1.0 - t);
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.5e-9], N[Not[LessEqual[a, 8.4e+71]], $MachinePrecision]], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.5000000000000001e-9 or 8.39999999999999957e71 < a

   1. Initial program 93.2%

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

   2. Taylor expanded in a around inf 59.5%

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

   if -2.5000000000000001e-9 < a < 8.39999999999999957e71

   1. Initial program 98.7%

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

   2. Taylor expanded in b around inf 44.9%

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

   3. Taylor expanded in y around 0 28.8%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-9} \lor \neg \left(a \leq 8.4 \cdot 10^{+71}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 19: 34.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+125}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.6e+125) (* y b) (if (<= y 1.22e+160) (* a (- 1.0 t)) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.6e+125) {
		tmp = y * b;
	} else if (y <= 1.22e+160) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.6d+125)) then
        tmp = y * b
    else if (y <= 1.22d+160) then
        tmp = a * (1.0d0 - t)
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.6e+125) {
		tmp = y * b;
	} else if (y <= 1.22e+160) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.6e+125:
		tmp = y * b
	elif y <= 1.22e+160:
		tmp = a * (1.0 - t)
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.6e+125)
		tmp = Float64(y * b);
	elseif (y <= 1.22e+160)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.6e+125)
		tmp = y * b;
	elseif (y <= 1.22e+160)
		tmp = a * (1.0 - t);
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.6e+125], N[(y * b), $MachinePrecision], If[LessEqual[y, 1.22e+160], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6000000000000002e125 or 1.22e160 < y

   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. Taylor expanded in y around inf 83.4%

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

   3. Taylor expanded in b around inf 45.6%

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

   if -5.6000000000000002e125 < y < 1.22e160

   1. Initial program 97.8%

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

   2. Taylor expanded in a around inf 34.0%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+125}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 20: 25.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+171}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 51:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6e+171) (* y b) (if (<= b 51.0) x (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6e+171) {
		tmp = y * b;
	} else if (b <= 51.0) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6d+171)) then
        tmp = y * b
    else if (b <= 51.0d0) then
        tmp = x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6e+171) {
		tmp = y * b;
	} else if (b <= 51.0) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6e+171:
		tmp = y * b
	elif b <= 51.0:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6e+171)
		tmp = Float64(y * b);
	elseif (b <= 51.0)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6e+171)
		tmp = y * b;
	elseif (b <= 51.0)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6e+171], N[(y * b), $MachinePrecision], If[LessEqual[b, 51.0], x, N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.0000000000000002e171 or 51 < b

   1. Initial program 90.1%

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

   2. Taylor expanded in y around inf 42.2%

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

   3. Taylor expanded in b around inf 35.8%

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

   if -6.0000000000000002e171 < b < 51

   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. Taylor expanded in x around inf 22.0%

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

4. Final simplification 26.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+171}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 51:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 21: 21.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+52}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.55e+54) x (if (<= x 1.7e+52) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.55e+54) {
		tmp = x;
	} else if (x <= 1.7e+52) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.55d+54)) then
        tmp = x
    else if (x <= 1.7d+52) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.55e+54) {
		tmp = x;
	} else if (x <= 1.7e+52) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.55e+54:
		tmp = x
	elif x <= 1.7e+52:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.55e+54)
		tmp = x;
	elseif (x <= 1.7e+52)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.55e+54)
		tmp = x;
	elseif (x <= 1.7e+52)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.55e+54], x, If[LessEqual[x, 1.7e+52], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55e54 or 1.7e52 < x

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 31.5%

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

   if -1.55e54 < x < 1.7e52

   1. Initial program 96.5%

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

   2. Taylor expanded in a around inf 32.9%

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

   3. Taylor expanded in t around 0 16.6%

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

4. Final simplification 23.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+52}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 10.5% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

2. Taylor expanded in a around inf 28.5%

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

3. Taylor expanded in t around 0 11.0%

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

4. Final simplification 11.0%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023275 
(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)))