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

Percentage Accurate: 95.3% → 98.0%

Time: 14.4s

Alternatives: 23

Speedup: 0.5×

• 35.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 79.0%

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

4. Final simplification 99.2%

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

Alternative 2: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-def 97.7%

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

   3. associate--l+ 97.7%

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

   4. sub-neg 97.7%

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

   5. metadata-eval 97.7%

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

   6. sub-neg 97.7%

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

   7. associate-+l- 97.7%

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

   8. fma-neg 98.4%

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

   9. sub-neg 98.4%

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

   10. metadata-eval 98.4%

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

   11. remove-double-neg 98.4%

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

   12. sub-neg 98.4%

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

   13. metadata-eval 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := x + b \cdot \left(y + \left(t + -2\right)\right)\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.7 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-181}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y))))
        (t_2 (+ x (* b (+ y (+ t -2.0)))))
        (t_3 (+ x (* a (- 1.0 t)))))
   (if (<= b -1.3e+26)
     t_2
     (if (<= b -7.7e-87)
       t_1
       (if (<= b -2.4e-181)
         t_3
         (if (<= b -1.1e-260)
           t_1
           (if (<= b 1.08e-215) t_3 (if (<= b 1.12e-8) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x + (b * (y + (t + -2.0)));
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -1.3e+26) {
		tmp = t_2;
	} else if (b <= -7.7e-87) {
		tmp = t_1;
	} else if (b <= -2.4e-181) {
		tmp = t_3;
	} else if (b <= -1.1e-260) {
		tmp = t_1;
	} else if (b <= 1.08e-215) {
		tmp = t_3;
	} else if (b <= 1.12e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = x + (b * (y + (t + (-2.0d0))))
    t_3 = x + (a * (1.0d0 - t))
    if (b <= (-1.3d+26)) then
        tmp = t_2
    else if (b <= (-7.7d-87)) then
        tmp = t_1
    else if (b <= (-2.4d-181)) then
        tmp = t_3
    else if (b <= (-1.1d-260)) then
        tmp = t_1
    else if (b <= 1.08d-215) then
        tmp = t_3
    else if (b <= 1.12d-8) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x + (b * (y + (t + -2.0)));
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -1.3e+26) {
		tmp = t_2;
	} else if (b <= -7.7e-87) {
		tmp = t_1;
	} else if (b <= -2.4e-181) {
		tmp = t_3;
	} else if (b <= -1.1e-260) {
		tmp = t_1;
	} else if (b <= 1.08e-215) {
		tmp = t_3;
	} else if (b <= 1.12e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = x + (b * (y + (t + -2.0)))
	t_3 = x + (a * (1.0 - t))
	tmp = 0
	if b <= -1.3e+26:
		tmp = t_2
	elif b <= -7.7e-87:
		tmp = t_1
	elif b <= -2.4e-181:
		tmp = t_3
	elif b <= -1.1e-260:
		tmp = t_1
	elif b <= 1.08e-215:
		tmp = t_3
	elif b <= 1.12e-8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(x + Float64(b * Float64(y + Float64(t + -2.0))))
	t_3 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (b <= -1.3e+26)
		tmp = t_2;
	elseif (b <= -7.7e-87)
		tmp = t_1;
	elseif (b <= -2.4e-181)
		tmp = t_3;
	elseif (b <= -1.1e-260)
		tmp = t_1;
	elseif (b <= 1.08e-215)
		tmp = t_3;
	elseif (b <= 1.12e-8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = x + (b * (y + (t + -2.0)));
	t_3 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (b <= -1.3e+26)
		tmp = t_2;
	elseif (b <= -7.7e-87)
		tmp = t_1;
	elseif (b <= -2.4e-181)
		tmp = t_3;
	elseif (b <= -1.1e-260)
		tmp = t_1;
	elseif (b <= 1.08e-215)
		tmp = t_3;
	elseif (b <= 1.12e-8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+26], t$95$2, If[LessEqual[b, -7.7e-87], t$95$1, If[LessEqual[b, -2.4e-181], t$95$3, If[LessEqual[b, -1.1e-260], t$95$1, If[LessEqual[b, 1.08e-215], t$95$3, If[LessEqual[b, 1.12e-8], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.30000000000000001e26 or 1.11999999999999994e-8 < b

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0 95.1%

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

   4. Taylor expanded in a around 0 87.3%

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

   5. Taylor expanded in z around 0 76.2%

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

      1. sub-neg 76.2%

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

      2. metadata-eval 76.2%

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

      3. distribute-lft-out 79.4%

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

      4. cancel-sign-sub 79.4%

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

      5. mul-1-neg 79.4%

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

      6. *-commutative 79.4%

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

      7. associate-*r* 79.4%

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

      8. distribute-lft-out 79.4%

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

      9. metadata-eval 79.4%

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

      10. sub-neg 79.4%

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

      11. unsub-neg 79.4%

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

      12. distribute-rgt-neg-in 79.4%

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

      13. sub-neg 79.4%

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

      14. metadata-eval 79.4%

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

      15. distribute-lft-out 79.4%

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

      16. mul-1-neg 79.4%

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

      17. remove-double-neg 79.4%

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

      18. +-commutative 79.4%

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

   7. Simplified 79.4%

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

   if -1.30000000000000001e26 < b < -7.6999999999999998e-87 or -2.4000000000000001e-181 < b < -1.10000000000000008e-260 or 1.08e-215 < b < 1.11999999999999994e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 86.5%

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

   4. Taylor expanded in a around 0 66.1%

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

   if -7.6999999999999998e-87 < b < -2.4000000000000001e-181 or -1.10000000000000008e-260 < b < 1.08e-215

   1. Initial program 96.5%

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

   3. Taylor expanded in b around 0 94.8%

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

   4. Taylor expanded in a around inf 74.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;x + b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq -7.7 \cdot 10^{-87}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-181}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-260}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-215}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y + \left(t + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+57}:\\ \;\;\;\;t_1 + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-68} \lor \neg \left(b \leq 1.7 \cdot 10^{-84}\right):\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -2.3e+57)
     (+ t_1 (* a (- 1.0 t)))
     (if (or (<= b -5.8e-68) (not (<= b 1.7e-84)))
       (+ t_1 (* z (- 1.0 y)))
       (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -2.3e+57) {
		tmp = t_1 + (a * (1.0 - t));
	} else if ((b <= -5.8e-68) || !(b <= 1.7e-84)) {
		tmp = t_1 + (z * (1.0 - y));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-2.3d+57)) then
        tmp = t_1 + (a * (1.0d0 - t))
    else if ((b <= (-5.8d-68)) .or. (.not. (b <= 1.7d-84))) then
        tmp = t_1 + (z * (1.0d0 - y))
    else
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -2.3e+57) {
		tmp = t_1 + (a * (1.0 - t));
	} else if ((b <= -5.8e-68) || !(b <= 1.7e-84)) {
		tmp = t_1 + (z * (1.0 - y));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -2.3e+57:
		tmp = t_1 + (a * (1.0 - t))
	elif (b <= -5.8e-68) or not (b <= 1.7e-84):
		tmp = t_1 + (z * (1.0 - y))
	else:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -2.3e+57)
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	elseif ((b <= -5.8e-68) || !(b <= 1.7e-84))
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -2.3e+57)
		tmp = t_1 + (a * (1.0 - t));
	elseif ((b <= -5.8e-68) || ~((b <= 1.7e-84)))
		tmp = t_1 + (z * (1.0 - y));
	else
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+57], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -5.8e-68], N[Not[LessEqual[b, 1.7e-84]], $MachinePrecision]], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2999999999999999e57

   1. Initial program 91.1%

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

   3. Taylor expanded in z around 0 91.3%

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

   if -2.2999999999999999e57 < b < -5.8000000000000001e-68 or 1.7000000000000001e-84 < b

   1. Initial program 98.0%

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

   3. Taylor expanded in a around 0 89.7%

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

   if -5.8000000000000001e-68 < b < 1.7000000000000001e-84

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0 95.9%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+57}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-68} \lor \neg \left(b \leq 1.7 \cdot 10^{-84}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+156}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-69} \lor \neg \left(b \leq 1.2 \cdot 10^{-87}\right):\\ \;\;\;\;z + \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.4e+156)
   (+ (+ x (* b (- (+ y t) 2.0))) (* a (- 1.0 t)))
   (if (or (<= b -1.85e-69) (not (<= b 1.2e-87)))
     (+ z (+ x (+ (* b (- t 2.0)) (* y (- b z)))))
     (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e+156) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else if ((b <= -1.85e-69) || !(b <= 1.2e-87)) {
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.4d+156)) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (a * (1.0d0 - t))
    else if ((b <= (-1.85d-69)) .or. (.not. (b <= 1.2d-87))) then
        tmp = z + (x + ((b * (t - 2.0d0)) + (y * (b - z))))
    else
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e+156) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else if ((b <= -1.85e-69) || !(b <= 1.2e-87)) {
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.4e+156:
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t))
	elif (b <= -1.85e-69) or not (b <= 1.2e-87):
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))))
	else:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.4e+156)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(a * Float64(1.0 - t)));
	elseif ((b <= -1.85e-69) || !(b <= 1.2e-87))
		tmp = Float64(z + Float64(x + Float64(Float64(b * Float64(t - 2.0)) + Float64(y * Float64(b - z)))));
	else
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.4e+156)
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	elseif ((b <= -1.85e-69) || ~((b <= 1.2e-87)))
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	else
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.4e+156], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.85e-69], N[Not[LessEqual[b, 1.2e-87]], $MachinePrecision]], N[(z + N[(x + N[(N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.39999999999999994e156

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 100.0%

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

   if -1.39999999999999994e156 < b < -1.8500000000000001e-69 or 1.2e-87 < b

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 96.9%

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

   4. Taylor expanded in a around 0 89.0%

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

   if -1.8500000000000001e-69 < b < 1.2e-87

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0 95.9%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+156}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-69} \lor \neg \left(b \leq 1.2 \cdot 10^{-87}\right):\\ \;\;\;\;z + \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+122}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+40}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-141}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-21}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= y -4.2e+122)
     (* y b)
     (if (<= y -7.5e+66)
       t_1
       (if (<= y -1.65e+40)
         (* y b)
         (if (<= y 3e-141)
           (+ x z)
           (if (<= y 7.8e-86)
             t_1
             (if (<= y 8.5e-21)
               (+ x z)
               (if (<= y 5.1e+107)
                 t_1
                 (if (<= y 6e+223) (* y (- z)) (* y b)))))))))))

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 (y <= -4.2e+122) {
		tmp = y * b;
	} else if (y <= -7.5e+66) {
		tmp = t_1;
	} else if (y <= -1.65e+40) {
		tmp = y * b;
	} else if (y <= 3e-141) {
		tmp = x + z;
	} else if (y <= 7.8e-86) {
		tmp = t_1;
	} else if (y <= 8.5e-21) {
		tmp = x + z;
	} else if (y <= 5.1e+107) {
		tmp = t_1;
	} else if (y <= 6e+223) {
		tmp = y * -z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (y <= (-4.2d+122)) then
        tmp = y * b
    else if (y <= (-7.5d+66)) then
        tmp = t_1
    else if (y <= (-1.65d+40)) then
        tmp = y * b
    else if (y <= 3d-141) then
        tmp = x + z
    else if (y <= 7.8d-86) then
        tmp = t_1
    else if (y <= 8.5d-21) then
        tmp = x + z
    else if (y <= 5.1d+107) then
        tmp = t_1
    else if (y <= 6d+223) then
        tmp = y * -z
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (y <= -4.2e+122) {
		tmp = y * b;
	} else if (y <= -7.5e+66) {
		tmp = t_1;
	} else if (y <= -1.65e+40) {
		tmp = y * b;
	} else if (y <= 3e-141) {
		tmp = x + z;
	} else if (y <= 7.8e-86) {
		tmp = t_1;
	} else if (y <= 8.5e-21) {
		tmp = x + z;
	} else if (y <= 5.1e+107) {
		tmp = t_1;
	} else if (y <= 6e+223) {
		tmp = y * -z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if y <= -4.2e+122:
		tmp = y * b
	elif y <= -7.5e+66:
		tmp = t_1
	elif y <= -1.65e+40:
		tmp = y * b
	elif y <= 3e-141:
		tmp = x + z
	elif y <= 7.8e-86:
		tmp = t_1
	elif y <= 8.5e-21:
		tmp = x + z
	elif y <= 5.1e+107:
		tmp = t_1
	elif y <= 6e+223:
		tmp = y * -z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (y <= -4.2e+122)
		tmp = Float64(y * b);
	elseif (y <= -7.5e+66)
		tmp = t_1;
	elseif (y <= -1.65e+40)
		tmp = Float64(y * b);
	elseif (y <= 3e-141)
		tmp = Float64(x + z);
	elseif (y <= 7.8e-86)
		tmp = t_1;
	elseif (y <= 8.5e-21)
		tmp = Float64(x + z);
	elseif (y <= 5.1e+107)
		tmp = t_1;
	elseif (y <= 6e+223)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(y * b);
	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 (y <= -4.2e+122)
		tmp = y * b;
	elseif (y <= -7.5e+66)
		tmp = t_1;
	elseif (y <= -1.65e+40)
		tmp = y * b;
	elseif (y <= 3e-141)
		tmp = x + z;
	elseif (y <= 7.8e-86)
		tmp = t_1;
	elseif (y <= 8.5e-21)
		tmp = x + z;
	elseif (y <= 5.1e+107)
		tmp = t_1;
	elseif (y <= 6e+223)
		tmp = y * -z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+122], N[(y * b), $MachinePrecision], If[LessEqual[y, -7.5e+66], t$95$1, If[LessEqual[y, -1.65e+40], N[(y * b), $MachinePrecision], If[LessEqual[y, 3e-141], N[(x + z), $MachinePrecision], If[LessEqual[y, 7.8e-86], t$95$1, If[LessEqual[y, 8.5e-21], N[(x + z), $MachinePrecision], If[LessEqual[y, 5.1e+107], t$95$1, If[LessEqual[y, 6e+223], N[(y * (-z)), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.20000000000000032e122 or -7.50000000000000024e66 < y < -1.6499999999999999e40 or 6.00000000000000002e223 < y

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 81.5%

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

   4. Taylor expanded in b around inf 58.3%

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

      1. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -4.20000000000000032e122 < y < -7.50000000000000024e66 or 2.99999999999999983e-141 < y < 7.8000000000000003e-86 or 8.4999999999999993e-21 < y < 5.1000000000000002e107

   1. Initial program 95.7%

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

   3. Taylor expanded in a around inf 56.6%

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

   if -1.6499999999999999e40 < y < 2.99999999999999983e-141 or 7.8000000000000003e-86 < y < 8.4999999999999993e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 67.0%

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

   4. Taylor expanded in a around 0 49.1%

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

   5. Taylor expanded in y around 0 48.4%

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

      1. sub-neg 48.4%

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

      2. mul-1-neg 48.4%

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

      3. remove-double-neg 48.4%

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

      4. +-commutative 48.4%

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

   7. Simplified 48.4%

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

   if 5.1000000000000002e107 < y < 6.00000000000000002e223

   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. Add Preprocessing

   3. Taylor expanded in b around 0 77.6%

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

   4. Taylor expanded in a around 0 53.1%

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

   5. Taylor expanded in y around inf 52.9%

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

      1. associate-*r* 52.9%

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

      2. mul-1-neg 52.9%

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

   7. Simplified 52.9%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+122}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+40}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-141}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-21}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-261}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- y 2.0)))) (t_2 (* t (- b a))) (t_3 (* z (- 1.0 y))))
   (if (<= t -1.35e+62)
     t_2
     (if (<= t -1.1e-204)
       t_1
       (if (<= t -4.5e-261)
         t_3
         (if (<= t 3e-185)
           t_1
           (if (<= t 3e-152) t_3 (if (<= t 5.2e+41) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (y - 2.0));
	double t_2 = t * (b - a);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (t <= -1.35e+62) {
		tmp = t_2;
	} else if (t <= -1.1e-204) {
		tmp = t_1;
	} else if (t <= -4.5e-261) {
		tmp = t_3;
	} else if (t <= 3e-185) {
		tmp = t_1;
	} else if (t <= 3e-152) {
		tmp = t_3;
	} else if (t <= 5.2e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (b * (y - 2.0d0))
    t_2 = t * (b - a)
    t_3 = z * (1.0d0 - y)
    if (t <= (-1.35d+62)) then
        tmp = t_2
    else if (t <= (-1.1d-204)) then
        tmp = t_1
    else if (t <= (-4.5d-261)) then
        tmp = t_3
    else if (t <= 3d-185) then
        tmp = t_1
    else if (t <= 3d-152) then
        tmp = t_3
    else if (t <= 5.2d+41) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (y - 2.0));
	double t_2 = t * (b - a);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (t <= -1.35e+62) {
		tmp = t_2;
	} else if (t <= -1.1e-204) {
		tmp = t_1;
	} else if (t <= -4.5e-261) {
		tmp = t_3;
	} else if (t <= 3e-185) {
		tmp = t_1;
	} else if (t <= 3e-152) {
		tmp = t_3;
	} else if (t <= 5.2e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * (y - 2.0))
	t_2 = t * (b - a)
	t_3 = z * (1.0 - y)
	tmp = 0
	if t <= -1.35e+62:
		tmp = t_2
	elif t <= -1.1e-204:
		tmp = t_1
	elif t <= -4.5e-261:
		tmp = t_3
	elif t <= 3e-185:
		tmp = t_1
	elif t <= 3e-152:
		tmp = t_3
	elif t <= 5.2e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(y - 2.0)))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -1.35e+62)
		tmp = t_2;
	elseif (t <= -1.1e-204)
		tmp = t_1;
	elseif (t <= -4.5e-261)
		tmp = t_3;
	elseif (t <= 3e-185)
		tmp = t_1;
	elseif (t <= 3e-152)
		tmp = t_3;
	elseif (t <= 5.2e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * (y - 2.0));
	t_2 = t * (b - a);
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (t <= -1.35e+62)
		tmp = t_2;
	elseif (t <= -1.1e-204)
		tmp = t_1;
	elseif (t <= -4.5e-261)
		tmp = t_3;
	elseif (t <= 3e-185)
		tmp = t_1;
	elseif (t <= 3e-152)
		tmp = t_3;
	elseif (t <= 5.2e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+62], t$95$2, If[LessEqual[t, -1.1e-204], t$95$1, If[LessEqual[t, -4.5e-261], t$95$3, If[LessEqual[t, 3e-185], t$95$1, If[LessEqual[t, 3e-152], t$95$3, If[LessEqual[t, 5.2e+41], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e62 or 5.2000000000000001e41 < t

   1. Initial program 93.5%

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

   3. Taylor expanded in t around inf 76.3%

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

   if -1.35e62 < t < -1.0999999999999999e-204 or -4.5000000000000001e-261 < t < 3.0000000000000003e-185 or 3e-152 < t < 5.2000000000000001e41

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in a around 0 85.6%

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

   5. Taylor expanded in z around 0 61.1%

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

      1. sub-neg 61.1%

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

      2. metadata-eval 61.1%

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

      3. distribute-lft-out 61.1%

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

      4. cancel-sign-sub 61.1%

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

      5. mul-1-neg 61.1%

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

      6. *-commutative 61.1%

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

      7. associate-*r* 61.1%

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

      8. distribute-lft-out 61.1%

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

      9. metadata-eval 61.1%

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

      10. sub-neg 61.1%

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

      11. unsub-neg 61.1%

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

      12. distribute-rgt-neg-in 61.1%

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

      13. sub-neg 61.1%

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

      14. metadata-eval 61.1%

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

      15. distribute-lft-out 61.1%

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

      16. mul-1-neg 61.1%

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

      17. remove-double-neg 61.1%

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

      18. +-commutative 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in t around 0 58.7%

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

   if -1.0999999999999999e-204 < t < -4.5000000000000001e-261 or 3.0000000000000003e-185 < t < 3e-152

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 67.5%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-204}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-185}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-152}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.35 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-182}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.16 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-223}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (+ x (* a (- 1.0 t)))))
   (if (<= b -2.35e+27)
     t_2
     (if (<= b -4.8e-89)
       t_1
       (if (<= b -1e-182)
         t_3
         (if (<= b -1.16e-259)
           t_1
           (if (<= b 4.7e-223) t_3 (if (<= b 4.2e+98) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -2.35e+27) {
		tmp = t_2;
	} else if (b <= -4.8e-89) {
		tmp = t_1;
	} else if (b <= -1e-182) {
		tmp = t_3;
	} else if (b <= -1.16e-259) {
		tmp = t_1;
	} else if (b <= 4.7e-223) {
		tmp = t_3;
	} else if (b <= 4.2e+98) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x + (a * (1.0d0 - t))
    if (b <= (-2.35d+27)) then
        tmp = t_2
    else if (b <= (-4.8d-89)) then
        tmp = t_1
    else if (b <= (-1d-182)) then
        tmp = t_3
    else if (b <= (-1.16d-259)) then
        tmp = t_1
    else if (b <= 4.7d-223) then
        tmp = t_3
    else if (b <= 4.2d+98) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -2.35e+27) {
		tmp = t_2;
	} else if (b <= -4.8e-89) {
		tmp = t_1;
	} else if (b <= -1e-182) {
		tmp = t_3;
	} else if (b <= -1.16e-259) {
		tmp = t_1;
	} else if (b <= 4.7e-223) {
		tmp = t_3;
	} else if (b <= 4.2e+98) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = b * ((y + t) - 2.0)
	t_3 = x + (a * (1.0 - t))
	tmp = 0
	if b <= -2.35e+27:
		tmp = t_2
	elif b <= -4.8e-89:
		tmp = t_1
	elif b <= -1e-182:
		tmp = t_3
	elif b <= -1.16e-259:
		tmp = t_1
	elif b <= 4.7e-223:
		tmp = t_3
	elif b <= 4.2e+98:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (b <= -2.35e+27)
		tmp = t_2;
	elseif (b <= -4.8e-89)
		tmp = t_1;
	elseif (b <= -1e-182)
		tmp = t_3;
	elseif (b <= -1.16e-259)
		tmp = t_1;
	elseif (b <= 4.7e-223)
		tmp = t_3;
	elseif (b <= 4.2e+98)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = b * ((y + t) - 2.0);
	t_3 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (b <= -2.35e+27)
		tmp = t_2;
	elseif (b <= -4.8e-89)
		tmp = t_1;
	elseif (b <= -1e-182)
		tmp = t_3;
	elseif (b <= -1.16e-259)
		tmp = t_1;
	elseif (b <= 4.7e-223)
		tmp = t_3;
	elseif (b <= 4.2e+98)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.35e+27], t$95$2, If[LessEqual[b, -4.8e-89], t$95$1, If[LessEqual[b, -1e-182], t$95$3, If[LessEqual[b, -1.16e-259], t$95$1, If[LessEqual[b, 4.7e-223], t$95$3, If[LessEqual[b, 4.2e+98], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.34999999999999988e27 or 4.20000000000000008e98 < b

   1. Initial program 93.5%

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

   3. Taylor expanded in b around inf 77.6%

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

   if -2.34999999999999988e27 < b < -4.80000000000000032e-89 or -1e-182 < b < -1.16e-259 or 4.70000000000000021e-223 < b < 4.20000000000000008e98

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 82.7%

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

   4. Taylor expanded in a around 0 62.8%

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

   if -4.80000000000000032e-89 < b < -1e-182 or -1.16e-259 < b < 4.70000000000000021e-223

   1. Initial program 96.5%

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

   3. Taylor expanded in b around 0 94.8%

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

   4. Taylor expanded in a around inf 74.2%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.35 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-182}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.16 \cdot 10^{-259}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-223}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+98}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+26} \lor \neg \left(b \leq 1.8 \cdot 10^{-5}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5e+26) (not (<= b 1.8e-5)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* a (- 1.0 t)))
   (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5e+26) || !(b <= 1.8e-5)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5d+26)) .or. (.not. (b <= 1.8d-5))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (a * (1.0d0 - t))
    else
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5e+26) || !(b <= 1.8e-5)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5e+26) or not (b <= 1.8e-5):
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t))
	else:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5e+26) || !(b <= 1.8e-5))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5e+26) || ~((b <= 1.8e-5)))
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	else
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5e+26], N[Not[LessEqual[b, 1.8e-5]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.0000000000000001e26 or 1.80000000000000005e-5 < b

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 87.2%

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

   if -5.0000000000000001e26 < b < 1.80000000000000005e-5

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 90.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+26} \lor \neg \left(b \leq 1.8 \cdot 10^{-5}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-43}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-239}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- y 2.0))))
   (if (<= b -5.2e+33)
     t_2
     (if (<= b -3.3e-43)
       (+ x z)
       (if (<= b -4.5e-167)
         t_1
         (if (<= b -6.6e-239)
           (+ x z)
           (if (<= b 7.4e-132) t_1 (if (<= b 2.4e+100) (+ x z) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -5.2e+33) {
		tmp = t_2;
	} else if (b <= -3.3e-43) {
		tmp = x + z;
	} else if (b <= -4.5e-167) {
		tmp = t_1;
	} else if (b <= -6.6e-239) {
		tmp = x + z;
	} else if (b <= 7.4e-132) {
		tmp = t_1;
	} else if (b <= 2.4e+100) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * (y - 2.0d0)
    if (b <= (-5.2d+33)) then
        tmp = t_2
    else if (b <= (-3.3d-43)) then
        tmp = x + z
    else if (b <= (-4.5d-167)) then
        tmp = t_1
    else if (b <= (-6.6d-239)) then
        tmp = x + z
    else if (b <= 7.4d-132) then
        tmp = t_1
    else if (b <= 2.4d+100) then
        tmp = x + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -5.2e+33) {
		tmp = t_2;
	} else if (b <= -3.3e-43) {
		tmp = x + z;
	} else if (b <= -4.5e-167) {
		tmp = t_1;
	} else if (b <= -6.6e-239) {
		tmp = x + z;
	} else if (b <= 7.4e-132) {
		tmp = t_1;
	} else if (b <= 2.4e+100) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * (y - 2.0)
	tmp = 0
	if b <= -5.2e+33:
		tmp = t_2
	elif b <= -3.3e-43:
		tmp = x + z
	elif b <= -4.5e-167:
		tmp = t_1
	elif b <= -6.6e-239:
		tmp = x + z
	elif b <= 7.4e-132:
		tmp = t_1
	elif b <= 2.4e+100:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -5.2e+33)
		tmp = t_2;
	elseif (b <= -3.3e-43)
		tmp = Float64(x + z);
	elseif (b <= -4.5e-167)
		tmp = t_1;
	elseif (b <= -6.6e-239)
		tmp = Float64(x + z);
	elseif (b <= 7.4e-132)
		tmp = t_1;
	elseif (b <= 2.4e+100)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -5.2e+33)
		tmp = t_2;
	elseif (b <= -3.3e-43)
		tmp = x + z;
	elseif (b <= -4.5e-167)
		tmp = t_1;
	elseif (b <= -6.6e-239)
		tmp = x + z;
	elseif (b <= 7.4e-132)
		tmp = t_1;
	elseif (b <= 2.4e+100)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+33], t$95$2, If[LessEqual[b, -3.3e-43], N[(x + z), $MachinePrecision], If[LessEqual[b, -4.5e-167], t$95$1, If[LessEqual[b, -6.6e-239], N[(x + z), $MachinePrecision], If[LessEqual[b, 7.4e-132], t$95$1, If[LessEqual[b, 2.4e+100], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.1999999999999995e33 or 2.40000000000000012e100 < b

   1. Initial program 93.3%

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

   3. Taylor expanded in b around inf 78.6%

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

   4. Taylor expanded in t around 0 53.6%

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

   if -5.1999999999999995e33 < b < -3.30000000000000016e-43 or -4.5000000000000001e-167 < b < -6.5999999999999999e-239 or 7.4000000000000004e-132 < b < 2.40000000000000012e100

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 81.5%

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

   4. Taylor expanded in a around 0 62.7%

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

   5. Taylor expanded in y around 0 47.9%

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

      1. sub-neg 47.9%

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

      2. mul-1-neg 47.9%

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

      3. remove-double-neg 47.9%

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

      4. +-commutative 47.9%

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

   7. Simplified 47.9%

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

   if -3.30000000000000016e-43 < b < -4.5000000000000001e-167 or -6.5999999999999999e-239 < b < 7.4000000000000004e-132

   1. Initial program 97.2%

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

   3. Taylor expanded in a around inf 50.0%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-43}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-239}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-59}:\\ \;\;\;\;z + \left(x + t \cdot b\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+19}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (+ y (+ t -2.0))))))
   (if (<= b -1.05e+28)
     t_1
     (if (<= b -1e-59)
       (+ z (+ x (* t b)))
       (if (<= b -9.5e-68)
         (* y (- b z))
         (if (<= b 9.8e+19) (- x (- (* a (+ t -1.0)) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (y + (t + -2.0)));
	double tmp;
	if (b <= -1.05e+28) {
		tmp = t_1;
	} else if (b <= -1e-59) {
		tmp = z + (x + (t * b));
	} else if (b <= -9.5e-68) {
		tmp = y * (b - z);
	} else if (b <= 9.8e+19) {
		tmp = x - ((a * (t + -1.0)) - 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 * (y + (t + (-2.0d0))))
    if (b <= (-1.05d+28)) then
        tmp = t_1
    else if (b <= (-1d-59)) then
        tmp = z + (x + (t * b))
    else if (b <= (-9.5d-68)) then
        tmp = y * (b - z)
    else if (b <= 9.8d+19) then
        tmp = x - ((a * (t + (-1.0d0))) - 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 * (y + (t + -2.0)));
	double tmp;
	if (b <= -1.05e+28) {
		tmp = t_1;
	} else if (b <= -1e-59) {
		tmp = z + (x + (t * b));
	} else if (b <= -9.5e-68) {
		tmp = y * (b - z);
	} else if (b <= 9.8e+19) {
		tmp = x - ((a * (t + -1.0)) - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * (y + (t + -2.0)))
	tmp = 0
	if b <= -1.05e+28:
		tmp = t_1
	elif b <= -1e-59:
		tmp = z + (x + (t * b))
	elif b <= -9.5e-68:
		tmp = y * (b - z)
	elif b <= 9.8e+19:
		tmp = x - ((a * (t + -1.0)) - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(y + Float64(t + -2.0))))
	tmp = 0.0
	if (b <= -1.05e+28)
		tmp = t_1;
	elseif (b <= -1e-59)
		tmp = Float64(z + Float64(x + Float64(t * b)));
	elseif (b <= -9.5e-68)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 9.8e+19)
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * (y + (t + -2.0)));
	tmp = 0.0;
	if (b <= -1.05e+28)
		tmp = t_1;
	elseif (b <= -1e-59)
		tmp = z + (x + (t * b));
	elseif (b <= -9.5e-68)
		tmp = y * (b - z);
	elseif (b <= 9.8e+19)
		tmp = x - ((a * (t + -1.0)) - 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[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+28], t$95$1, If[LessEqual[b, -1e-59], N[(z + N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.5e-68], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e+19], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.04999999999999995e28 or 9.8e19 < b

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 94.8%

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

   4. Taylor expanded in a around 0 88.1%

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

   5. Taylor expanded in z around 0 76.9%

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

      1. sub-neg 76.9%

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

      2. metadata-eval 76.9%

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

      3. distribute-lft-out 80.4%

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

      4. cancel-sign-sub 80.4%

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

      5. mul-1-neg 80.4%

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

      6. *-commutative 80.4%

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

      7. associate-*r* 80.4%

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

      8. distribute-lft-out 80.4%

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

      9. metadata-eval 80.4%

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

      10. sub-neg 80.4%

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

      11. unsub-neg 80.4%

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

      12. distribute-rgt-neg-in 80.4%

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

      13. sub-neg 80.4%

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

      14. metadata-eval 80.4%

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

      15. distribute-lft-out 80.4%

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

      16. mul-1-neg 80.4%

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

      17. remove-double-neg 80.4%

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

      18. +-commutative 80.4%

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

   7. Simplified 80.4%

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

   if -1.04999999999999995e28 < b < -1e-59

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in a around 0 87.0%

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

   5. Taylor expanded in t around inf 75.6%

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

   if -1e-59 < b < -9.4999999999999997e-68

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -9.4999999999999997e-68 < b < 9.8e19

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0 92.0%

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

   4. Taylor expanded in y around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. sub-neg 77.1%

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

      3. metadata-eval 77.1%

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

      4. mul-1-neg 77.1%

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

      5. unsub-neg 77.1%

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

      6. +-commutative 77.1%

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

   6. Simplified 77.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;x + b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-59}:\\ \;\;\;\;z + \left(x + t \cdot b\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+19}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y + \left(t + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+27} \lor \neg \left(b \leq 6.8 \cdot 10^{+51}\right):\\ \;\;\;\;x + b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.2e+27) (not (<= b 6.8e+51)))
   (+ x (* b (+ y (+ t -2.0))))
   (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.2e+27) || !(b <= 6.8e+51)) {
		tmp = x + (b * (y + (t + -2.0)));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.2d+27)) .or. (.not. (b <= 6.8d+51))) then
        tmp = x + (b * (y + (t + (-2.0d0))))
    else
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.2e+27) || !(b <= 6.8e+51)) {
		tmp = x + (b * (y + (t + -2.0)));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.2e+27) or not (b <= 6.8e+51):
		tmp = x + (b * (y + (t + -2.0)))
	else:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.2e+27) || !(b <= 6.8e+51))
		tmp = Float64(x + Float64(b * Float64(y + Float64(t + -2.0))));
	else
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.2e+27) || ~((b <= 6.8e+51)))
		tmp = x + (b * (y + (t + -2.0)));
	else
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.2e+27], N[Not[LessEqual[b, 6.8e+51]], $MachinePrecision]], N[(x + N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.19999999999999989e27 or 6.79999999999999969e51 < b

   1. Initial program 93.7%

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

   3. Taylor expanded in y around 0 94.6%

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

   4. Taylor expanded in a around 0 88.5%

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

   5. Taylor expanded in z around 0 79.3%

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

      1. sub-neg 79.3%

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

      2. metadata-eval 79.3%

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

      3. distribute-lft-out 82.9%

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

      4. cancel-sign-sub 82.9%

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

      5. mul-1-neg 82.9%

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

      6. *-commutative 82.9%

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

      7. associate-*r* 82.9%

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

      8. distribute-lft-out 82.9%

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

      9. metadata-eval 82.9%

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

      10. sub-neg 82.9%

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

      11. unsub-neg 82.9%

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

      12. distribute-rgt-neg-in 82.9%

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

      13. sub-neg 82.9%

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

      14. metadata-eval 82.9%

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

      15. distribute-lft-out 82.9%

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

      16. mul-1-neg 82.9%

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

      17. remove-double-neg 82.9%

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

      18. +-commutative 82.9%

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

   7. Simplified 82.9%

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

   if -4.19999999999999989e27 < b < 6.79999999999999969e51

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0 87.8%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+27} \lor \neg \left(b \leq 6.8 \cdot 10^{+51}\right):\\ \;\;\;\;x + b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-151}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -4.2e+29)
     t_2
     (if (<= t 9.5e-257)
       t_1
       (if (<= t 3.9e-151)
         (+ x z)
         (if (<= t 4.5e-13) t_1 (if (<= t 2.4e+38) (+ x z) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.2e+29) {
		tmp = t_2;
	} else if (t <= 9.5e-257) {
		tmp = t_1;
	} else if (t <= 3.9e-151) {
		tmp = x + z;
	} else if (t <= 4.5e-13) {
		tmp = t_1;
	} else if (t <= 2.4e+38) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-4.2d+29)) then
        tmp = t_2
    else if (t <= 9.5d-257) then
        tmp = t_1
    else if (t <= 3.9d-151) then
        tmp = x + z
    else if (t <= 4.5d-13) then
        tmp = t_1
    else if (t <= 2.4d+38) then
        tmp = x + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.2e+29) {
		tmp = t_2;
	} else if (t <= 9.5e-257) {
		tmp = t_1;
	} else if (t <= 3.9e-151) {
		tmp = x + z;
	} else if (t <= 4.5e-13) {
		tmp = t_1;
	} else if (t <= 2.4e+38) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -4.2e+29:
		tmp = t_2
	elif t <= 9.5e-257:
		tmp = t_1
	elif t <= 3.9e-151:
		tmp = x + z
	elif t <= 4.5e-13:
		tmp = t_1
	elif t <= 2.4e+38:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.2e+29)
		tmp = t_2;
	elseif (t <= 9.5e-257)
		tmp = t_1;
	elseif (t <= 3.9e-151)
		tmp = Float64(x + z);
	elseif (t <= 4.5e-13)
		tmp = t_1;
	elseif (t <= 2.4e+38)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.2e+29)
		tmp = t_2;
	elseif (t <= 9.5e-257)
		tmp = t_1;
	elseif (t <= 3.9e-151)
		tmp = x + z;
	elseif (t <= 4.5e-13)
		tmp = t_1;
	elseif (t <= 2.4e+38)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+29], t$95$2, If[LessEqual[t, 9.5e-257], t$95$1, If[LessEqual[t, 3.9e-151], N[(x + z), $MachinePrecision], If[LessEqual[t, 4.5e-13], t$95$1, If[LessEqual[t, 2.4e+38], N[(x + z), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2000000000000003e29 or 2.40000000000000017e38 < t

   1. Initial program 93.3%

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

   3. Taylor expanded in t around inf 72.8%

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

   if -4.2000000000000003e29 < t < 9.49999999999999941e-257 or 3.90000000000000007e-151 < t < 4.5e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 42.6%

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

   4. Taylor expanded in t around 0 41.7%

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

   if 9.49999999999999941e-257 < t < 3.90000000000000007e-151 or 4.5e-13 < t < 2.40000000000000017e38

   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. Add Preprocessing

   3. Taylor expanded in b around 0 85.3%

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

   4. Taylor expanded in a around 0 75.2%

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

   5. Taylor expanded in y around 0 61.5%

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

      1. sub-neg 61.5%

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

      2. mul-1-neg 61.5%

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

      3. remove-double-neg 61.5%

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

      4. +-commutative 61.5%

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

   7. Simplified 61.5%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-257}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-151}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-256}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-152}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.9e+32)
     t_1
     (if (<= t 1e-256)
       (* y (- b z))
       (if (<= t 5.2e-152)
         (+ x z)
         (if (<= t 2.4e+27) (* b (- (+ y t) 2.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.9e+32) {
		tmp = t_1;
	} else if (t <= 1e-256) {
		tmp = y * (b - z);
	} else if (t <= 5.2e-152) {
		tmp = x + z;
	} else if (t <= 2.4e+27) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1.9d+32)) then
        tmp = t_1
    else if (t <= 1d-256) then
        tmp = y * (b - z)
    else if (t <= 5.2d-152) then
        tmp = x + z
    else if (t <= 2.4d+27) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.9e+32) {
		tmp = t_1;
	} else if (t <= 1e-256) {
		tmp = y * (b - z);
	} else if (t <= 5.2e-152) {
		tmp = x + z;
	} else if (t <= 2.4e+27) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.9e+32:
		tmp = t_1
	elif t <= 1e-256:
		tmp = y * (b - z)
	elif t <= 5.2e-152:
		tmp = x + z
	elif t <= 2.4e+27:
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.9e+32)
		tmp = t_1;
	elseif (t <= 1e-256)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 5.2e-152)
		tmp = Float64(x + z);
	elseif (t <= 2.4e+27)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.9e+32)
		tmp = t_1;
	elseif (t <= 1e-256)
		tmp = y * (b - z);
	elseif (t <= 5.2e-152)
		tmp = x + z;
	elseif (t <= 2.4e+27)
		tmp = b * ((y + t) - 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+32], t$95$1, If[LessEqual[t, 1e-256], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-152], N[(x + z), $MachinePrecision], If[LessEqual[t, 2.4e+27], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9000000000000002e32 or 2.39999999999999998e27 < t

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 71.2%

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

   if -1.9000000000000002e32 < t < 9.99999999999999977e-257

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 43.7%

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

   if 9.99999999999999977e-257 < t < 5.20000000000000026e-152

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 89.7%

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

   4. Taylor expanded in a around 0 79.5%

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

   5. Taylor expanded in y around 0 63.8%

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

      1. sub-neg 63.8%

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

      2. mul-1-neg 63.8%

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

      3. remove-double-neg 63.8%

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

      4. +-commutative 63.8%

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

   7. Simplified 63.8%

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

   if 5.20000000000000026e-152 < t < 2.39999999999999998e27

   1. Initial program 97.0%

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

   3. Taylor expanded in b around inf 45.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 10^{-256}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-152}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+125}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+40}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-20}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= y -6e+125)
     (* y b)
     (if (<= y -1.55e+67)
       t_1
       (if (<= y -1.85e+40)
         (* y b)
         (if (<= y 1.15e-20) (+ x z) (if (<= y 4.8e+216) t_1 (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (y <= -6e+125) {
		tmp = y * b;
	} else if (y <= -1.55e+67) {
		tmp = t_1;
	} else if (y <= -1.85e+40) {
		tmp = y * b;
	} else if (y <= 1.15e-20) {
		tmp = x + z;
	} else if (y <= 4.8e+216) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (y <= (-6d+125)) then
        tmp = y * b
    else if (y <= (-1.55d+67)) then
        tmp = t_1
    else if (y <= (-1.85d+40)) then
        tmp = y * b
    else if (y <= 1.15d-20) then
        tmp = x + z
    else if (y <= 4.8d+216) then
        tmp = t_1
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (y <= -6e+125) {
		tmp = y * b;
	} else if (y <= -1.55e+67) {
		tmp = t_1;
	} else if (y <= -1.85e+40) {
		tmp = y * b;
	} else if (y <= 1.15e-20) {
		tmp = x + z;
	} else if (y <= 4.8e+216) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if y <= -6e+125:
		tmp = y * b
	elif y <= -1.55e+67:
		tmp = t_1
	elif y <= -1.85e+40:
		tmp = y * b
	elif y <= 1.15e-20:
		tmp = x + z
	elif y <= 4.8e+216:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (y <= -6e+125)
		tmp = Float64(y * b);
	elseif (y <= -1.55e+67)
		tmp = t_1;
	elseif (y <= -1.85e+40)
		tmp = Float64(y * b);
	elseif (y <= 1.15e-20)
		tmp = Float64(x + z);
	elseif (y <= 4.8e+216)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (y <= -6e+125)
		tmp = y * b;
	elseif (y <= -1.55e+67)
		tmp = t_1;
	elseif (y <= -1.85e+40)
		tmp = y * b;
	elseif (y <= 1.15e-20)
		tmp = x + z;
	elseif (y <= 4.8e+216)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[y, -6e+125], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.55e+67], t$95$1, If[LessEqual[y, -1.85e+40], N[(y * b), $MachinePrecision], If[LessEqual[y, 1.15e-20], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.8e+216], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.0000000000000003e125 or -1.54999999999999998e67 < y < -1.85e40 or 4.7999999999999999e216 < y

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf 82.1%

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

   4. Taylor expanded in b around inf 56.4%

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

      1. *-commutative 56.4%

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

   6. Simplified 56.4%

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

   if -6.0000000000000003e125 < y < -1.54999999999999998e67 or 1.15e-20 < y < 4.7999999999999999e216

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 46.1%

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

   4. Taylor expanded in t around inf 36.4%

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

      1. associate-*r* 36.4%

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

      2. mul-1-neg 36.4%

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

   6. Simplified 36.4%

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

   if -1.85e40 < y < 1.15e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 68.2%

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

   4. Taylor expanded in a around 0 47.1%

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

   5. Taylor expanded in y around 0 46.5%

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

      1. sub-neg 46.5%

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

      2. mul-1-neg 46.5%

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

      3. remove-double-neg 46.5%

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

      4. +-commutative 46.5%

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

   7. Simplified 46.5%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+125}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+40}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-20}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+216}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+117}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+40}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.5e+117)
   (* y b)
   (if (<= y -4.1e+66)
     (* t (- a))
     (if (<= y -1.35e+40)
       (* y b)
       (if (<= y 3e+25) (+ x z) (if (<= y 3.4e+223) (* y (- z)) (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e+117) {
		tmp = y * b;
	} else if (y <= -4.1e+66) {
		tmp = t * -a;
	} else if (y <= -1.35e+40) {
		tmp = y * b;
	} else if (y <= 3e+25) {
		tmp = x + z;
	} else if (y <= 3.4e+223) {
		tmp = y * -z;
	} 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 <= (-8.5d+117)) then
        tmp = y * b
    else if (y <= (-4.1d+66)) then
        tmp = t * -a
    else if (y <= (-1.35d+40)) then
        tmp = y * b
    else if (y <= 3d+25) then
        tmp = x + z
    else if (y <= 3.4d+223) then
        tmp = y * -z
    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 <= -8.5e+117) {
		tmp = y * b;
	} else if (y <= -4.1e+66) {
		tmp = t * -a;
	} else if (y <= -1.35e+40) {
		tmp = y * b;
	} else if (y <= 3e+25) {
		tmp = x + z;
	} else if (y <= 3.4e+223) {
		tmp = y * -z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.5e+117:
		tmp = y * b
	elif y <= -4.1e+66:
		tmp = t * -a
	elif y <= -1.35e+40:
		tmp = y * b
	elif y <= 3e+25:
		tmp = x + z
	elif y <= 3.4e+223:
		tmp = y * -z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.5e+117)
		tmp = Float64(y * b);
	elseif (y <= -4.1e+66)
		tmp = Float64(t * Float64(-a));
	elseif (y <= -1.35e+40)
		tmp = Float64(y * b);
	elseif (y <= 3e+25)
		tmp = Float64(x + z);
	elseif (y <= 3.4e+223)
		tmp = Float64(y * Float64(-z));
	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 <= -8.5e+117)
		tmp = y * b;
	elseif (y <= -4.1e+66)
		tmp = t * -a;
	elseif (y <= -1.35e+40)
		tmp = y * b;
	elseif (y <= 3e+25)
		tmp = x + z;
	elseif (y <= 3.4e+223)
		tmp = y * -z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.5e+117], N[(y * b), $MachinePrecision], If[LessEqual[y, -4.1e+66], N[(t * (-a)), $MachinePrecision], If[LessEqual[y, -1.35e+40], N[(y * b), $MachinePrecision], If[LessEqual[y, 3e+25], N[(x + z), $MachinePrecision], If[LessEqual[y, 3.4e+223], N[(y * (-z)), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.49999999999999966e117 or -4.09999999999999994e66 < y < -1.35000000000000005e40 or 3.3999999999999998e223 < y

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 81.5%

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

   4. Taylor expanded in b around inf 58.3%

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

      1. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -8.49999999999999966e117 < y < -4.09999999999999994e66

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 59.3%

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

   4. Taylor expanded in t around inf 59.3%

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

      1. associate-*r* 59.3%

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

      2. mul-1-neg 59.3%

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

   6. Simplified 59.3%

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

   if -1.35000000000000005e40 < y < 3.00000000000000006e25

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 67.6%

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

   4. Taylor expanded in a around 0 44.8%

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

   5. Taylor expanded in y around 0 43.9%

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

      1. sub-neg 43.9%

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

      2. mul-1-neg 43.9%

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

      3. remove-double-neg 43.9%

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

      4. +-commutative 43.9%

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

   7. Simplified 43.9%

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

   if 3.00000000000000006e25 < y < 3.3999999999999998e223

   1. Initial program 92.1%

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

   3. Taylor expanded in b around 0 78.7%

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

   4. Taylor expanded in a around 0 43.6%

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

   5. Taylor expanded in y around inf 40.9%

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

      1. associate-*r* 40.9%

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

      2. mul-1-neg 40.9%

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

   7. Simplified 40.9%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+117}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+40}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.32 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-151}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -1.32e+32)
     t_2
     (if (<= t 1.4e-256)
       t_1
       (if (<= t 8.4e-151) (+ x z) (if (<= t 7e+27) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.32e+32) {
		tmp = t_2;
	} else if (t <= 1.4e-256) {
		tmp = t_1;
	} else if (t <= 8.4e-151) {
		tmp = x + z;
	} else if (t <= 7e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-1.32d+32)) then
        tmp = t_2
    else if (t <= 1.4d-256) then
        tmp = t_1
    else if (t <= 8.4d-151) then
        tmp = x + z
    else if (t <= 7d+27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.32e+32) {
		tmp = t_2;
	} else if (t <= 1.4e-256) {
		tmp = t_1;
	} else if (t <= 8.4e-151) {
		tmp = x + z;
	} else if (t <= 7e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1.32e+32:
		tmp = t_2
	elif t <= 1.4e-256:
		tmp = t_1
	elif t <= 8.4e-151:
		tmp = x + z
	elif t <= 7e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.32e+32)
		tmp = t_2;
	elseif (t <= 1.4e-256)
		tmp = t_1;
	elseif (t <= 8.4e-151)
		tmp = Float64(x + z);
	elseif (t <= 7e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.32e+32)
		tmp = t_2;
	elseif (t <= 1.4e-256)
		tmp = t_1;
	elseif (t <= 8.4e-151)
		tmp = x + z;
	elseif (t <= 7e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.32e+32], t$95$2, If[LessEqual[t, 1.4e-256], t$95$1, If[LessEqual[t, 8.4e-151], N[(x + z), $MachinePrecision], If[LessEqual[t, 7e+27], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.31999999999999997e32 or 7.0000000000000004e27 < t

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 71.2%

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

   if -1.31999999999999997e32 < t < 1.40000000000000012e-256 or 8.39999999999999962e-151 < t < 7.0000000000000004e27

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 44.1%

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

   if 1.40000000000000012e-256 < t < 8.39999999999999962e-151

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 85.9%

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

   4. Taylor expanded in a around 0 76.2%

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

   5. Taylor expanded in y around 0 61.3%

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

      1. sub-neg 61.3%

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

      2. mul-1-neg 61.3%

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

      3. remove-double-neg 61.3%

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

      4. +-commutative 61.3%

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

   7. Simplified 61.3%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-256}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-151}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 72.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+27} \lor \neg \left(b \leq 9 \cdot 10^{+19}\right):\\ \;\;\;\;x + b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.6e+27) (not (<= b 9e+19)))
   (+ x (* b (+ y (+ t -2.0))))
   (- x (- (* a (+ t -1.0)) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.6e+27) || !(b <= 9e+19)) {
		tmp = x + (b * (y + (t + -2.0)));
	} else {
		tmp = x - ((a * (t + -1.0)) - 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 <= (-7.6d+27)) .or. (.not. (b <= 9d+19))) then
        tmp = x + (b * (y + (t + (-2.0d0))))
    else
        tmp = x - ((a * (t + (-1.0d0))) - 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 <= -7.6e+27) || !(b <= 9e+19)) {
		tmp = x + (b * (y + (t + -2.0)));
	} else {
		tmp = x - ((a * (t + -1.0)) - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.6e+27) or not (b <= 9e+19):
		tmp = x + (b * (y + (t + -2.0)))
	else:
		tmp = x - ((a * (t + -1.0)) - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.6e+27) || !(b <= 9e+19))
		tmp = Float64(x + Float64(b * Float64(y + Float64(t + -2.0))));
	else
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.6e+27) || ~((b <= 9e+19)))
		tmp = x + (b * (y + (t + -2.0)));
	else
		tmp = x - ((a * (t + -1.0)) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.6e+27], N[Not[LessEqual[b, 9e+19]], $MachinePrecision]], N[(x + N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.60000000000000043e27 or 9e19 < b

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 94.9%

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

   4. Taylor expanded in a around 0 88.2%

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

   5. Taylor expanded in z around 0 77.1%

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

      1. sub-neg 77.1%

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

      2. metadata-eval 77.1%

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

      3. distribute-lft-out 80.5%

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

      4. cancel-sign-sub 80.5%

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

      5. mul-1-neg 80.5%

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

      6. *-commutative 80.5%

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

      7. associate-*r* 80.5%

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

      8. distribute-lft-out 80.5%

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

      9. metadata-eval 80.5%

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

      10. sub-neg 80.5%

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

      11. unsub-neg 80.5%

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

      12. distribute-rgt-neg-in 80.5%

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

      13. sub-neg 80.5%

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

      14. metadata-eval 80.5%

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

      15. distribute-lft-out 80.5%

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

      16. mul-1-neg 80.5%

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

      17. remove-double-neg 80.5%

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

      18. +-commutative 80.5%

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

   7. Simplified 80.5%

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

   if -7.60000000000000043e27 < b < 9e19

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 89.3%

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

   4. Taylor expanded in y around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. sub-neg 73.7%

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

      3. metadata-eval 73.7%

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

      4. mul-1-neg 73.7%

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

      5. unsub-neg 73.7%

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

      6. +-commutative 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+27} \lor \neg \left(b \leq 9 \cdot 10^{+19}\right):\\ \;\;\;\;x + b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+40} \lor \neg \left(y \leq 1.3 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1e+40) (not (<= y 1.3e+17))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e+40) || !(y <= 1.3e+17)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1d+40)) .or. (.not. (y <= 1.3d+17))) then
        tmp = y * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e+40) || !(y <= 1.3e+17)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1e+40) or not (y <= 1.3e+17):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1e+40) || !(y <= 1.3e+17))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1e+40) || ~((y <= 1.3e+17)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1e+40], N[Not[LessEqual[y, 1.3e+17]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000003e40 or 1.3e17 < y

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 67.3%

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

   4. Taylor expanded in b around inf 41.0%

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

      1. *-commutative 41.0%

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

   6. Simplified 41.0%

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

   if -1.00000000000000003e40 < y < 1.3e17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 20.5%

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

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+40} \lor \neg \left(y \leq 1.3 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+39} \lor \neg \left(y \leq 1.9 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.2e+39) (not (<= y 1.9e+17))) (* y b) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+39) || !(y <= 1.9e+17)) {
		tmp = y * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.2d+39)) .or. (.not. (y <= 1.9d+17))) then
        tmp = y * b
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+39) || !(y <= 1.9e+17)) {
		tmp = y * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.2e+39) or not (y <= 1.9e+17):
		tmp = y * b
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.2e+39) || !(y <= 1.9e+17))
		tmp = Float64(y * b);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.2e+39) || ~((y <= 1.9e+17)))
		tmp = y * b;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.2e+39], N[Not[LessEqual[y, 1.9e+17]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000005e39 or 1.9e17 < y

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 67.3%

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

   4. Taylor expanded in b around inf 41.0%

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

      1. *-commutative 41.0%

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

   6. Simplified 41.0%

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

   if -6.2000000000000005e39 < y < 1.9e17

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 68.5%

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

   4. Taylor expanded in a around 0 45.4%

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

   5. Taylor expanded in y around 0 44.4%

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

      1. sub-neg 44.4%

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

      2. mul-1-neg 44.4%

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

      3. remove-double-neg 44.4%

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

      4. +-commutative 44.4%

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

   7. Simplified 44.4%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+39} \lor \neg \left(y \leq 1.9 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+18}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.45e+24) x (if (<= x 5.6e+18) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x;
	} else if (x <= 5.6e+18) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.45d+24)) then
        tmp = x
    else if (x <= 5.6d+18) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x;
	} else if (x <= 5.6e+18) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.45e+24:
		tmp = x
	elif x <= 5.6e+18:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.45e+24)
		tmp = x;
	elseif (x <= 5.6e+18)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.45e+24)
		tmp = x;
	elseif (x <= 5.6e+18)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.45e+24], x, If[LessEqual[x, 5.6e+18], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4499999999999999e24 or 5.6e18 < x

   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. Add Preprocessing

   3. Taylor expanded in x around inf 27.0%

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

   if -1.4499999999999999e24 < x < 5.6e18

   1. Initial program 96.3%

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

   3. Taylor expanded in a around inf 32.7%

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

   4. Taylor expanded in t around 0 11.2%

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

4. Final simplification 18.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+18}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 17.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+59}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b -1.75e+59) (* -2.0 b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+59) {
		tmp = -2.0 * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.75d+59)) then
        tmp = (-2.0d0) * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+59) {
		tmp = -2.0 * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.75e+59:
		tmp = -2.0 * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.75e+59)
		tmp = Float64(-2.0 * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.75e+59)
		tmp = -2.0 * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.75e+59], N[(-2.0 * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -1.75e59

   1. Initial program 90.9%

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

   3. Taylor expanded in b around inf 84.1%

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

   4. Taylor expanded in t around 0 57.4%

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

   5. Taylor expanded in y around 0 17.7%

      \[\leadsto \color{blue}{-2 \cdot b} \]
   6. Step-by-step derivation

      1. *-commutative 17.7%

         \[\leadsto \color{blue}{b \cdot -2} \]

   7. Simplified 17.7%

      \[\leadsto \color{blue}{b \cdot -2} \]

   if -1.75e59 < b

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 16.9%

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

4. Final simplification 17.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+59}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 11.3% 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 96.5%

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

3. Taylor expanded in a around inf 26.5%

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

4. Taylor expanded in t around 0 8.2%

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

5. Final simplification 8.2%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(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)))