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

Percentage Accurate: 95.2% → 97.9%

Time: 15.6s

Alternatives: 24

Speedup: 0.5×

• 36.1% 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: 95.2% 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: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 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 y around inf 62.1%

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

4. Final simplification 96.9%

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

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 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. Step-by-step derivation

   1. +-commutative 91.8%

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

   2. fma-def 95.3%

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

   3. associate--l+ 95.3%

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

   4. sub-neg 95.3%

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

   5. metadata-eval 95.3%

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

   6. sub-neg 95.3%

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

   7. associate-+l- 95.3%

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

   8. fma-neg 96.1%

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

   9. sub-neg 96.1%

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

   10. metadata-eval 96.1%

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

   11. remove-double-neg 96.1%

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

   12. sub-neg 96.1%

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

   13. metadata-eval 96.1%

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

3. Simplified 96.1%

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

4. Final simplification 96.1%

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

Alternative 3: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x - y \cdot z\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-260}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+22}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+71} \lor \neg \left(b \leq 3.2 \cdot 10^{+103}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- (+ y t) 2.0))) (t_3 (- x (* y z))))
   (if (<= b -2.4e+40)
     t_2
     (if (<= b -3e-180)
       t_1
       (if (<= b -2.9e-260)
         t_3
         (if (<= b 1.28e-275)
           t_1
           (if (<= b 3.7e+22)
             (* z (- 1.0 y))
             (if (or (<= b 3.7e+71) (not (<= b 3.2e+103))) 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 = b * ((y + t) - 2.0);
	double t_3 = x - (y * z);
	double tmp;
	if (b <= -2.4e+40) {
		tmp = t_2;
	} else if (b <= -3e-180) {
		tmp = t_1;
	} else if (b <= -2.9e-260) {
		tmp = t_3;
	} else if (b <= 1.28e-275) {
		tmp = t_1;
	} else if (b <= 3.7e+22) {
		tmp = z * (1.0 - y);
	} else if ((b <= 3.7e+71) || !(b <= 3.2e+103)) {
		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 = a * (1.0d0 - t)
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x - (y * z)
    if (b <= (-2.4d+40)) then
        tmp = t_2
    else if (b <= (-3d-180)) then
        tmp = t_1
    else if (b <= (-2.9d-260)) then
        tmp = t_3
    else if (b <= 1.28d-275) then
        tmp = t_1
    else if (b <= 3.7d+22) then
        tmp = z * (1.0d0 - y)
    else if ((b <= 3.7d+71) .or. (.not. (b <= 3.2d+103))) 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 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x - (y * z);
	double tmp;
	if (b <= -2.4e+40) {
		tmp = t_2;
	} else if (b <= -3e-180) {
		tmp = t_1;
	} else if (b <= -2.9e-260) {
		tmp = t_3;
	} else if (b <= 1.28e-275) {
		tmp = t_1;
	} else if (b <= 3.7e+22) {
		tmp = z * (1.0 - y);
	} else if ((b <= 3.7e+71) || !(b <= 3.2e+103)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * ((y + t) - 2.0)
	t_3 = x - (y * z)
	tmp = 0
	if b <= -2.4e+40:
		tmp = t_2
	elif b <= -3e-180:
		tmp = t_1
	elif b <= -2.9e-260:
		tmp = t_3
	elif b <= 1.28e-275:
		tmp = t_1
	elif b <= 3.7e+22:
		tmp = z * (1.0 - y)
	elif (b <= 3.7e+71) or not (b <= 3.2e+103):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (b <= -2.4e+40)
		tmp = t_2;
	elseif (b <= -3e-180)
		tmp = t_1;
	elseif (b <= -2.9e-260)
		tmp = t_3;
	elseif (b <= 1.28e-275)
		tmp = t_1;
	elseif (b <= 3.7e+22)
		tmp = Float64(z * Float64(1.0 - y));
	elseif ((b <= 3.7e+71) || !(b <= 3.2e+103))
		tmp = t_2;
	else
		tmp = 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 = b * ((y + t) - 2.0);
	t_3 = x - (y * z);
	tmp = 0.0;
	if (b <= -2.4e+40)
		tmp = t_2;
	elseif (b <= -3e-180)
		tmp = t_1;
	elseif (b <= -2.9e-260)
		tmp = t_3;
	elseif (b <= 1.28e-275)
		tmp = t_1;
	elseif (b <= 3.7e+22)
		tmp = z * (1.0 - y);
	elseif ((b <= 3.7e+71) || ~((b <= 3.2e+103)))
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+40], t$95$2, If[LessEqual[b, -3e-180], t$95$1, If[LessEqual[b, -2.9e-260], t$95$3, If[LessEqual[b, 1.28e-275], t$95$1, If[LessEqual[b, 3.7e+22], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 3.7e+71], N[Not[LessEqual[b, 3.2e+103]], $MachinePrecision]], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.4e40 or 3.6999999999999998e22 < b < 3.7e71 or 3.19999999999999993e103 < b

   1. Initial program 85.6%

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

   2. Taylor expanded in b around inf 71.1%

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

   if -2.4e40 < b < -3.0000000000000001e-180 or -2.8999999999999999e-260 < b < 1.27999999999999996e-275

   1. Initial program 97.0%

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

   2. Taylor expanded in a around inf 52.3%

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

   if -3.0000000000000001e-180 < b < -2.8999999999999999e-260 or 3.7e71 < b < 3.19999999999999993e103

   1. Initial program 89.5%

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

   2. Taylor expanded in 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 y around inf 69.4%

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

   if 1.27999999999999996e-275 < b < 3.6999999999999998e22

   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 56.3%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-260}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+22}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+71} \lor \neg \left(b \leq 3.2 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]

Alternative 4: 58.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+22}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+71} \lor \neg \left(b \leq 2.25 \cdot 10^{+100}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -2.15e+63)
     t_2
     (if (<= b 4.6e-265)
       t_1
       (if (<= b 1.45e-61)
         (* z (- 1.0 y))
         (if (<= b 1.7e+20)
           t_1
           (if (<= b 4.2e+22)
             z
             (if (or (<= b 3.7e+71) (not (<= b 2.25e+100)))
               t_2
               (- x (* y z))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.15e+63) {
		tmp = t_2;
	} else if (b <= 4.6e-265) {
		tmp = t_1;
	} else if (b <= 1.45e-61) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.7e+20) {
		tmp = t_1;
	} else if (b <= 4.2e+22) {
		tmp = z;
	} else if ((b <= 3.7e+71) || !(b <= 2.25e+100)) {
		tmp = t_2;
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-2.15d+63)) then
        tmp = t_2
    else if (b <= 4.6d-265) then
        tmp = t_1
    else if (b <= 1.45d-61) then
        tmp = z * (1.0d0 - y)
    else if (b <= 1.7d+20) then
        tmp = t_1
    else if (b <= 4.2d+22) then
        tmp = z
    else if ((b <= 3.7d+71) .or. (.not. (b <= 2.25d+100))) then
        tmp = t_2
    else
        tmp = x - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.15e+63) {
		tmp = t_2;
	} else if (b <= 4.6e-265) {
		tmp = t_1;
	} else if (b <= 1.45e-61) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.7e+20) {
		tmp = t_1;
	} else if (b <= 4.2e+22) {
		tmp = z;
	} else if ((b <= 3.7e+71) || !(b <= 2.25e+100)) {
		tmp = t_2;
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2.15e+63:
		tmp = t_2
	elif b <= 4.6e-265:
		tmp = t_1
	elif b <= 1.45e-61:
		tmp = z * (1.0 - y)
	elif b <= 1.7e+20:
		tmp = t_1
	elif b <= 4.2e+22:
		tmp = z
	elif (b <= 3.7e+71) or not (b <= 2.25e+100):
		tmp = t_2
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2.15e+63)
		tmp = t_2;
	elseif (b <= 4.6e-265)
		tmp = t_1;
	elseif (b <= 1.45e-61)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 1.7e+20)
		tmp = t_1;
	elseif (b <= 4.2e+22)
		tmp = z;
	elseif ((b <= 3.7e+71) || !(b <= 2.25e+100))
		tmp = t_2;
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.15e+63)
		tmp = t_2;
	elseif (b <= 4.6e-265)
		tmp = t_1;
	elseif (b <= 1.45e-61)
		tmp = z * (1.0 - y);
	elseif (b <= 1.7e+20)
		tmp = t_1;
	elseif (b <= 4.2e+22)
		tmp = z;
	elseif ((b <= 3.7e+71) || ~((b <= 2.25e+100)))
		tmp = t_2;
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+63], t$95$2, If[LessEqual[b, 4.6e-265], t$95$1, If[LessEqual[b, 1.45e-61], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+20], t$95$1, If[LessEqual[b, 4.2e+22], z, If[Or[LessEqual[b, 3.7e+71], N[Not[LessEqual[b, 2.25e+100]], $MachinePrecision]], t$95$2, N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.15e63 or 4.1999999999999996e22 < b < 3.7e71 or 2.25000000000000018e100 < b

   1. Initial program 84.8%

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

   2. Taylor expanded in b around inf 72.6%

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

   if -2.15e63 < b < 4.5999999999999998e-265 or 1.45e-61 < b < 1.7e20

   1. Initial program 97.9%

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

   2. Taylor expanded in b around 0 90.4%

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

   3. Taylor expanded in a around inf 65.0%

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

   if 4.5999999999999998e-265 < b < 1.45e-61

   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 63.6%

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

   if 1.7e20 < b < 4.1999999999999996e22

   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 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   if 3.7e71 < b < 2.25000000000000018e100

   1. Initial program 71.4%

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

   2. 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 y around inf 72.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-265}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+22}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+71} \lor \neg \left(b \leq 2.25 \cdot 10^{+100}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]

Alternative 5: 55.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := b \cdot \left(t - 2\right)\\ t_3 := x + t_2\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.12 \cdot 10^{-187}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-30}:\\ \;\;\;\;z + t_2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* b (- t 2.0))) (t_3 (+ x t_2)))
   (if (<= y -4.4e+109)
     t_1
     (if (<= y -5.4e+63)
       (* t (- b a))
       (if (<= y -2.65e+47)
         t_1
         (if (<= y -2.12e-187)
           t_3
           (if (<= y 1.4e-30)
             (+ z t_2)
             (if (<= y 4e+44) (* a (- 1.0 t)) (if (<= y 9e+78) t_3 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 = b * (t - 2.0);
	double t_3 = x + t_2;
	double tmp;
	if (y <= -4.4e+109) {
		tmp = t_1;
	} else if (y <= -5.4e+63) {
		tmp = t * (b - a);
	} else if (y <= -2.65e+47) {
		tmp = t_1;
	} else if (y <= -2.12e-187) {
		tmp = t_3;
	} else if (y <= 1.4e-30) {
		tmp = z + t_2;
	} else if (y <= 4e+44) {
		tmp = a * (1.0 - t);
	} else if (y <= 9e+78) {
		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 = y * (b - z)
    t_2 = b * (t - 2.0d0)
    t_3 = x + t_2
    if (y <= (-4.4d+109)) then
        tmp = t_1
    else if (y <= (-5.4d+63)) then
        tmp = t * (b - a)
    else if (y <= (-2.65d+47)) then
        tmp = t_1
    else if (y <= (-2.12d-187)) then
        tmp = t_3
    else if (y <= 1.4d-30) then
        tmp = z + t_2
    else if (y <= 4d+44) then
        tmp = a * (1.0d0 - t)
    else if (y <= 9d+78) 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 = y * (b - z);
	double t_2 = b * (t - 2.0);
	double t_3 = x + t_2;
	double tmp;
	if (y <= -4.4e+109) {
		tmp = t_1;
	} else if (y <= -5.4e+63) {
		tmp = t * (b - a);
	} else if (y <= -2.65e+47) {
		tmp = t_1;
	} else if (y <= -2.12e-187) {
		tmp = t_3;
	} else if (y <= 1.4e-30) {
		tmp = z + t_2;
	} else if (y <= 4e+44) {
		tmp = a * (1.0 - t);
	} else if (y <= 9e+78) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = b * (t - 2.0)
	t_3 = x + t_2
	tmp = 0
	if y <= -4.4e+109:
		tmp = t_1
	elif y <= -5.4e+63:
		tmp = t * (b - a)
	elif y <= -2.65e+47:
		tmp = t_1
	elif y <= -2.12e-187:
		tmp = t_3
	elif y <= 1.4e-30:
		tmp = z + t_2
	elif y <= 4e+44:
		tmp = a * (1.0 - t)
	elif y <= 9e+78:
		tmp = t_3
	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(b * Float64(t - 2.0))
	t_3 = Float64(x + t_2)
	tmp = 0.0
	if (y <= -4.4e+109)
		tmp = t_1;
	elseif (y <= -5.4e+63)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= -2.65e+47)
		tmp = t_1;
	elseif (y <= -2.12e-187)
		tmp = t_3;
	elseif (y <= 1.4e-30)
		tmp = Float64(z + t_2);
	elseif (y <= 4e+44)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 9e+78)
		tmp = t_3;
	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 = b * (t - 2.0);
	t_3 = x + t_2;
	tmp = 0.0;
	if (y <= -4.4e+109)
		tmp = t_1;
	elseif (y <= -5.4e+63)
		tmp = t * (b - a);
	elseif (y <= -2.65e+47)
		tmp = t_1;
	elseif (y <= -2.12e-187)
		tmp = t_3;
	elseif (y <= 1.4e-30)
		tmp = z + t_2;
	elseif (y <= 4e+44)
		tmp = a * (1.0 - t);
	elseif (y <= 9e+78)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + t$95$2), $MachinePrecision]}, If[LessEqual[y, -4.4e+109], t$95$1, If[LessEqual[y, -5.4e+63], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.65e+47], t$95$1, If[LessEqual[y, -2.12e-187], t$95$3, If[LessEqual[y, 1.4e-30], N[(z + t$95$2), $MachinePrecision], If[LessEqual[y, 4e+44], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+78], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.3999999999999998e109 or -5.40000000000000035e63 < y < -2.65e47 or 8.9999999999999999e78 < y

   1. Initial program 81.7%

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

   2. Taylor expanded in y around inf 71.6%

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

   if -4.3999999999999998e109 < y < -5.40000000000000035e63

   1. Initial program 83.3%

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

   2. Taylor expanded in t around inf 67.4%

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

   if -2.65e47 < y < -2.12000000000000006e-187 or 4.0000000000000004e44 < y < 8.9999999999999999e78

   1. Initial program 98.2%

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

   2. Taylor expanded in a around 0 81.0%

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

   3. Taylor expanded in y around 0 76.0%

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

      1. associate--l+ 76.0%

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

      2. sub-neg 76.0%

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

      3. metadata-eval 76.0%

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

      4. neg-mul-1 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in z around 0 62.8%

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

   if -2.12000000000000006e-187 < y < 1.39999999999999994e-30

   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 a around 0 72.0%

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

   3. Taylor expanded in y around 0 72.0%

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

      1. associate--l+ 72.0%

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

      2. sub-neg 72.0%

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

      3. metadata-eval 72.0%

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

      4. neg-mul-1 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in x around 0 58.7%

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

   if 1.39999999999999994e-30 < y < 4.0000000000000004e44

   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 58.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.12 \cdot 10^{-187}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-30}:\\ \;\;\;\;z + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+78}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 6: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+71}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+22} \lor \neg \left(b \leq 6.5 \cdot 10^{+22}\right):\\ \;\;\;\;t_2 + t_3\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_3 + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (- x (* b (- 2.0 (+ y t)))))
        (t_3 (* a (- 1.0 t))))
   (if (<= b -2.15e+71)
     (+ t_2 t_1)
     (if (or (<= b -5.5e+22) (not (<= b 6.5e+22)))
       (+ t_2 t_3)
       (+ x (+ t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x - (b * (2.0 - (y + t)));
	double t_3 = a * (1.0 - t);
	double tmp;
	if (b <= -2.15e+71) {
		tmp = t_2 + t_1;
	} else if ((b <= -5.5e+22) || !(b <= 6.5e+22)) {
		tmp = t_2 + t_3;
	} else {
		tmp = x + (t_3 + 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 = z * (1.0d0 - y)
    t_2 = x - (b * (2.0d0 - (y + t)))
    t_3 = a * (1.0d0 - t)
    if (b <= (-2.15d+71)) then
        tmp = t_2 + t_1
    else if ((b <= (-5.5d+22)) .or. (.not. (b <= 6.5d+22))) then
        tmp = t_2 + t_3
    else
        tmp = x + (t_3 + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x - (b * (2.0 - (y + t)));
	double t_3 = a * (1.0 - t);
	double tmp;
	if (b <= -2.15e+71) {
		tmp = t_2 + t_1;
	} else if ((b <= -5.5e+22) || !(b <= 6.5e+22)) {
		tmp = t_2 + t_3;
	} else {
		tmp = x + (t_3 + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x - (b * (2.0 - (y + t)))
	t_3 = a * (1.0 - t)
	tmp = 0
	if b <= -2.15e+71:
		tmp = t_2 + t_1
	elif (b <= -5.5e+22) or not (b <= 6.5e+22):
		tmp = t_2 + t_3
	else:
		tmp = x + (t_3 + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	t_3 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -2.15e+71)
		tmp = Float64(t_2 + t_1);
	elseif ((b <= -5.5e+22) || !(b <= 6.5e+22))
		tmp = Float64(t_2 + t_3);
	else
		tmp = Float64(x + Float64(t_3 + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x - (b * (2.0 - (y + t)));
	t_3 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -2.15e+71)
		tmp = t_2 + t_1;
	elseif ((b <= -5.5e+22) || ~((b <= 6.5e+22)))
		tmp = t_2 + t_3;
	else
		tmp = x + (t_3 + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+71], N[(t$95$2 + t$95$1), $MachinePrecision], If[Or[LessEqual[b, -5.5e+22], N[Not[LessEqual[b, 6.5e+22]], $MachinePrecision]], N[(t$95$2 + t$95$3), $MachinePrecision], N[(x + N[(t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.14999999999999992e71

   1. Initial program 80.8%

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

   2. Taylor expanded in a around 0 84.6%

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

   if -2.14999999999999992e71 < b < -5.50000000000000021e22 or 6.49999999999999979e22 < b

   1. Initial program 87.2%

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

   2. Taylor expanded in z around 0 83.4%

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

   if -5.50000000000000021e22 < b < 6.49999999999999979e22

   1. Initial program 99.2%

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

   2. 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 3 regimes into one program.

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+71}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+22} \lor \neg \left(b \leq 6.5 \cdot 10^{+22}\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 7: 86.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+22} \lor \neg \left(b \leq 1.25 \cdot 10^{+23}\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_1 + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -3.8e+22) (not (<= b 1.25e+23)))
     (+ (- x (* b (- 2.0 (+ y t)))) 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 <= -3.8e+22) || !(b <= 1.25e+23)) {
		tmp = (x - (b * (2.0 - (y + t)))) + 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 <= (-3.8d+22)) .or. (.not. (b <= 1.25d+23))) then
        tmp = (x - (b * (2.0d0 - (y + t)))) + 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 <= -3.8e+22) || !(b <= 1.25e+23)) {
		tmp = (x - (b * (2.0 - (y + t)))) + 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 <= -3.8e+22) or not (b <= 1.25e+23):
		tmp = (x - (b * (2.0 - (y + t)))) + 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 <= -3.8e+22) || !(b <= 1.25e+23))
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + 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 <= -3.8e+22) || ~((b <= 1.25e+23)))
		tmp = (x - (b * (2.0 - (y + t)))) + 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, -3.8e+22], N[Not[LessEqual[b, 1.25e+23]], $MachinePrecision]], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $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 < -3.8000000000000004e22 or 1.25e23 < b

   1. Initial program 85.0%

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

   2. Taylor expanded in z around 0 79.2%

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

   if -3.8000000000000004e22 < b < 1.25e23

   1. Initial program 99.2%

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

   2. 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 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+22} \lor \neg \left(b \leq 1.25 \cdot 10^{+23}\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 8: 34.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+110}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-89}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-119}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+66}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -1.3e+110)
     (* y b)
     (if (<= y -5.6e+63)
       (* t (- a))
       (if (<= y -8e+37)
         t_1
         (if (<= y -2.15e-89)
           (+ x z)
           (if (<= y -1.16e-119)
             (* t b)
             (if (<= y 2.1e-48) (+ x z) (if (<= y 5.6e+66) (* t b) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.3e+110) {
		tmp = y * b;
	} else if (y <= -5.6e+63) {
		tmp = t * -a;
	} else if (y <= -8e+37) {
		tmp = t_1;
	} else if (y <= -2.15e-89) {
		tmp = x + z;
	} else if (y <= -1.16e-119) {
		tmp = t * b;
	} else if (y <= 2.1e-48) {
		tmp = x + z;
	} else if (y <= 5.6e+66) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-1.3d+110)) then
        tmp = y * b
    else if (y <= (-5.6d+63)) then
        tmp = t * -a
    else if (y <= (-8d+37)) then
        tmp = t_1
    else if (y <= (-2.15d-89)) then
        tmp = x + z
    else if (y <= (-1.16d-119)) then
        tmp = t * b
    else if (y <= 2.1d-48) then
        tmp = x + z
    else if (y <= 5.6d+66) then
        tmp = t * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.3e+110) {
		tmp = y * b;
	} else if (y <= -5.6e+63) {
		tmp = t * -a;
	} else if (y <= -8e+37) {
		tmp = t_1;
	} else if (y <= -2.15e-89) {
		tmp = x + z;
	} else if (y <= -1.16e-119) {
		tmp = t * b;
	} else if (y <= 2.1e-48) {
		tmp = x + z;
	} else if (y <= 5.6e+66) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -1.3e+110:
		tmp = y * b
	elif y <= -5.6e+63:
		tmp = t * -a
	elif y <= -8e+37:
		tmp = t_1
	elif y <= -2.15e-89:
		tmp = x + z
	elif y <= -1.16e-119:
		tmp = t * b
	elif y <= 2.1e-48:
		tmp = x + z
	elif y <= 5.6e+66:
		tmp = t * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -1.3e+110)
		tmp = Float64(y * b);
	elseif (y <= -5.6e+63)
		tmp = Float64(t * Float64(-a));
	elseif (y <= -8e+37)
		tmp = t_1;
	elseif (y <= -2.15e-89)
		tmp = Float64(x + z);
	elseif (y <= -1.16e-119)
		tmp = Float64(t * b);
	elseif (y <= 2.1e-48)
		tmp = Float64(x + z);
	elseif (y <= 5.6e+66)
		tmp = Float64(t * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -1.3e+110)
		tmp = y * b;
	elseif (y <= -5.6e+63)
		tmp = t * -a;
	elseif (y <= -8e+37)
		tmp = t_1;
	elseif (y <= -2.15e-89)
		tmp = x + z;
	elseif (y <= -1.16e-119)
		tmp = t * b;
	elseif (y <= 2.1e-48)
		tmp = x + z;
	elseif (y <= 5.6e+66)
		tmp = t * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.3e+110], N[(y * b), $MachinePrecision], If[LessEqual[y, -5.6e+63], N[(t * (-a)), $MachinePrecision], If[LessEqual[y, -8e+37], t$95$1, If[LessEqual[y, -2.15e-89], N[(x + z), $MachinePrecision], If[LessEqual[y, -1.16e-119], N[(t * b), $MachinePrecision], If[LessEqual[y, 2.1e-48], N[(x + z), $MachinePrecision], If[LessEqual[y, 5.6e+66], N[(t * b), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.3e110

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 81.9%

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

   3. Taylor expanded in b around inf 60.4%

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

   if -1.3e110 < y < -5.59999999999999974e63

   1. Initial program 83.3%

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

   2. Taylor expanded in a around inf 59.0%

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

   3. Taylor expanded in t around inf 51.1%

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

      1. associate-*r* 51.1%

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

      2. mul-1-neg 51.1%

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

   5. Simplified 51.1%

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

   if -5.59999999999999974e63 < y < -7.99999999999999963e37 or 5.6000000000000001e66 < y

   1. Initial program 84.8%

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

   2. Taylor expanded in z around inf 41.9%

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

   3. Taylor expanded in y around inf 41.9%

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

      1. mul-1-neg 41.9%

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

      2. distribute-rgt-neg-in 41.9%

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

   5. Simplified 41.9%

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

   if -7.99999999999999963e37 < y < -2.14999999999999993e-89 or -1.16e-119 < y < 2.09999999999999989e-48

   1. Initial program 98.2%

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

   2. Taylor expanded in a around 0 74.3%

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

   3. Taylor expanded in y around 0 73.5%

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

      1. associate--l+ 73.5%

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

      2. sub-neg 73.5%

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

      3. metadata-eval 73.5%

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

      4. neg-mul-1 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in b around 0 48.0%

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

   if -2.14999999999999993e-89 < y < -1.16e-119 or 2.09999999999999989e-48 < y < 5.6000000000000001e66

   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 53.4%

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

   3. Taylor expanded in t around inf 43.8%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+110}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-89}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-119}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+66}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 9: 39.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-167}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-276}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 125:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 10^{+44}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -7.8e+32)
     t_1
     (if (<= a -2.25e-167)
       (+ x z)
       (if (<= a 1.75e-276)
         (* y b)
         (if (<= a 125.0)
           (+ x z)
           (if (<= a 1e+44) (* t b) (if (<= a 2.5e+73) (* y (- z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -7.8e+32) {
		tmp = t_1;
	} else if (a <= -2.25e-167) {
		tmp = x + z;
	} else if (a <= 1.75e-276) {
		tmp = y * b;
	} else if (a <= 125.0) {
		tmp = x + z;
	} else if (a <= 1e+44) {
		tmp = t * b;
	} else if (a <= 2.5e+73) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-7.8d+32)) then
        tmp = t_1
    else if (a <= (-2.25d-167)) then
        tmp = x + z
    else if (a <= 1.75d-276) then
        tmp = y * b
    else if (a <= 125.0d0) then
        tmp = x + z
    else if (a <= 1d+44) then
        tmp = t * b
    else if (a <= 2.5d+73) then
        tmp = y * -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -7.8e+32) {
		tmp = t_1;
	} else if (a <= -2.25e-167) {
		tmp = x + z;
	} else if (a <= 1.75e-276) {
		tmp = y * b;
	} else if (a <= 125.0) {
		tmp = x + z;
	} else if (a <= 1e+44) {
		tmp = t * b;
	} else if (a <= 2.5e+73) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -7.8e+32:
		tmp = t_1
	elif a <= -2.25e-167:
		tmp = x + z
	elif a <= 1.75e-276:
		tmp = y * b
	elif a <= 125.0:
		tmp = x + z
	elif a <= 1e+44:
		tmp = t * b
	elif a <= 2.5e+73:
		tmp = y * -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -7.8e+32)
		tmp = t_1;
	elseif (a <= -2.25e-167)
		tmp = Float64(x + z);
	elseif (a <= 1.75e-276)
		tmp = Float64(y * b);
	elseif (a <= 125.0)
		tmp = Float64(x + z);
	elseif (a <= 1e+44)
		tmp = Float64(t * b);
	elseif (a <= 2.5e+73)
		tmp = Float64(y * Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -7.8e+32)
		tmp = t_1;
	elseif (a <= -2.25e-167)
		tmp = x + z;
	elseif (a <= 1.75e-276)
		tmp = y * b;
	elseif (a <= 125.0)
		tmp = x + z;
	elseif (a <= 1e+44)
		tmp = t * b;
	elseif (a <= 2.5e+73)
		tmp = y * -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+32], t$95$1, If[LessEqual[a, -2.25e-167], N[(x + z), $MachinePrecision], If[LessEqual[a, 1.75e-276], N[(y * b), $MachinePrecision], If[LessEqual[a, 125.0], N[(x + z), $MachinePrecision], If[LessEqual[a, 1e+44], N[(t * b), $MachinePrecision], If[LessEqual[a, 2.5e+73], N[(y * (-z)), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.7999999999999998e32 or 2.49999999999999988e73 < a

   1. Initial program 86.9%

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

   2. Taylor expanded in a around inf 58.5%

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

   if -7.7999999999999998e32 < a < -2.2500000000000001e-167 or 1.74999999999999996e-276 < a < 125

   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 0 95.6%

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

   3. Taylor expanded in y around 0 71.0%

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

      1. associate--l+ 71.0%

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

      2. sub-neg 71.0%

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

      3. metadata-eval 71.0%

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

      4. neg-mul-1 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in b around 0 44.9%

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

   if -2.2500000000000001e-167 < a < 1.74999999999999996e-276

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 49.1%

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

   3. Taylor expanded in b around inf 32.5%

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

   if 125 < a < 1.0000000000000001e44

   1. Initial program 83.3%

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

   2. Taylor expanded in b around inf 84.3%

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

   3. Taylor expanded in t around inf 83.4%

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

   if 1.0000000000000001e44 < a < 2.49999999999999988e73

   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 z around inf 75.8%

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

   3. Taylor expanded in y around inf 40.5%

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

      1. mul-1-neg 40.5%

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

      2. distribute-rgt-neg-in 40.5%

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

   5. Simplified 40.5%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-167}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-276}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 125:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 10^{+44}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 10: 49.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-102}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -4.4e+109)
     t_2
     (if (<= y -3.7e+15)
       t_1
       (if (<= y -3.2e-87)
         (+ x z)
         (if (<= y -1.55e-134)
           t_1
           (if (<= y 1.25e-102) (+ x z) (if (<= y 1.12e+79) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -4.4e+109) {
		tmp = t_2;
	} else if (y <= -3.7e+15) {
		tmp = t_1;
	} else if (y <= -3.2e-87) {
		tmp = x + z;
	} else if (y <= -1.55e-134) {
		tmp = t_1;
	} else if (y <= 1.25e-102) {
		tmp = x + z;
	} else if (y <= 1.12e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-4.4d+109)) then
        tmp = t_2
    else if (y <= (-3.7d+15)) then
        tmp = t_1
    else if (y <= (-3.2d-87)) then
        tmp = x + z
    else if (y <= (-1.55d-134)) then
        tmp = t_1
    else if (y <= 1.25d-102) then
        tmp = x + z
    else if (y <= 1.12d+79) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -4.4e+109) {
		tmp = t_2;
	} else if (y <= -3.7e+15) {
		tmp = t_1;
	} else if (y <= -3.2e-87) {
		tmp = x + z;
	} else if (y <= -1.55e-134) {
		tmp = t_1;
	} else if (y <= 1.25e-102) {
		tmp = x + z;
	} else if (y <= 1.12e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -4.4e+109:
		tmp = t_2
	elif y <= -3.7e+15:
		tmp = t_1
	elif y <= -3.2e-87:
		tmp = x + z
	elif y <= -1.55e-134:
		tmp = t_1
	elif y <= 1.25e-102:
		tmp = x + z
	elif y <= 1.12e+79:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4.4e+109)
		tmp = t_2;
	elseif (y <= -3.7e+15)
		tmp = t_1;
	elseif (y <= -3.2e-87)
		tmp = Float64(x + z);
	elseif (y <= -1.55e-134)
		tmp = t_1;
	elseif (y <= 1.25e-102)
		tmp = Float64(x + z);
	elseif (y <= 1.12e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -4.4e+109)
		tmp = t_2;
	elseif (y <= -3.7e+15)
		tmp = t_1;
	elseif (y <= -3.2e-87)
		tmp = x + z;
	elseif (y <= -1.55e-134)
		tmp = t_1;
	elseif (y <= 1.25e-102)
		tmp = x + z;
	elseif (y <= 1.12e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+109], t$95$2, If[LessEqual[y, -3.7e+15], t$95$1, If[LessEqual[y, -3.2e-87], N[(x + z), $MachinePrecision], If[LessEqual[y, -1.55e-134], t$95$1, If[LessEqual[y, 1.25e-102], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.12e+79], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3999999999999998e109 or 1.12e79 < y

   1. Initial program 81.1%

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

   2. Taylor expanded in y around inf 71.6%

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

   if -4.3999999999999998e109 < y < -3.7e15 or -3.19999999999999979e-87 < y < -1.55000000000000003e-134 or 1.25000000000000006e-102 < y < 1.12e79

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 51.9%

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

   if -3.7e15 < y < -3.19999999999999979e-87 or -1.55000000000000003e-134 < y < 1.25000000000000006e-102

   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 a around 0 75.4%

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

   3. Taylor expanded in y around 0 75.3%

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

      1. associate--l+ 75.3%

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

      2. sub-neg 75.3%

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

      3. metadata-eval 75.3%

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

      4. neg-mul-1 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in b around 0 52.8%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-134}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-102}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 11: 62.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-290}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+24} \lor \neg \left(b \leq 1.35 \cdot 10^{+42}\right) \land b \leq 8.5 \cdot 10^{+100}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -1.2e+64)
     t_1
     (if (<= b 2.05e-290)
       (+ x (* a (- 1.0 t)))
       (if (or (<= b 1.7e+24) (and (not (<= b 1.35e+42)) (<= b 8.5e+100)))
         (+ x (- z (* y z)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.2e+64) {
		tmp = t_1;
	} else if (b <= 2.05e-290) {
		tmp = x + (a * (1.0 - t));
	} else if ((b <= 1.7e+24) || (!(b <= 1.35e+42) && (b <= 8.5e+100))) {
		tmp = x + (z - (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-1.2d+64)) then
        tmp = t_1
    else if (b <= 2.05d-290) then
        tmp = x + (a * (1.0d0 - t))
    else if ((b <= 1.7d+24) .or. (.not. (b <= 1.35d+42)) .and. (b <= 8.5d+100)) then
        tmp = x + (z - (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.2e+64) {
		tmp = t_1;
	} else if (b <= 2.05e-290) {
		tmp = x + (a * (1.0 - t));
	} else if ((b <= 1.7e+24) || (!(b <= 1.35e+42) && (b <= 8.5e+100))) {
		tmp = x + (z - (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.2e+64:
		tmp = t_1
	elif b <= 2.05e-290:
		tmp = x + (a * (1.0 - t))
	elif (b <= 1.7e+24) or (not (b <= 1.35e+42) and (b <= 8.5e+100)):
		tmp = x + (z - (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.2e+64)
		tmp = t_1;
	elseif (b <= 2.05e-290)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif ((b <= 1.7e+24) || (!(b <= 1.35e+42) && (b <= 8.5e+100)))
		tmp = Float64(x + Float64(z - Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.2e+64)
		tmp = t_1;
	elseif (b <= 2.05e-290)
		tmp = x + (a * (1.0 - t));
	elseif ((b <= 1.7e+24) || (~((b <= 1.35e+42)) && (b <= 8.5e+100)))
		tmp = x + (z - (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e+64], t$95$1, If[LessEqual[b, 2.05e-290], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.7e+24], And[N[Not[LessEqual[b, 1.35e+42]], $MachinePrecision], LessEqual[b, 8.5e+100]]], N[(x + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2e64 or 1.7e24 < b < 1.35e42 or 8.50000000000000043e100 < b

   1. Initial program 84.4%

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

   2. Taylor expanded in b around inf 73.7%

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

   if -1.2e64 < b < 2.0500000000000001e-290

   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 b around 0 88.8%

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

   3. Taylor expanded in a around inf 62.6%

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

   if 2.0500000000000001e-290 < b < 1.7e24 or 1.35e42 < b < 8.50000000000000043e100

   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 0 97.1%

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

   3. Taylor expanded in a around 0 73.8%

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

      1. sub-neg 73.8%

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

      2. metadata-eval 73.8%

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

      3. distribute-rgt-in 73.8%

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

      4. neg-mul-1 73.8%

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

      5. unsub-neg 73.8%

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

   5. Simplified 73.8%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-290}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+24} \lor \neg \left(b \leq 1.35 \cdot 10^{+42}\right) \land b \leq 8.5 \cdot 10^{+100}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 12: 71.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+42} \lor \neg \left(b \leq 1.5 \cdot 10^{+24}\right) \land \left(b \leq 7.5 \cdot 10^{+38} \lor \neg \left(b \leq 3.1 \cdot 10^{+98}\right)\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.5e+42)
         (and (not (<= b 1.5e+24)) (or (<= b 7.5e+38) (not (<= b 3.1e+98)))))
   (- x (* b (- 2.0 (+ y t))))
   (+ x (+ a (- z (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.5e+42) || (!(b <= 1.5e+24) && ((b <= 7.5e+38) || !(b <= 3.1e+98)))) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + (a + (z - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.5d+42)) .or. (.not. (b <= 1.5d+24)) .and. (b <= 7.5d+38) .or. (.not. (b <= 3.1d+98))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x + (a + (z - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.5e+42) || (!(b <= 1.5e+24) && ((b <= 7.5e+38) || !(b <= 3.1e+98)))) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + (a + (z - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.5e+42) or (not (b <= 1.5e+24) and ((b <= 7.5e+38) or not (b <= 3.1e+98))):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x + (a + (z - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.5e+42) || (!(b <= 1.5e+24) && ((b <= 7.5e+38) || !(b <= 3.1e+98))))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x + Float64(a + Float64(z - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.5e+42) || (~((b <= 1.5e+24)) && ((b <= 7.5e+38) || ~((b <= 3.1e+98)))))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x + (a + (z - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.5e+42], And[N[Not[LessEqual[b, 1.5e+24]], $MachinePrecision], Or[LessEqual[b, 7.5e+38], N[Not[LessEqual[b, 3.1e+98]], $MachinePrecision]]]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.50000000000000052e42 or 1.49999999999999997e24 < b < 7.4999999999999999e38 or 3.10000000000000019e98 < b

   1. Initial program 85.1%

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

   2. Taylor expanded in a around 0 83.3%

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

   3. Taylor expanded in z around 0 79.1%

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

   if -6.50000000000000052e42 < b < 1.49999999999999997e24 or 7.4999999999999999e38 < b < 3.10000000000000019e98

   1. Initial program 97.2%

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

   2. Taylor expanded in b around 0 93.6%

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

   3. Taylor expanded in t around 0 69.7%

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

      1. +-commutative 69.7%

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

      2. sub-neg 69.7%

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

      3. metadata-eval 69.7%

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

      4. mul-1-neg 69.7%

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

      5. unsub-neg 69.7%

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

      6. distribute-rgt-in 69.7%

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

      7. neg-mul-1 69.7%

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

      8. unsub-neg 69.7%

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

   5. Simplified 69.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+42} \lor \neg \left(b \leq 1.5 \cdot 10^{+24}\right) \land \left(b \leq 7.5 \cdot 10^{+38} \lor \neg \left(b \leq 3.1 \cdot 10^{+98}\right)\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \end{array} \]

Alternative 13: 83.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+24}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+39} \lor \neg \left(b \leq 2.5 \cdot 10^{+97}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -9e+42)
     t_1
     (if (<= b 1.7e+24)
       (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))
       (if (or (<= b 1.15e+39) (not (<= b 2.5e+97)))
         t_1
         (+ x (+ a (- z (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -9e+42) {
		tmp = t_1;
	} else if (b <= 1.7e+24) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else if ((b <= 1.15e+39) || !(b <= 2.5e+97)) {
		tmp = t_1;
	} else {
		tmp = x + (a + (z - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-9d+42)) then
        tmp = t_1
    else if (b <= 1.7d+24) then
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    else if ((b <= 1.15d+39) .or. (.not. (b <= 2.5d+97))) then
        tmp = t_1
    else
        tmp = x + (a + (z - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -9e+42) {
		tmp = t_1;
	} else if (b <= 1.7e+24) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else if ((b <= 1.15e+39) || !(b <= 2.5e+97)) {
		tmp = t_1;
	} else {
		tmp = x + (a + (z - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -9e+42:
		tmp = t_1
	elif b <= 1.7e+24:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	elif (b <= 1.15e+39) or not (b <= 2.5e+97):
		tmp = t_1
	else:
		tmp = x + (a + (z - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -9e+42)
		tmp = t_1;
	elseif (b <= 1.7e+24)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	elseif ((b <= 1.15e+39) || !(b <= 2.5e+97))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a + Float64(z - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -9e+42)
		tmp = t_1;
	elseif (b <= 1.7e+24)
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	elseif ((b <= 1.15e+39) || ~((b <= 2.5e+97)))
		tmp = t_1;
	else
		tmp = x + (a + (z - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e+42], t$95$1, If[LessEqual[b, 1.7e+24], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.15e+39], N[Not[LessEqual[b, 2.5e+97]], $MachinePrecision]], t$95$1, N[(x + N[(a + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.00000000000000025e42 or 1.7e24 < b < 1.15000000000000006e39 or 2.49999999999999999e97 < b

   1. Initial program 85.1%

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

   2. Taylor expanded in a around 0 83.3%

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

   3. Taylor expanded in z around 0 79.1%

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

   if -9.00000000000000025e42 < b < 1.7e24

   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 b around 0 94.6%

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

   if 1.15000000000000006e39 < b < 2.49999999999999999e97

   1. Initial program 81.8%

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

   2. Taylor expanded in b around 0 82.2%

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

   3. Taylor expanded in t around 0 82.6%

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

      1. +-commutative 82.6%

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

      2. sub-neg 82.6%

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

      3. metadata-eval 82.6%

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

      4. mul-1-neg 82.6%

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

      5. unsub-neg 82.6%

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

      6. distribute-rgt-in 82.6%

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

      7. neg-mul-1 82.6%

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

      8. unsub-neg 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+42}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+24}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+39} \lor \neg \left(b \leq 2.5 \cdot 10^{+97}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \end{array} \]

Alternative 14: 41.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-140}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= a -4e+31)
     t_2
     (if (<= a -7.5e-140)
       (+ x z)
       (if (<= a 4.3e-277)
         t_1
         (if (<= a 1.15e-40) (+ x z) (if (<= a 2e+106) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -4e+31) {
		tmp = t_2;
	} else if (a <= -7.5e-140) {
		tmp = x + z;
	} else if (a <= 4.3e-277) {
		tmp = t_1;
	} else if (a <= 1.15e-40) {
		tmp = x + z;
	} else if (a <= 2e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    t_2 = a * (1.0d0 - t)
    if (a <= (-4d+31)) then
        tmp = t_2
    else if (a <= (-7.5d-140)) then
        tmp = x + z
    else if (a <= 4.3d-277) then
        tmp = t_1
    else if (a <= 1.15d-40) then
        tmp = x + z
    else if (a <= 2d+106) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -4e+31) {
		tmp = t_2;
	} else if (a <= -7.5e-140) {
		tmp = x + z;
	} else if (a <= 4.3e-277) {
		tmp = t_1;
	} else if (a <= 1.15e-40) {
		tmp = x + z;
	} else if (a <= 2e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -4e+31:
		tmp = t_2
	elif a <= -7.5e-140:
		tmp = x + z
	elif a <= 4.3e-277:
		tmp = t_1
	elif a <= 1.15e-40:
		tmp = x + z
	elif a <= 2e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -4e+31)
		tmp = t_2;
	elseif (a <= -7.5e-140)
		tmp = Float64(x + z);
	elseif (a <= 4.3e-277)
		tmp = t_1;
	elseif (a <= 1.15e-40)
		tmp = Float64(x + z);
	elseif (a <= 2e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -4e+31)
		tmp = t_2;
	elseif (a <= -7.5e-140)
		tmp = x + z;
	elseif (a <= 4.3e-277)
		tmp = t_1;
	elseif (a <= 1.15e-40)
		tmp = x + z;
	elseif (a <= 2e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+31], t$95$2, If[LessEqual[a, -7.5e-140], N[(x + z), $MachinePrecision], If[LessEqual[a, 4.3e-277], t$95$1, If[LessEqual[a, 1.15e-40], N[(x + z), $MachinePrecision], If[LessEqual[a, 2e+106], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.9999999999999999e31 or 2.00000000000000018e106 < a

   1. Initial program 87.5%

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

   2. Taylor expanded in a around inf 59.6%

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

   if -3.9999999999999999e31 < a < -7.4999999999999998e-140 or 4.2999999999999999e-277 < a < 1.15e-40

   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 a around 0 95.1%

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

   3. Taylor expanded in y around 0 69.9%

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

      1. associate--l+ 69.9%

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

      2. sub-neg 69.9%

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

      3. metadata-eval 69.9%

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

      4. neg-mul-1 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in b around 0 47.9%

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

   if -7.4999999999999998e-140 < a < 4.2999999999999999e-277 or 1.15e-40 < a < 2.00000000000000018e106

   1. Initial program 91.7%

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

   2. Taylor expanded in b around inf 62.1%

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

   3. Taylor expanded in y around 0 40.8%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-140}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 15: 65.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-290}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+23}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -2.6e+42)
     t_1
     (if (<= b 4.4e-290)
       (+ x (* a (- 1.0 t)))
       (if (<= b 7.8e+23) (+ x (- z (* y z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -2.6e+42) {
		tmp = t_1;
	} else if (b <= 4.4e-290) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 7.8e+23) {
		tmp = x + (z - (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-2.6d+42)) then
        tmp = t_1
    else if (b <= 4.4d-290) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 7.8d+23) then
        tmp = x + (z - (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -2.6e+42) {
		tmp = t_1;
	} else if (b <= 4.4e-290) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 7.8e+23) {
		tmp = x + (z - (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -2.6e+42:
		tmp = t_1
	elif b <= 4.4e-290:
		tmp = x + (a * (1.0 - t))
	elif b <= 7.8e+23:
		tmp = x + (z - (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -2.6e+42)
		tmp = t_1;
	elseif (b <= 4.4e-290)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 7.8e+23)
		tmp = Float64(x + Float64(z - Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -2.6e+42)
		tmp = t_1;
	elseif (b <= 4.4e-290)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 7.8e+23)
		tmp = x + (z - (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.6e+42], t$95$1, If[LessEqual[b, 4.4e-290], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+23], N[(x + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5999999999999999e42 or 7.8000000000000001e23 < b

   1. Initial program 84.8%

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

   2. Taylor expanded in a around 0 81.6%

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

   3. Taylor expanded in z around 0 75.4%

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

   if -2.5999999999999999e42 < b < 4.4000000000000002e-290

   1. Initial program 97.3%

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

   2. Taylor expanded in b around 0 91.7%

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

   3. Taylor expanded in a around inf 63.6%

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

   if 4.4000000000000002e-290 < b < 7.8000000000000001e23

   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 98.3%

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

   3. Taylor expanded in a around 0 72.6%

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

      1. sub-neg 72.6%

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

      2. metadata-eval 72.6%

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

      3. distribute-rgt-in 72.6%

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

      4. neg-mul-1 72.6%

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

      5. unsub-neg 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-290}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+23}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]

Alternative 16: 35.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-90}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-119}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-46}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+66}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.5e+79)
   (* y b)
   (if (<= y -6.8e-90)
     (+ x z)
     (if (<= y -3.2e-119)
       (* t b)
       (if (<= y 1.8e-46) (+ x z) (if (<= y 5.6e+66) (* t b) (* y (- z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e+79) {
		tmp = y * b;
	} else if (y <= -6.8e-90) {
		tmp = x + z;
	} else if (y <= -3.2e-119) {
		tmp = t * b;
	} else if (y <= 1.8e-46) {
		tmp = x + z;
	} else if (y <= 5.6e+66) {
		tmp = t * b;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.5d+79)) then
        tmp = y * b
    else if (y <= (-6.8d-90)) then
        tmp = x + z
    else if (y <= (-3.2d-119)) then
        tmp = t * b
    else if (y <= 1.8d-46) then
        tmp = x + z
    else if (y <= 5.6d+66) then
        tmp = t * b
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e+79) {
		tmp = y * b;
	} else if (y <= -6.8e-90) {
		tmp = x + z;
	} else if (y <= -3.2e-119) {
		tmp = t * b;
	} else if (y <= 1.8e-46) {
		tmp = x + z;
	} else if (y <= 5.6e+66) {
		tmp = t * b;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.5e+79:
		tmp = y * b
	elif y <= -6.8e-90:
		tmp = x + z
	elif y <= -3.2e-119:
		tmp = t * b
	elif y <= 1.8e-46:
		tmp = x + z
	elif y <= 5.6e+66:
		tmp = t * b
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.5e+79)
		tmp = Float64(y * b);
	elseif (y <= -6.8e-90)
		tmp = Float64(x + z);
	elseif (y <= -3.2e-119)
		tmp = Float64(t * b);
	elseif (y <= 1.8e-46)
		tmp = Float64(x + z);
	elseif (y <= 5.6e+66)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.5e+79)
		tmp = y * b;
	elseif (y <= -6.8e-90)
		tmp = x + z;
	elseif (y <= -3.2e-119)
		tmp = t * b;
	elseif (y <= 1.8e-46)
		tmp = x + z;
	elseif (y <= 5.6e+66)
		tmp = t * b;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.5e+79], N[(y * b), $MachinePrecision], If[LessEqual[y, -6.8e-90], N[(x + z), $MachinePrecision], If[LessEqual[y, -3.2e-119], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.8e-46], N[(x + z), $MachinePrecision], If[LessEqual[y, 5.6e+66], N[(t * b), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4999999999999998e79

   1. Initial program 78.4%

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

   2. Taylor expanded in y around inf 76.3%

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

   3. Taylor expanded in b around inf 57.7%

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

   if -3.4999999999999998e79 < y < -6.79999999999999988e-90 or -3.19999999999999993e-119 < y < 1.8e-46

   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 0 71.9%

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

   3. Taylor expanded in y around 0 68.3%

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

      1. associate--l+ 68.3%

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

      2. sub-neg 68.3%

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

      3. metadata-eval 68.3%

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

      4. neg-mul-1 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in b around 0 44.1%

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

   if -6.79999999999999988e-90 < y < -3.19999999999999993e-119 or 1.8e-46 < y < 5.6000000000000001e66

   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 53.4%

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

   3. Taylor expanded in t around inf 43.8%

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

   if 5.6000000000000001e66 < y

   1. Initial program 83.8%

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

   2. Taylor expanded in z around inf 41.3%

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

   3. Taylor expanded in y around inf 41.3%

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

      1. mul-1-neg 41.3%

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

      2. distribute-rgt-neg-in 41.3%

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

   5. Simplified 41.3%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-90}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-119}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-46}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+66}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 17: 26.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+37}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-273}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-99}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.8e+37)
   (* t b)
   (if (<= t -1.95e-292)
     x
     (if (<= t 3.3e-273)
       z
       (if (<= t 5.5e-99) a (if (<= t 2.1e+33) z (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.8e+37) {
		tmp = t * b;
	} else if (t <= -1.95e-292) {
		tmp = x;
	} else if (t <= 3.3e-273) {
		tmp = z;
	} else if (t <= 5.5e-99) {
		tmp = a;
	} else if (t <= 2.1e+33) {
		tmp = z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.8d+37)) then
        tmp = t * b
    else if (t <= (-1.95d-292)) then
        tmp = x
    else if (t <= 3.3d-273) then
        tmp = z
    else if (t <= 5.5d-99) then
        tmp = a
    else if (t <= 2.1d+33) then
        tmp = z
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.8e+37) {
		tmp = t * b;
	} else if (t <= -1.95e-292) {
		tmp = x;
	} else if (t <= 3.3e-273) {
		tmp = z;
	} else if (t <= 5.5e-99) {
		tmp = a;
	} else if (t <= 2.1e+33) {
		tmp = z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.8e+37:
		tmp = t * b
	elif t <= -1.95e-292:
		tmp = x
	elif t <= 3.3e-273:
		tmp = z
	elif t <= 5.5e-99:
		tmp = a
	elif t <= 2.1e+33:
		tmp = z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.8e+37)
		tmp = Float64(t * b);
	elseif (t <= -1.95e-292)
		tmp = x;
	elseif (t <= 3.3e-273)
		tmp = z;
	elseif (t <= 5.5e-99)
		tmp = a;
	elseif (t <= 2.1e+33)
		tmp = z;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.8e+37)
		tmp = t * b;
	elseif (t <= -1.95e-292)
		tmp = x;
	elseif (t <= 3.3e-273)
		tmp = z;
	elseif (t <= 5.5e-99)
		tmp = a;
	elseif (t <= 2.1e+33)
		tmp = z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.8e+37], N[(t * b), $MachinePrecision], If[LessEqual[t, -1.95e-292], x, If[LessEqual[t, 3.3e-273], z, If[LessEqual[t, 5.5e-99], a, If[LessEqual[t, 2.1e+33], z, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.79999999999999999e37 or 2.1000000000000001e33 < t

   1. Initial program 86.0%

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

   2. Taylor expanded in b around inf 45.4%

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

   3. Taylor expanded in t around inf 36.4%

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

   if -1.79999999999999999e37 < t < -1.95e-292

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 24.5%

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

   if -1.95e-292 < t < 3.2999999999999999e-273 or 5.49999999999999991e-99 < t < 2.1000000000000001e33

   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 41.7%

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

   3. Taylor expanded in y around 0 27.7%

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

   if 3.2999999999999999e-273 < t < 5.49999999999999991e-99

   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 inf 36.7%

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

   3. Taylor expanded in t around 0 36.7%

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

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+37}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-273}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-99}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 18: 34.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+83}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-86}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-48}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 10^{+79}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.2e+83)
   (* y b)
   (if (<= y -5e-86)
     (+ x z)
     (if (<= y -1.35e-120)
       (* t b)
       (if (<= y 9.5e-48) (+ x z) (if (<= y 1e+79) (* t b) (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.2e+83) {
		tmp = y * b;
	} else if (y <= -5e-86) {
		tmp = x + z;
	} else if (y <= -1.35e-120) {
		tmp = t * b;
	} else if (y <= 9.5e-48) {
		tmp = x + z;
	} else if (y <= 1e+79) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.2d+83)) then
        tmp = y * b
    else if (y <= (-5d-86)) then
        tmp = x + z
    else if (y <= (-1.35d-120)) then
        tmp = t * b
    else if (y <= 9.5d-48) then
        tmp = x + z
    else if (y <= 1d+79) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.2e+83) {
		tmp = y * b;
	} else if (y <= -5e-86) {
		tmp = x + z;
	} else if (y <= -1.35e-120) {
		tmp = t * b;
	} else if (y <= 9.5e-48) {
		tmp = x + z;
	} else if (y <= 1e+79) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.2e+83:
		tmp = y * b
	elif y <= -5e-86:
		tmp = x + z
	elif y <= -1.35e-120:
		tmp = t * b
	elif y <= 9.5e-48:
		tmp = x + z
	elif y <= 1e+79:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.2e+83)
		tmp = Float64(y * b);
	elseif (y <= -5e-86)
		tmp = Float64(x + z);
	elseif (y <= -1.35e-120)
		tmp = Float64(t * b);
	elseif (y <= 9.5e-48)
		tmp = Float64(x + z);
	elseif (y <= 1e+79)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.2e+83)
		tmp = y * b;
	elseif (y <= -5e-86)
		tmp = x + z;
	elseif (y <= -1.35e-120)
		tmp = t * b;
	elseif (y <= 9.5e-48)
		tmp = x + z;
	elseif (y <= 1e+79)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.2e+83], N[(y * b), $MachinePrecision], If[LessEqual[y, -5e-86], N[(x + z), $MachinePrecision], If[LessEqual[y, -1.35e-120], N[(t * b), $MachinePrecision], If[LessEqual[y, 9.5e-48], N[(x + z), $MachinePrecision], If[LessEqual[y, 1e+79], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000002e83 or 9.99999999999999967e78 < y

   1. Initial program 81.0%

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

   2. Taylor expanded in y around inf 70.0%

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

   3. Taylor expanded in b around inf 40.1%

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

   if -5.2000000000000002e83 < y < -4.9999999999999999e-86 or -1.3499999999999999e-120 < y < 9.50000000000000036e-48

   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 0 71.9%

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

   3. Taylor expanded in y around 0 68.3%

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

      1. associate--l+ 68.3%

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

      2. sub-neg 68.3%

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

      3. metadata-eval 68.3%

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

      4. neg-mul-1 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in b around 0 44.1%

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

   if -4.9999999999999999e-86 < y < -1.3499999999999999e-120 or 9.50000000000000036e-48 < y < 9.99999999999999967e78

   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 50.3%

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

   3. Taylor expanded in t around inf 41.7%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+83}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-86}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-48}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 10^{+79}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 19: 26.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-198}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-52}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+79}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.7e+83)
   (* y b)
   (if (<= y -1.7e-198)
     (* t b)
     (if (<= y 1.7e-52) z (if (<= y 1.05e+79) (* t b) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e+83) {
		tmp = y * b;
	} else if (y <= -1.7e-198) {
		tmp = t * b;
	} else if (y <= 1.7e-52) {
		tmp = z;
	} else if (y <= 1.05e+79) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.7d+83)) then
        tmp = y * b
    else if (y <= (-1.7d-198)) then
        tmp = t * b
    else if (y <= 1.7d-52) then
        tmp = z
    else if (y <= 1.05d+79) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e+83) {
		tmp = y * b;
	} else if (y <= -1.7e-198) {
		tmp = t * b;
	} else if (y <= 1.7e-52) {
		tmp = z;
	} else if (y <= 1.05e+79) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.7e+83:
		tmp = y * b
	elif y <= -1.7e-198:
		tmp = t * b
	elif y <= 1.7e-52:
		tmp = z
	elif y <= 1.05e+79:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.7e+83)
		tmp = Float64(y * b);
	elseif (y <= -1.7e-198)
		tmp = Float64(t * b);
	elseif (y <= 1.7e-52)
		tmp = z;
	elseif (y <= 1.05e+79)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.7e+83)
		tmp = y * b;
	elseif (y <= -1.7e-198)
		tmp = t * b;
	elseif (y <= 1.7e-52)
		tmp = z;
	elseif (y <= 1.05e+79)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.7e+83], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.7e-198], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.7e-52], z, If[LessEqual[y, 1.05e+79], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6999999999999999e83 or 1.05000000000000004e79 < y

   1. Initial program 81.0%

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

   2. Taylor expanded in y around inf 70.0%

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

   3. Taylor expanded in b around inf 40.1%

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

   if -1.6999999999999999e83 < y < -1.6999999999999999e-198 or 1.70000000000000009e-52 < y < 1.05000000000000004e79

   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 b around inf 38.6%

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

   3. Taylor expanded in t around inf 31.1%

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

   if -1.6999999999999999e-198 < y < 1.70000000000000009e-52

   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 z around inf 35.5%

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

   3. Taylor expanded in y around 0 35.5%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-198}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-52}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+79}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 20: 34.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-48}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+33}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1e+37)
   (* t b)
   (if (<= t 8.5e-48)
     (+ x a)
     (if (<= t 2.2e+33) z (if (<= t 2.8e+52) (* y b) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e+37) {
		tmp = t * b;
	} else if (t <= 8.5e-48) {
		tmp = x + a;
	} else if (t <= 2.2e+33) {
		tmp = z;
	} else if (t <= 2.8e+52) {
		tmp = y * b;
	} 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 <= (-1d+37)) then
        tmp = t * b
    else if (t <= 8.5d-48) then
        tmp = x + a
    else if (t <= 2.2d+33) then
        tmp = z
    else if (t <= 2.8d+52) then
        tmp = y * b
    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 <= -1e+37) {
		tmp = t * b;
	} else if (t <= 8.5e-48) {
		tmp = x + a;
	} else if (t <= 2.2e+33) {
		tmp = z;
	} else if (t <= 2.8e+52) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1e+37:
		tmp = t * b
	elif t <= 8.5e-48:
		tmp = x + a
	elif t <= 2.2e+33:
		tmp = z
	elif t <= 2.8e+52:
		tmp = y * b
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1e+37)
		tmp = Float64(t * b);
	elseif (t <= 8.5e-48)
		tmp = Float64(x + a);
	elseif (t <= 2.2e+33)
		tmp = z;
	elseif (t <= 2.8e+52)
		tmp = Float64(y * b);
	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 <= -1e+37)
		tmp = t * b;
	elseif (t <= 8.5e-48)
		tmp = x + a;
	elseif (t <= 2.2e+33)
		tmp = z;
	elseif (t <= 2.8e+52)
		tmp = y * b;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1e+37], N[(t * b), $MachinePrecision], If[LessEqual[t, 8.5e-48], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.2e+33], z, If[LessEqual[t, 2.8e+52], N[(y * b), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.99999999999999954e36 or 2.8e52 < t

   1. Initial program 86.3%

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

   2. Taylor expanded in b around inf 44.3%

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

   3. Taylor expanded in t around inf 36.7%

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

   if -9.99999999999999954e36 < t < 8.5000000000000004e-48

   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 b around 0 73.5%

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

   3. Taylor expanded in a around inf 41.0%

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

   4. Taylor expanded in t around 0 39.4%

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

      1. cancel-sign-sub-inv 39.4%

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

      2. metadata-eval 39.4%

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

      3. *-lft-identity 39.4%

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

   6. Simplified 39.4%

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

   if 8.5000000000000004e-48 < t < 2.19999999999999994e33

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 42.4%

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

   3. Taylor expanded in y around 0 28.9%

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

   if 2.19999999999999994e33 < t < 2.8e52

   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 y around inf 93.1%

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

   3. Taylor expanded in b around inf 68.1%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-48}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+33}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 21: 50.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -62000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -62000000.0)
     t_1
     (if (<= t 8.5e-83) (+ x a) (if (<= t 4e+25) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -62000000.0) {
		tmp = t_1;
	} else if (t <= 8.5e-83) {
		tmp = x + a;
	} else if (t <= 4e+25) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-62000000.0d0)) then
        tmp = t_1
    else if (t <= 8.5d-83) then
        tmp = x + a
    else if (t <= 4d+25) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -62000000.0) {
		tmp = t_1;
	} else if (t <= 8.5e-83) {
		tmp = x + a;
	} else if (t <= 4e+25) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -62000000.0:
		tmp = t_1
	elif t <= 8.5e-83:
		tmp = x + a
	elif t <= 4e+25:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -62000000.0)
		tmp = t_1;
	elseif (t <= 8.5e-83)
		tmp = Float64(x + a);
	elseif (t <= 4e+25)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -62000000.0)
		tmp = t_1;
	elseif (t <= 8.5e-83)
		tmp = x + a;
	elseif (t <= 4e+25)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -62000000.0], t$95$1, If[LessEqual[t, 8.5e-83], N[(x + a), $MachinePrecision], If[LessEqual[t, 4e+25], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2e7 or 4.00000000000000036e25 < t

   1. Initial program 87.1%

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

   2. Taylor expanded in t around inf 65.7%

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

   if -6.2e7 < t < 8.49999999999999938e-83

   1. Initial program 94.8%

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

   2. Taylor expanded in b around 0 73.1%

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

   3. Taylor expanded in a around inf 41.0%

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

   4. Taylor expanded in t around 0 41.0%

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

      1. cancel-sign-sub-inv 41.0%

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

      2. metadata-eval 41.0%

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

      3. *-lft-identity 41.0%

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

   6. Simplified 41.0%

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

   if 8.49999999999999938e-83 < t < 4.00000000000000036e25

   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 0 94.4%

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

   3. Taylor expanded in y around 0 65.2%

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

      1. associate--l+ 65.2%

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

      2. sub-neg 65.2%

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

      3. metadata-eval 65.2%

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

      4. neg-mul-1 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in b around 0 43.1%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -62000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 22: 21.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-179}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+120}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.3e+74) x (if (<= x 5.6e-179) z (if (<= x 3.7e+120) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.3e+74) {
		tmp = x;
	} else if (x <= 5.6e-179) {
		tmp = z;
	} else if (x <= 3.7e+120) {
		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 <= (-2.3d+74)) then
        tmp = x
    else if (x <= 5.6d-179) then
        tmp = z
    else if (x <= 3.7d+120) 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 <= -2.3e+74) {
		tmp = x;
	} else if (x <= 5.6e-179) {
		tmp = z;
	} else if (x <= 3.7e+120) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.3e+74:
		tmp = x
	elif x <= 5.6e-179:
		tmp = z
	elif x <= 3.7e+120:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.3e+74)
		tmp = x;
	elseif (x <= 5.6e-179)
		tmp = z;
	elseif (x <= 3.7e+120)
		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 <= -2.3e+74)
		tmp = x;
	elseif (x <= 5.6e-179)
		tmp = z;
	elseif (x <= 3.7e+120)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.3e+74], x, If[LessEqual[x, 5.6e-179], z, If[LessEqual[x, 3.7e+120], a, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999999e74 or 3.70000000000000024e120 < x

   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 x around inf 32.2%

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

   if -2.2999999999999999e74 < x < 5.6000000000000001e-179

   1. Initial program 91.6%

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

   2. Taylor expanded in z around inf 41.5%

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

   3. Taylor expanded in y around 0 22.4%

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

   if 5.6000000000000001e-179 < x < 3.70000000000000024e120

   1. Initial program 90.6%

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

   2. Taylor expanded in a around inf 37.4%

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

   3. Taylor expanded in t around 0 20.8%

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

4. Final simplification 25.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-179}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+120}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 20.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+166}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 95000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.46e+166) a (if (<= a 95000.0) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.46e+166) {
		tmp = a;
	} else if (a <= 95000.0) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.46d+166)) then
        tmp = a
    else if (a <= 95000.0d0) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.46e+166) {
		tmp = a;
	} else if (a <= 95000.0) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.46e+166:
		tmp = a
	elif a <= 95000.0:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.46e+166)
		tmp = a;
	elseif (a <= 95000.0)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.46e+166)
		tmp = a;
	elseif (a <= 95000.0)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.46e+166], a, If[LessEqual[a, 95000.0], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4600000000000001e166 or 95000 < a

   1. Initial program 85.4%

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

   2. Taylor expanded in a around inf 59.7%

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

   3. Taylor expanded in t around 0 25.2%

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

   if -1.4600000000000001e166 < a < 95000

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf 17.3%

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

4. Final simplification 20.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+166}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 95000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 24: 10.3% 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 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 inf 27.3%

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

3. Taylor expanded in t around 0 11.3%

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

4. Final simplification 11.3%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023297 
(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)))