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

Percentage Accurate: 95.3% → 98.0%

Time: 19.2s

Alternatives: 22

Speedup: 0.5×

• 35.8% 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 #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 67.7%

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

4. Final simplification 98.4%

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

Alternative 2: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. +-commutative 95.3%

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

   2. fma-define 96.8%

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

   3. associate--l+ 96.8%

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

   4. sub-neg 96.8%

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

   5. metadata-eval 96.8%

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

   6. sub-neg 96.8%

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

   7. associate-+l- 96.8%

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

   8. fma-neg 97.2%

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

   9. sub-neg 97.2%

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

   10. metadata-eval 97.2%

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

   11. remove-double-neg 97.2%

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

   12. sub-neg 97.2%

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

   13. metadata-eval 97.2%

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

3. Simplified 97.2%

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

5. Final simplification 97.2%

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

Alternative 3: 39.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-235}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-83}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-22}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= a -1.4e+41)
     t_2
     (if (<= a -5.3e-20)
       t_1
       (if (<= a 5.2e-235)
         (+ x z)
         (if (<= a 2.75e-131)
           t_1
           (if (<= a 4.5e-83)
             (* t b)
             (if (<= a 7e-22)
               (+ x z)
               (if (<= a 2e-9)
                 (* y (- z))
                 (if (<= a 6.2e+104) (+ 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 = a * (1.0 - t);
	double tmp;
	if (a <= -1.4e+41) {
		tmp = t_2;
	} else if (a <= -5.3e-20) {
		tmp = t_1;
	} else if (a <= 5.2e-235) {
		tmp = x + z;
	} else if (a <= 2.75e-131) {
		tmp = t_1;
	} else if (a <= 4.5e-83) {
		tmp = t * b;
	} else if (a <= 7e-22) {
		tmp = x + z;
	} else if (a <= 2e-9) {
		tmp = y * -z;
	} else if (a <= 6.2e+104) {
		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 = a * (1.0d0 - t)
    if (a <= (-1.4d+41)) then
        tmp = t_2
    else if (a <= (-5.3d-20)) then
        tmp = t_1
    else if (a <= 5.2d-235) then
        tmp = x + z
    else if (a <= 2.75d-131) then
        tmp = t_1
    else if (a <= 4.5d-83) then
        tmp = t * b
    else if (a <= 7d-22) then
        tmp = x + z
    else if (a <= 2d-9) then
        tmp = y * -z
    else if (a <= 6.2d+104) 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 = a * (1.0 - t);
	double tmp;
	if (a <= -1.4e+41) {
		tmp = t_2;
	} else if (a <= -5.3e-20) {
		tmp = t_1;
	} else if (a <= 5.2e-235) {
		tmp = x + z;
	} else if (a <= 2.75e-131) {
		tmp = t_1;
	} else if (a <= 4.5e-83) {
		tmp = t * b;
	} else if (a <= 7e-22) {
		tmp = x + z;
	} else if (a <= 2e-9) {
		tmp = y * -z;
	} else if (a <= 6.2e+104) {
		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 = a * (1.0 - t)
	tmp = 0
	if a <= -1.4e+41:
		tmp = t_2
	elif a <= -5.3e-20:
		tmp = t_1
	elif a <= 5.2e-235:
		tmp = x + z
	elif a <= 2.75e-131:
		tmp = t_1
	elif a <= 4.5e-83:
		tmp = t * b
	elif a <= 7e-22:
		tmp = x + z
	elif a <= 2e-9:
		tmp = y * -z
	elif a <= 6.2e+104:
		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(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.4e+41)
		tmp = t_2;
	elseif (a <= -5.3e-20)
		tmp = t_1;
	elseif (a <= 5.2e-235)
		tmp = Float64(x + z);
	elseif (a <= 2.75e-131)
		tmp = t_1;
	elseif (a <= 4.5e-83)
		tmp = Float64(t * b);
	elseif (a <= 7e-22)
		tmp = Float64(x + z);
	elseif (a <= 2e-9)
		tmp = Float64(y * Float64(-z));
	elseif (a <= 6.2e+104)
		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 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.4e+41)
		tmp = t_2;
	elseif (a <= -5.3e-20)
		tmp = t_1;
	elseif (a <= 5.2e-235)
		tmp = x + z;
	elseif (a <= 2.75e-131)
		tmp = t_1;
	elseif (a <= 4.5e-83)
		tmp = t * b;
	elseif (a <= 7e-22)
		tmp = x + z;
	elseif (a <= 2e-9)
		tmp = y * -z;
	elseif (a <= 6.2e+104)
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+41], t$95$2, If[LessEqual[a, -5.3e-20], t$95$1, If[LessEqual[a, 5.2e-235], N[(x + z), $MachinePrecision], If[LessEqual[a, 2.75e-131], t$95$1, If[LessEqual[a, 4.5e-83], N[(t * b), $MachinePrecision], If[LessEqual[a, 7e-22], N[(x + z), $MachinePrecision], If[LessEqual[a, 2e-9], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, 6.2e+104], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.4e41 or 6.20000000000000033e104 < a

   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 a around inf 72.3%

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

   if -1.4e41 < a < -5.3000000000000002e-20 or 5.2000000000000001e-235 < a < 2.7499999999999998e-131

   1. Initial program 91.2%

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

   3. Taylor expanded in t around inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. distribute-rgt-neg-in 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in t around 0 45.3%

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

   if -5.3000000000000002e-20 < a < 5.2000000000000001e-235 or 4.49999999999999997e-83 < a < 7.00000000000000011e-22 or 2.00000000000000012e-9 < a < 6.20000000000000033e104

   1. Initial program 96.9%

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

   3. Taylor expanded in b around 0 68.3%

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

   4. Taylor expanded in a around 0 57.4%

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

   5. Taylor expanded in y around 0 38.8%

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

      1. cancel-sign-sub-inv 38.8%

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

      2. metadata-eval 38.8%

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

      3. *-lft-identity 38.8%

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

   7. Simplified 38.8%

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

   if 2.7499999999999998e-131 < a < 4.49999999999999997e-83

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 61.0%

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

   4. Taylor expanded in b around inf 48.2%

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

      1. *-commutative 48.2%

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

   6. Simplified 48.2%

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

   if 7.00000000000000011e-22 < a < 2.00000000000000012e-9

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 99.6%

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

   4. Taylor expanded in b around 0 88.8%

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

      1. associate-*r* 88.8%

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

      2. mul-1-neg 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in y around inf 88.8%

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

      1. associate-*r* 88.8%

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

      2. mul-1-neg 88.8%

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

   9. Simplified 88.8%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-235}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-83}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-22}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ t_3 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_4 := t\_3 + t\_1\\ t_5 := x + t\_3\\ \mathbf{if}\;b \leq -6 \cdot 10^{+208}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{+186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{+56}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-86}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (+ x (+ t_1 (* z (- 1.0 y)))))
        (t_3 (* b (- (+ y t) 2.0)))
        (t_4 (+ t_3 t_1))
        (t_5 (+ x t_3)))
   (if (<= b -6e+208)
     t_5
     (if (<= b -1.55e+186)
       t_2
       (if (<= b -3.3e+56)
         t_4
         (if (<= b -2.3e-44)
           t_2
           (if (<= b -5.2e-86) t_4 (if (<= b 1.3e+88) t_2 t_5))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (t_1 + (z * (1.0 - y)));
	double t_3 = b * ((y + t) - 2.0);
	double t_4 = t_3 + t_1;
	double t_5 = x + t_3;
	double tmp;
	if (b <= -6e+208) {
		tmp = t_5;
	} else if (b <= -1.55e+186) {
		tmp = t_2;
	} else if (b <= -3.3e+56) {
		tmp = t_4;
	} else if (b <= -2.3e-44) {
		tmp = t_2;
	} else if (b <= -5.2e-86) {
		tmp = t_4;
	} else if (b <= 1.3e+88) {
		tmp = t_2;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (t_1 + (z * (1.0d0 - y)))
    t_3 = b * ((y + t) - 2.0d0)
    t_4 = t_3 + t_1
    t_5 = x + t_3
    if (b <= (-6d+208)) then
        tmp = t_5
    else if (b <= (-1.55d+186)) then
        tmp = t_2
    else if (b <= (-3.3d+56)) then
        tmp = t_4
    else if (b <= (-2.3d-44)) then
        tmp = t_2
    else if (b <= (-5.2d-86)) then
        tmp = t_4
    else if (b <= 1.3d+88) then
        tmp = t_2
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (t_1 + (z * (1.0 - y)));
	double t_3 = b * ((y + t) - 2.0);
	double t_4 = t_3 + t_1;
	double t_5 = x + t_3;
	double tmp;
	if (b <= -6e+208) {
		tmp = t_5;
	} else if (b <= -1.55e+186) {
		tmp = t_2;
	} else if (b <= -3.3e+56) {
		tmp = t_4;
	} else if (b <= -2.3e-44) {
		tmp = t_2;
	} else if (b <= -5.2e-86) {
		tmp = t_4;
	} else if (b <= 1.3e+88) {
		tmp = t_2;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (t_1 + (z * (1.0 - y)))
	t_3 = b * ((y + t) - 2.0)
	t_4 = t_3 + t_1
	t_5 = x + t_3
	tmp = 0
	if b <= -6e+208:
		tmp = t_5
	elif b <= -1.55e+186:
		tmp = t_2
	elif b <= -3.3e+56:
		tmp = t_4
	elif b <= -2.3e-44:
		tmp = t_2
	elif b <= -5.2e-86:
		tmp = t_4
	elif b <= 1.3e+88:
		tmp = t_2
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))))
	t_3 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_4 = Float64(t_3 + t_1)
	t_5 = Float64(x + t_3)
	tmp = 0.0
	if (b <= -6e+208)
		tmp = t_5;
	elseif (b <= -1.55e+186)
		tmp = t_2;
	elseif (b <= -3.3e+56)
		tmp = t_4;
	elseif (b <= -2.3e-44)
		tmp = t_2;
	elseif (b <= -5.2e-86)
		tmp = t_4;
	elseif (b <= 1.3e+88)
		tmp = t_2;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (t_1 + (z * (1.0 - y)));
	t_3 = b * ((y + t) - 2.0);
	t_4 = t_3 + t_1;
	t_5 = x + t_3;
	tmp = 0.0;
	if (b <= -6e+208)
		tmp = t_5;
	elseif (b <= -1.55e+186)
		tmp = t_2;
	elseif (b <= -3.3e+56)
		tmp = t_4;
	elseif (b <= -2.3e-44)
		tmp = t_2;
	elseif (b <= -5.2e-86)
		tmp = t_4;
	elseif (b <= 1.3e+88)
		tmp = t_2;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(x + t$95$3), $MachinePrecision]}, If[LessEqual[b, -6e+208], t$95$5, If[LessEqual[b, -1.55e+186], t$95$2, If[LessEqual[b, -3.3e+56], t$95$4, If[LessEqual[b, -2.3e-44], t$95$2, If[LessEqual[b, -5.2e-86], t$95$4, If[LessEqual[b, 1.3e+88], t$95$2, t$95$5]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.99999999999999989e208 or 1.3e88 < b

   1. Initial program 82.9%

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

   3. Taylor expanded in y around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. +-commutative 56.3%

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

      3. associate-+l+ 56.3%

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

      4. sub-neg 56.3%

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

      5. metadata-eval 56.3%

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

      6. associate-/l* 54.2%

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

      7. +-commutative 54.2%

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

      8. mul-1-neg 54.2%

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

      9. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in x around inf 89.7%

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

   if -5.99999999999999989e208 < b < -1.5500000000000001e186 or -3.30000000000000002e56 < b < -2.29999999999999998e-44 or -5.2000000000000002e-86 < b < 1.3e88

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0 91.5%

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

   if -1.5500000000000001e186 < b < -3.30000000000000002e56 or -2.29999999999999998e-44 < b < -5.2000000000000002e-86

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf 88.4%

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

   4. Taylor expanded in a around inf 88.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+208}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{+186}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-44}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+88}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.95 \cdot 10^{-227}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.65e+41)
     t_2
     (if (<= b -1.1e-153)
       t_1
       (if (<= b -3.95e-227)
         (+ x z)
         (if (<= b 5.8e-307)
           t_1
           (if (<= b 1.3e-255) (* y (- z)) (if (<= b 1.36e+88) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.65e+41) {
		tmp = t_2;
	} else if (b <= -1.1e-153) {
		tmp = t_1;
	} else if (b <= -3.95e-227) {
		tmp = x + z;
	} else if (b <= 5.8e-307) {
		tmp = t_1;
	} else if (b <= 1.3e-255) {
		tmp = y * -z;
	} else if (b <= 1.36e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.65d+41)) then
        tmp = t_2
    else if (b <= (-1.1d-153)) then
        tmp = t_1
    else if (b <= (-3.95d-227)) then
        tmp = x + z
    else if (b <= 5.8d-307) then
        tmp = t_1
    else if (b <= 1.3d-255) then
        tmp = y * -z
    else if (b <= 1.36d+88) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.65e+41) {
		tmp = t_2;
	} else if (b <= -1.1e-153) {
		tmp = t_1;
	} else if (b <= -3.95e-227) {
		tmp = x + z;
	} else if (b <= 5.8e-307) {
		tmp = t_1;
	} else if (b <= 1.3e-255) {
		tmp = y * -z;
	} else if (b <= 1.36e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.65e+41:
		tmp = t_2
	elif b <= -1.1e-153:
		tmp = t_1
	elif b <= -3.95e-227:
		tmp = x + z
	elif b <= 5.8e-307:
		tmp = t_1
	elif b <= 1.3e-255:
		tmp = y * -z
	elif b <= 1.36e+88:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.65e+41)
		tmp = t_2;
	elseif (b <= -1.1e-153)
		tmp = t_1;
	elseif (b <= -3.95e-227)
		tmp = Float64(x + z);
	elseif (b <= 5.8e-307)
		tmp = t_1;
	elseif (b <= 1.3e-255)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 1.36e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.65e+41)
		tmp = t_2;
	elseif (b <= -1.1e-153)
		tmp = t_1;
	elseif (b <= -3.95e-227)
		tmp = x + z;
	elseif (b <= 5.8e-307)
		tmp = t_1;
	elseif (b <= 1.3e-255)
		tmp = y * -z;
	elseif (b <= 1.36e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+41], t$95$2, If[LessEqual[b, -1.1e-153], t$95$1, If[LessEqual[b, -3.95e-227], N[(x + z), $MachinePrecision], If[LessEqual[b, 5.8e-307], t$95$1, If[LessEqual[b, 1.3e-255], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 1.36e+88], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.65e41 or 1.3600000000000001e88 < b

   1. Initial program 86.5%

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

   3. Taylor expanded in b around inf 73.5%

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

   if -1.65e41 < b < -1.1e-153 or -3.9500000000000001e-227 < b < 5.8000000000000001e-307 or 1.3000000000000001e-255 < b < 1.3600000000000001e88

   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 a around inf 51.8%

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

   if -1.1e-153 < b < -3.9500000000000001e-227

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0 97.7%

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

   4. Taylor expanded in a around 0 68.6%

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

   5. Taylor expanded in y around 0 52.6%

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

      1. cancel-sign-sub-inv 52.6%

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

      2. metadata-eval 52.6%

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

      3. *-lft-identity 52.6%

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

   7. Simplified 52.6%

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

   if 5.8000000000000001e-307 < b < 1.3000000000000001e-255

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in b around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 73.4%

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

      1. associate-*r* 73.4%

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

      2. mul-1-neg 73.4%

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

   9. Simplified 73.4%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -3.95 \cdot 10^{-227}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-307}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-256}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -9e+57)
     t_2
     (if (<= b 5.8e-307)
       t_1
       (if (<= b 7.5e-256)
         (* y (- z))
         (if (<= b 1.95e+34)
           t_1
           (if (<= b 9e+64) (* y (- b z)) (if (<= b 6.5e+88) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9e+57) {
		tmp = t_2;
	} else if (b <= 5.8e-307) {
		tmp = t_1;
	} else if (b <= 7.5e-256) {
		tmp = y * -z;
	} else if (b <= 1.95e+34) {
		tmp = t_1;
	} else if (b <= 9e+64) {
		tmp = y * (b - z);
	} else if (b <= 6.5e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-9d+57)) then
        tmp = t_2
    else if (b <= 5.8d-307) then
        tmp = t_1
    else if (b <= 7.5d-256) then
        tmp = y * -z
    else if (b <= 1.95d+34) then
        tmp = t_1
    else if (b <= 9d+64) then
        tmp = y * (b - z)
    else if (b <= 6.5d+88) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9e+57) {
		tmp = t_2;
	} else if (b <= 5.8e-307) {
		tmp = t_1;
	} else if (b <= 7.5e-256) {
		tmp = y * -z;
	} else if (b <= 1.95e+34) {
		tmp = t_1;
	} else if (b <= 9e+64) {
		tmp = y * (b - z);
	} else if (b <= 6.5e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -9e+57:
		tmp = t_2
	elif b <= 5.8e-307:
		tmp = t_1
	elif b <= 7.5e-256:
		tmp = y * -z
	elif b <= 1.95e+34:
		tmp = t_1
	elif b <= 9e+64:
		tmp = y * (b - z)
	elif b <= 6.5e+88:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -9e+57)
		tmp = t_2;
	elseif (b <= 5.8e-307)
		tmp = t_1;
	elseif (b <= 7.5e-256)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 1.95e+34)
		tmp = t_1;
	elseif (b <= 9e+64)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 6.5e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -9e+57)
		tmp = t_2;
	elseif (b <= 5.8e-307)
		tmp = t_1;
	elseif (b <= 7.5e-256)
		tmp = y * -z;
	elseif (b <= 1.95e+34)
		tmp = t_1;
	elseif (b <= 9e+64)
		tmp = y * (b - z);
	elseif (b <= 6.5e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e+57], t$95$2, If[LessEqual[b, 5.8e-307], t$95$1, If[LessEqual[b, 7.5e-256], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 1.95e+34], t$95$1, If[LessEqual[b, 9e+64], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+88], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.99999999999999991e57 or 6.5000000000000002e88 < b

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf 76.9%

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

   if -8.99999999999999991e57 < b < 5.8000000000000001e-307 or 7.50000000000000005e-256 < b < 1.9500000000000001e34 or 8.99999999999999946e64 < b < 6.5000000000000002e88

   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 y around 0 99.4%

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

   4. Taylor expanded in b around 0 90.2%

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

      1. associate-*r* 90.2%

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

      2. mul-1-neg 90.2%

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

   6. Simplified 90.2%

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

   7. Taylor expanded in z around 0 66.7%

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

   if 5.8000000000000001e-307 < b < 7.50000000000000005e-256

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in b around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 73.4%

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

      1. associate-*r* 73.4%

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

      2. mul-1-neg 73.4%

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

   9. Simplified 73.4%

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

   if 1.9500000000000001e34 < b < 8.99999999999999946e64

   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 83.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-307}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-256}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+88}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ t_2 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* b (- (+ y t) 2.0)) (* a (- 1.0 t))))
        (t_2 (+ x (+ a (* z (- 1.0 y))))))
   (if (<= z -1.3e+142)
     t_2
     (if (<= z 6.9e-12)
       t_1
       (if (<= z 2.1e+48)
         t_2
         (if (<= z 1.25e+185) t_1 (+ z (- x (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((y + t) - 2.0)) + (a * (1.0 - t));
	double t_2 = x + (a + (z * (1.0 - y)));
	double tmp;
	if (z <= -1.3e+142) {
		tmp = t_2;
	} else if (z <= 6.9e-12) {
		tmp = t_1;
	} else if (z <= 2.1e+48) {
		tmp = t_2;
	} else if (z <= 1.25e+185) {
		tmp = t_1;
	} else {
		tmp = z + (x - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * ((y + t) - 2.0d0)) + (a * (1.0d0 - t))
    t_2 = x + (a + (z * (1.0d0 - y)))
    if (z <= (-1.3d+142)) then
        tmp = t_2
    else if (z <= 6.9d-12) then
        tmp = t_1
    else if (z <= 2.1d+48) then
        tmp = t_2
    else if (z <= 1.25d+185) then
        tmp = t_1
    else
        tmp = z + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((y + t) - 2.0)) + (a * (1.0 - t));
	double t_2 = x + (a + (z * (1.0 - y)));
	double tmp;
	if (z <= -1.3e+142) {
		tmp = t_2;
	} else if (z <= 6.9e-12) {
		tmp = t_1;
	} else if (z <= 2.1e+48) {
		tmp = t_2;
	} else if (z <= 1.25e+185) {
		tmp = t_1;
	} else {
		tmp = z + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * ((y + t) - 2.0)) + (a * (1.0 - t))
	t_2 = x + (a + (z * (1.0 - y)))
	tmp = 0
	if z <= -1.3e+142:
		tmp = t_2
	elif z <= 6.9e-12:
		tmp = t_1
	elif z <= 2.1e+48:
		tmp = t_2
	elif z <= 1.25e+185:
		tmp = t_1
	else:
		tmp = z + (x - (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	tmp = 0.0
	if (z <= -1.3e+142)
		tmp = t_2;
	elseif (z <= 6.9e-12)
		tmp = t_1;
	elseif (z <= 2.1e+48)
		tmp = t_2;
	elseif (z <= 1.25e+185)
		tmp = t_1;
	else
		tmp = Float64(z + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * ((y + t) - 2.0)) + (a * (1.0 - t));
	t_2 = x + (a + (z * (1.0 - y)));
	tmp = 0.0;
	if (z <= -1.3e+142)
		tmp = t_2;
	elseif (z <= 6.9e-12)
		tmp = t_1;
	elseif (z <= 2.1e+48)
		tmp = t_2;
	elseif (z <= 1.25e+185)
		tmp = t_1;
	else
		tmp = z + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+142], t$95$2, If[LessEqual[z, 6.9e-12], t$95$1, If[LessEqual[z, 2.1e+48], t$95$2, If[LessEqual[z, 1.25e+185], t$95$1, N[(z + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.30000000000000011e142 or 6.9000000000000001e-12 < z < 2.0999999999999998e48

   1. Initial program 92.9%

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

   3. Taylor expanded in b around 0 81.9%

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

   4. Taylor expanded in t around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. sub-neg 77.3%

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

      3. metadata-eval 77.3%

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

      4. mul-1-neg 77.3%

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

      5. unsub-neg 77.3%

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

      6. +-commutative 77.3%

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

   6. Simplified 77.3%

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

   if -1.30000000000000011e142 < z < 6.9000000000000001e-12 or 2.0999999999999998e48 < z < 1.24999999999999997e185

   1. Initial program 96.8%

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

   3. Taylor expanded in a around inf 82.3%

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

   4. Taylor expanded in a around inf 74.7%

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

   if 1.24999999999999997e185 < z

   1. Initial program 87.4%

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

   3. Taylor expanded in y around 0 87.5%

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

   4. Taylor expanded in b around 0 87.8%

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

      1. associate-*r* 87.8%

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

      2. mul-1-neg 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in a around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. sub-neg 83.6%

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

      3. mul-1-neg 83.6%

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

   9. Simplified 83.6%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+142}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+48}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+185}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-20}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-284}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-83}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+108}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.6e+41)
     t_1
     (if (<= a -3.1e-20)
       (* y b)
       (if (<= a 3.5e-284)
         (+ x z)
         (if (<= a 3.5e-83) (* t b) (if (<= a 2.3e+108) (+ x z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.6e+41) {
		tmp = t_1;
	} else if (a <= -3.1e-20) {
		tmp = y * b;
	} else if (a <= 3.5e-284) {
		tmp = x + z;
	} else if (a <= 3.5e-83) {
		tmp = t * b;
	} else if (a <= 2.3e+108) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-1.6d+41)) then
        tmp = t_1
    else if (a <= (-3.1d-20)) then
        tmp = y * b
    else if (a <= 3.5d-284) then
        tmp = x + z
    else if (a <= 3.5d-83) then
        tmp = t * b
    else if (a <= 2.3d+108) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.6e+41) {
		tmp = t_1;
	} else if (a <= -3.1e-20) {
		tmp = y * b;
	} else if (a <= 3.5e-284) {
		tmp = x + z;
	} else if (a <= 3.5e-83) {
		tmp = t * b;
	} else if (a <= 2.3e+108) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -1.6e+41:
		tmp = t_1
	elif a <= -3.1e-20:
		tmp = y * b
	elif a <= 3.5e-284:
		tmp = x + z
	elif a <= 3.5e-83:
		tmp = t * b
	elif a <= 2.3e+108:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.6e+41)
		tmp = t_1;
	elseif (a <= -3.1e-20)
		tmp = Float64(y * b);
	elseif (a <= 3.5e-284)
		tmp = Float64(x + z);
	elseif (a <= 3.5e-83)
		tmp = Float64(t * b);
	elseif (a <= 2.3e+108)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.6e+41)
		tmp = t_1;
	elseif (a <= -3.1e-20)
		tmp = y * b;
	elseif (a <= 3.5e-284)
		tmp = x + z;
	elseif (a <= 3.5e-83)
		tmp = t * b;
	elseif (a <= 2.3e+108)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+41], t$95$1, If[LessEqual[a, -3.1e-20], N[(y * b), $MachinePrecision], If[LessEqual[a, 3.5e-284], N[(x + z), $MachinePrecision], If[LessEqual[a, 3.5e-83], N[(t * b), $MachinePrecision], If[LessEqual[a, 2.3e+108], N[(x + z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.60000000000000005e41 or 2.2999999999999999e108 < a

   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 a around inf 72.3%

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

   if -1.60000000000000005e41 < a < -3.1e-20

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf 77.8%

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

   4. Taylor expanded in b around inf 47.8%

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

      1. *-commutative 47.8%

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

   6. Simplified 47.8%

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

   if -3.1e-20 < a < 3.49999999999999975e-284 or 3.5000000000000003e-83 < a < 2.2999999999999999e108

   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 71.2%

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

   4. Taylor expanded in a around 0 59.1%

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

   5. Taylor expanded in y around 0 39.0%

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

      1. cancel-sign-sub-inv 39.0%

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

      2. metadata-eval 39.0%

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

      3. *-lft-identity 39.0%

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

   7. Simplified 39.0%

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

   if 3.49999999999999975e-284 < a < 3.5000000000000003e-83

   1. Initial program 95.9%

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

   3. Taylor expanded in t around inf 36.2%

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

   4. Taylor expanded in b around inf 30.2%

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

      1. *-commutative 30.2%

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

   6. Simplified 30.2%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-20}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-284}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-83}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+108}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-215}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))) (t_2 (+ x (* a (- 1.0 t)))))
   (if (<= a -3e+41)
     t_2
     (if (<= a -7.8e-138)
       t_1
       (if (<= a -9.5e-215)
         (+ x (* z (- 1.0 y)))
         (if (<= a 3.6e-28) 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 + t) - 2.0));
	double t_2 = x + (a * (1.0 - t));
	double tmp;
	if (a <= -3e+41) {
		tmp = t_2;
	} else if (a <= -7.8e-138) {
		tmp = t_1;
	} else if (a <= -9.5e-215) {
		tmp = x + (z * (1.0 - y));
	} else if (a <= 3.6e-28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    t_2 = x + (a * (1.0d0 - t))
    if (a <= (-3d+41)) then
        tmp = t_2
    else if (a <= (-7.8d-138)) then
        tmp = t_1
    else if (a <= (-9.5d-215)) then
        tmp = x + (z * (1.0d0 - y))
    else if (a <= 3.6d-28) 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 + t) - 2.0));
	double t_2 = x + (a * (1.0 - t));
	double tmp;
	if (a <= -3e+41) {
		tmp = t_2;
	} else if (a <= -7.8e-138) {
		tmp = t_1;
	} else if (a <= -9.5e-215) {
		tmp = x + (z * (1.0 - y));
	} else if (a <= 3.6e-28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	t_2 = x + (a * (1.0 - t))
	tmp = 0
	if a <= -3e+41:
		tmp = t_2
	elif a <= -7.8e-138:
		tmp = t_1
	elif a <= -9.5e-215:
		tmp = x + (z * (1.0 - y))
	elif a <= 3.6e-28:
		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(Float64(y + t) - 2.0)))
	t_2 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (a <= -3e+41)
		tmp = t_2;
	elseif (a <= -7.8e-138)
		tmp = t_1;
	elseif (a <= -9.5e-215)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (a <= 3.6e-28)
		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 + t) - 2.0));
	t_2 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (a <= -3e+41)
		tmp = t_2;
	elseif (a <= -7.8e-138)
		tmp = t_1;
	elseif (a <= -9.5e-215)
		tmp = x + (z * (1.0 - y));
	elseif (a <= 3.6e-28)
		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[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+41], t$95$2, If[LessEqual[a, -7.8e-138], t$95$1, If[LessEqual[a, -9.5e-215], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.9999999999999998e41 or 3.5999999999999999e-28 < a

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 94.2%

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

   4. Taylor expanded in b around 0 85.3%

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

      1. associate-*r* 85.3%

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

      2. mul-1-neg 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in z around 0 70.5%

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

   if -2.9999999999999998e41 < a < -7.7999999999999999e-138 or -9.5000000000000007e-215 < a < 3.5999999999999999e-28

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. +-commutative 77.9%

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

      2. +-commutative 77.9%

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

      3. associate-+l+ 77.9%

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

      4. sub-neg 77.9%

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

      5. metadata-eval 77.9%

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

      6. associate-/l* 75.0%

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

      7. +-commutative 75.0%

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

      8. mul-1-neg 75.0%

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

      9. unsub-neg 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in x around inf 67.2%

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

   if -7.7999999999999999e-138 < a < -9.5000000000000007e-215

   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 84.1%

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

   4. Taylor expanded in a around 0 78.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+41}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-138}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-215}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-28}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-255}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -3.6e+55)
     t_2
     (if (<= b 3.2e-307)
       t_1
       (if (<= b 2.5e-255)
         (+ x (* z (- 1.0 y)))
         (if (<= b 1.26e+88) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -3.6e+55) {
		tmp = t_2;
	} else if (b <= 3.2e-307) {
		tmp = t_1;
	} else if (b <= 2.5e-255) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.26e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-3.6d+55)) then
        tmp = t_2
    else if (b <= 3.2d-307) then
        tmp = t_1
    else if (b <= 2.5d-255) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 1.26d+88) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -3.6e+55) {
		tmp = t_2;
	} else if (b <= 3.2e-307) {
		tmp = t_1;
	} else if (b <= 2.5e-255) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.26e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -3.6e+55:
		tmp = t_2
	elif b <= 3.2e-307:
		tmp = t_1
	elif b <= 2.5e-255:
		tmp = x + (z * (1.0 - y))
	elif b <= 1.26e+88:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -3.6e+55)
		tmp = t_2;
	elseif (b <= 3.2e-307)
		tmp = t_1;
	elseif (b <= 2.5e-255)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 1.26e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -3.6e+55)
		tmp = t_2;
	elseif (b <= 3.2e-307)
		tmp = t_1;
	elseif (b <= 2.5e-255)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 1.26e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e+55], t$95$2, If[LessEqual[b, 3.2e-307], t$95$1, If[LessEqual[b, 2.5e-255], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.26e+88], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.59999999999999987e55 or 1.26e88 < b

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf 76.9%

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

   if -3.59999999999999987e55 < b < 3.20000000000000011e-307 or 2.4999999999999998e-255 < b < 1.26e88

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 99.4%

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

   4. Taylor expanded in b around 0 88.8%

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

      1. associate-*r* 88.8%

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

      2. mul-1-neg 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in z around 0 64.4%

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

   if 3.20000000000000011e-307 < b < 2.4999999999999998e-255

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in a around 0 82.1%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-307}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-255}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+88}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+22}:\\ \;\;\;\;x + \left(a + t\_1\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;y \cdot b - t \cdot a\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+87}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* t (- b a))))
   (if (<= t -3.5e+43)
     t_2
     (if (<= t 1.85e+22)
       (+ x (+ a t_1))
       (if (<= t 2.7e+51)
         (- (* y b) (* t a))
         (if (<= t 3.1e+87) (+ x t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3.5e+43) {
		tmp = t_2;
	} else if (t <= 1.85e+22) {
		tmp = x + (a + t_1);
	} else if (t <= 2.7e+51) {
		tmp = (y * b) - (t * a);
	} else if (t <= 3.1e+87) {
		tmp = x + 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 = z * (1.0d0 - y)
    t_2 = t * (b - a)
    if (t <= (-3.5d+43)) then
        tmp = t_2
    else if (t <= 1.85d+22) then
        tmp = x + (a + t_1)
    else if (t <= 2.7d+51) then
        tmp = (y * b) - (t * a)
    else if (t <= 3.1d+87) then
        tmp = x + 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 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3.5e+43) {
		tmp = t_2;
	} else if (t <= 1.85e+22) {
		tmp = x + (a + t_1);
	} else if (t <= 2.7e+51) {
		tmp = (y * b) - (t * a);
	} else if (t <= 3.1e+87) {
		tmp = x + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -3.5e+43:
		tmp = t_2
	elif t <= 1.85e+22:
		tmp = x + (a + t_1)
	elif t <= 2.7e+51:
		tmp = (y * b) - (t * a)
	elif t <= 3.1e+87:
		tmp = x + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.5e+43)
		tmp = t_2;
	elseif (t <= 1.85e+22)
		tmp = Float64(x + Float64(a + t_1));
	elseif (t <= 2.7e+51)
		tmp = Float64(Float64(y * b) - Float64(t * a));
	elseif (t <= 3.1e+87)
		tmp = Float64(x + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.5e+43)
		tmp = t_2;
	elseif (t <= 1.85e+22)
		tmp = x + (a + t_1);
	elseif (t <= 2.7e+51)
		tmp = (y * b) - (t * a);
	elseif (t <= 3.1e+87)
		tmp = x + t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+43], t$95$2, If[LessEqual[t, 1.85e+22], N[(x + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+51], N[(N[(y * b), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+87], N[(x + t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.5000000000000001e43 or 3.1e87 < t

   1. Initial program 90.8%

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

   3. Taylor expanded in t around inf 73.1%

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

   if -3.5000000000000001e43 < t < 1.8499999999999999e22

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0 73.1%

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

   4. Taylor expanded in t around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. sub-neg 69.5%

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

      3. metadata-eval 69.5%

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

      4. mul-1-neg 69.5%

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

      5. unsub-neg 69.5%

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

      6. +-commutative 69.5%

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

   6. Simplified 69.5%

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

   if 1.8499999999999999e22 < t < 2.69999999999999992e51

   1. Initial program 83.3%

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

   3. Taylor expanded in t around inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. distribute-rgt-neg-in 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in y around inf 90.5%

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

   if 2.69999999999999992e51 < t < 3.1e87

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0 90.6%

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

   4. Taylor expanded in a around 0 71.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+22}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;y \cdot b - t \cdot a\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+87}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -8000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;t \leq 10^{+22}:\\ \;\;\;\;x + \left(a + t\_1\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+50}:\\ \;\;\;\;y \cdot b - t \cdot a\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+87}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= t -8000.0)
     (- (* b (- (+ y t) 2.0)) (* t a))
     (if (<= t 1e+22)
       (+ x (+ a t_1))
       (if (<= t 9.5e+50)
         (- (* y b) (* t a))
         (if (<= t 3.4e+87) (+ x t_1) (* t (- b a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (t <= -8000.0) {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	} else if (t <= 1e+22) {
		tmp = x + (a + t_1);
	} else if (t <= 9.5e+50) {
		tmp = (y * b) - (t * a);
	} else if (t <= 3.4e+87) {
		tmp = x + t_1;
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (t <= (-8000.0d0)) then
        tmp = (b * ((y + t) - 2.0d0)) - (t * a)
    else if (t <= 1d+22) then
        tmp = x + (a + t_1)
    else if (t <= 9.5d+50) then
        tmp = (y * b) - (t * a)
    else if (t <= 3.4d+87) then
        tmp = x + t_1
    else
        tmp = t * (b - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (t <= -8000.0) {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	} else if (t <= 1e+22) {
		tmp = x + (a + t_1);
	} else if (t <= 9.5e+50) {
		tmp = (y * b) - (t * a);
	} else if (t <= 3.4e+87) {
		tmp = x + t_1;
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if t <= -8000.0:
		tmp = (b * ((y + t) - 2.0)) - (t * a)
	elif t <= 1e+22:
		tmp = x + (a + t_1)
	elif t <= 9.5e+50:
		tmp = (y * b) - (t * a)
	elif t <= 3.4e+87:
		tmp = x + t_1
	else:
		tmp = t * (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -8000.0)
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(t * a));
	elseif (t <= 1e+22)
		tmp = Float64(x + Float64(a + t_1));
	elseif (t <= 9.5e+50)
		tmp = Float64(Float64(y * b) - Float64(t * a));
	elseif (t <= 3.4e+87)
		tmp = Float64(x + 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 = z * (1.0 - y);
	tmp = 0.0;
	if (t <= -8000.0)
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	elseif (t <= 1e+22)
		tmp = x + (a + t_1);
	elseif (t <= 9.5e+50)
		tmp = (y * b) - (t * a);
	elseif (t <= 3.4e+87)
		tmp = x + 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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8000.0], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+22], N[(x + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+50], N[(N[(y * b), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+87], N[(x + t$95$1), $MachinePrecision], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8e3

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. distribute-rgt-neg-in 77.0%

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

   5. Simplified 77.0%

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

   if -8e3 < t < 1e22

   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 b around 0 72.9%

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

   4. Taylor expanded in t around 0 71.4%

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

      1. +-commutative 71.4%

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

      2. sub-neg 71.4%

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

      3. metadata-eval 71.4%

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

      4. mul-1-neg 71.4%

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

      5. unsub-neg 71.4%

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

      6. +-commutative 71.4%

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

   6. Simplified 71.4%

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

   if 1e22 < t < 9.4999999999999993e50

   1. Initial program 83.3%

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

   3. Taylor expanded in t around inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. distribute-rgt-neg-in 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in y around inf 90.5%

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

   if 9.4999999999999993e50 < t < 3.4000000000000002e87

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0 90.6%

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

   4. Taylor expanded in a around 0 71.1%

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

   if 3.4000000000000002e87 < t

   1. Initial program 84.4%

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

   3. Taylor expanded in t around inf 71.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;t \leq 10^{+22}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+50}:\\ \;\;\;\;y \cdot b - t \cdot a\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+87}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 40.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-285}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.4e+41)
     t_1
     (if (<= a -2.2e-20)
       (* b (- y 2.0))
       (if (<= a 1.65e-285) (+ x z) (if (<= a 5.5e+111) (* t (- b a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.4e+41) {
		tmp = t_1;
	} else if (a <= -2.2e-20) {
		tmp = b * (y - 2.0);
	} else if (a <= 1.65e-285) {
		tmp = x + z;
	} else if (a <= 5.5e+111) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-1.4d+41)) then
        tmp = t_1
    else if (a <= (-2.2d-20)) then
        tmp = b * (y - 2.0d0)
    else if (a <= 1.65d-285) then
        tmp = x + z
    else if (a <= 5.5d+111) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.4e+41) {
		tmp = t_1;
	} else if (a <= -2.2e-20) {
		tmp = b * (y - 2.0);
	} else if (a <= 1.65e-285) {
		tmp = x + z;
	} else if (a <= 5.5e+111) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -1.4e+41:
		tmp = t_1
	elif a <= -2.2e-20:
		tmp = b * (y - 2.0)
	elif a <= 1.65e-285:
		tmp = x + z
	elif a <= 5.5e+111:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.4e+41)
		tmp = t_1;
	elseif (a <= -2.2e-20)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (a <= 1.65e-285)
		tmp = Float64(x + z);
	elseif (a <= 5.5e+111)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.4e+41)
		tmp = t_1;
	elseif (a <= -2.2e-20)
		tmp = b * (y - 2.0);
	elseif (a <= 1.65e-285)
		tmp = x + z;
	elseif (a <= 5.5e+111)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+41], t$95$1, If[LessEqual[a, -2.2e-20], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-285], N[(x + z), $MachinePrecision], If[LessEqual[a, 5.5e+111], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.4e41 or 5.4999999999999998e111 < a

   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 a around inf 72.3%

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

   if -1.4e41 < a < -2.19999999999999991e-20

   1. Initial program 92.3%

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

   3. Taylor expanded in t around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. distribute-rgt-neg-in 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in t around 0 48.0%

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

   if -2.19999999999999991e-20 < a < 1.64999999999999993e-285

   1. Initial program 95.6%

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

   3. Taylor expanded in b around 0 66.9%

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

   4. Taylor expanded in a around 0 62.8%

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

   5. Taylor expanded in y around 0 42.2%

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

      1. cancel-sign-sub-inv 42.2%

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

      2. metadata-eval 42.2%

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

      3. *-lft-identity 42.2%

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

   7. Simplified 42.2%

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

   if 1.64999999999999993e-285 < a < 5.4999999999999998e111

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 34.8%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-285}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{-86} \lor \neg \left(b \leq 3.3 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -5.2e-86) (not (<= b 3.3e+44)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (+ t_1 (* z (- 1.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -5.2e-86) || !(b <= 3.3e+44)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-5.2d-86)) .or. (.not. (b <= 3.3d+44))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -5.2e-86) || !(b <= 3.3e+44)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -5.2e-86) or not (b <= 3.3e+44):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + (t_1 + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -5.2e-86) || !(b <= 3.3e+44))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((b <= -5.2e-86) || ~((b <= 3.3e+44)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + (t_1 + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -5.2e-86], N[Not[LessEqual[b, 3.3e+44]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.2000000000000002e-86 or 3.30000000000000013e44 < b

   1. Initial program 90.3%

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

   3. Taylor expanded in z around 0 83.5%

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

   if -5.2000000000000002e-86 < b < 3.30000000000000013e44

   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 94.0%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-86} \lor \neg \left(b \leq 3.3 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+250}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-14} \lor \neg \left(t \leq 1.42 \cdot 10^{+77}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- t))))
   (if (<= t -8.5e+273)
     t_1
     (if (<= t -2.4e+250)
       (* t b)
       (if (or (<= t -1.05e-14) (not (<= t 1.42e+77))) t_1 (+ x z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * -t;
	double tmp;
	if (t <= -8.5e+273) {
		tmp = t_1;
	} else if (t <= -2.4e+250) {
		tmp = t * b;
	} else if ((t <= -1.05e-14) || !(t <= 1.42e+77)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * -t
    if (t <= (-8.5d+273)) then
        tmp = t_1
    else if (t <= (-2.4d+250)) then
        tmp = t * b
    else if ((t <= (-1.05d-14)) .or. (.not. (t <= 1.42d+77))) then
        tmp = t_1
    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 t_1 = a * -t;
	double tmp;
	if (t <= -8.5e+273) {
		tmp = t_1;
	} else if (t <= -2.4e+250) {
		tmp = t * b;
	} else if ((t <= -1.05e-14) || !(t <= 1.42e+77)) {
		tmp = t_1;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * -t
	tmp = 0
	if t <= -8.5e+273:
		tmp = t_1
	elif t <= -2.4e+250:
		tmp = t * b
	elif (t <= -1.05e-14) or not (t <= 1.42e+77):
		tmp = t_1
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(-t))
	tmp = 0.0
	if (t <= -8.5e+273)
		tmp = t_1;
	elseif (t <= -2.4e+250)
		tmp = Float64(t * b);
	elseif ((t <= -1.05e-14) || !(t <= 1.42e+77))
		tmp = t_1;
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * -t;
	tmp = 0.0;
	if (t <= -8.5e+273)
		tmp = t_1;
	elseif (t <= -2.4e+250)
		tmp = t * b;
	elseif ((t <= -1.05e-14) || ~((t <= 1.42e+77)))
		tmp = t_1;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * (-t)), $MachinePrecision]}, If[LessEqual[t, -8.5e+273], t$95$1, If[LessEqual[t, -2.4e+250], N[(t * b), $MachinePrecision], If[Or[LessEqual[t, -1.05e-14], N[Not[LessEqual[t, 1.42e+77]], $MachinePrecision]], t$95$1, N[(x + z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5000000000000002e273 or -2.40000000000000013e250 < t < -1.0499999999999999e-14 or 1.41999999999999993e77 < t

   1. Initial program 92.0%

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

   3. Taylor expanded in t around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. distribute-rgt-neg-in 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in a around inf 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-rgt-neg-out 48.2%

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

   8. Simplified 48.2%

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

   if -8.5000000000000002e273 < t < -2.40000000000000013e250

   1. Initial program 90.0%

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

   3. Taylor expanded in t around inf 81.4%

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

   4. Taylor expanded in b around inf 71.7%

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

      1. *-commutative 71.7%

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

   6. Simplified 71.7%

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

   if -1.0499999999999999e-14 < t < 1.41999999999999993e77

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0 74.2%

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

   4. Taylor expanded in a around 0 46.4%

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

   5. Taylor expanded in y around 0 32.9%

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

      1. cancel-sign-sub-inv 32.9%

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

      2. metadata-eval 32.9%

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

      3. *-lft-identity 32.9%

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

   7. Simplified 32.9%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+273}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+250}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-14} \lor \neg \left(t \leq 1.42 \cdot 10^{+77}\right):\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2e+47)
     t_1
     (if (<= y 2.5e-190)
       (* t (- b a))
       (if (<= y 6.5e+58) (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2e+47) {
		tmp = t_1;
	} else if (y <= 2.5e-190) {
		tmp = t * (b - a);
	} else if (y <= 6.5e+58) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-2d+47)) then
        tmp = t_1
    else if (y <= 2.5d-190) then
        tmp = t * (b - a)
    else if (y <= 6.5d+58) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2e+47) {
		tmp = t_1;
	} else if (y <= 2.5e-190) {
		tmp = t * (b - a);
	} else if (y <= 6.5e+58) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2e+47:
		tmp = t_1
	elif y <= 2.5e-190:
		tmp = t * (b - a)
	elif y <= 6.5e+58:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2e+47)
		tmp = t_1;
	elseif (y <= 2.5e-190)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 6.5e+58)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -2e+47)
		tmp = t_1;
	elseif (y <= 2.5e-190)
		tmp = t * (b - a);
	elseif (y <= 6.5e+58)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+47], t$95$1, If[LessEqual[y, 2.5e-190], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+58], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0000000000000001e47 or 6.49999999999999998e58 < y

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 61.3%

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

   if -2.0000000000000001e47 < y < 2.50000000000000017e-190

   1. Initial program 96.9%

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

   3. Taylor expanded in t around inf 46.3%

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

   if 2.50000000000000017e-190 < y < 6.49999999999999998e58

   1. Initial program 97.6%

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

   3. Taylor expanded in a around inf 49.4%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+68}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.05e+68)
   (* t b)
   (if (<= t -2.8e-52) (* y b) (if (<= t 8.5e+63) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e+68) {
		tmp = t * b;
	} else if (t <= -2.8e-52) {
		tmp = y * b;
	} else if (t <= 8.5e+63) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.05d+68)) then
        tmp = t * b
    else if (t <= (-2.8d-52)) then
        tmp = y * b
    else if (t <= 8.5d+63) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e+68) {
		tmp = t * b;
	} else if (t <= -2.8e-52) {
		tmp = y * b;
	} else if (t <= 8.5e+63) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.05e+68:
		tmp = t * b
	elif t <= -2.8e-52:
		tmp = y * b
	elif t <= 8.5e+63:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.05e+68)
		tmp = Float64(t * b);
	elseif (t <= -2.8e-52)
		tmp = Float64(y * b);
	elseif (t <= 8.5e+63)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.05e+68)
		tmp = t * b;
	elseif (t <= -2.8e-52)
		tmp = y * b;
	elseif (t <= 8.5e+63)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.05e+68], N[(t * b), $MachinePrecision], If[LessEqual[t, -2.8e-52], N[(y * b), $MachinePrecision], If[LessEqual[t, 8.5e+63], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e68 or 8.5000000000000004e63 < t

   1. Initial program 90.5%

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

   3. Taylor expanded in t around inf 72.6%

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

   4. Taylor expanded in b around inf 31.2%

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

      1. *-commutative 31.2%

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

   6. Simplified 31.2%

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

   if -1.05e68 < t < -2.79999999999999995e-52

   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 44.7%

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

   4. Taylor expanded in b around inf 23.7%

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

      1. *-commutative 23.7%

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

   6. Simplified 23.7%

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

   if -2.79999999999999995e-52 < t < 8.5000000000000004e63

   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 x around inf 22.4%

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

4. Final simplification 26.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+68}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 56.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -950000 \lor \neg \left(t \leq 3500\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -950000.0) (not (<= t 3500.0)))
   (* t (- b a))
   (+ a (* b (- y 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -950000.0) || !(t <= 3500.0)) {
		tmp = t * (b - a);
	} else {
		tmp = a + (b * (y - 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-950000.0d0)) .or. (.not. (t <= 3500.0d0))) then
        tmp = t * (b - a)
    else
        tmp = a + (b * (y - 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -950000.0) || !(t <= 3500.0)) {
		tmp = t * (b - a);
	} else {
		tmp = a + (b * (y - 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -950000.0) or not (t <= 3500.0):
		tmp = t * (b - a)
	else:
		tmp = a + (b * (y - 2.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -950000.0) || !(t <= 3500.0))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(a + Float64(b * Float64(y - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -950000.0) || ~((t <= 3500.0)))
		tmp = t * (b - a);
	else
		tmp = a + (b * (y - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -950000.0], N[Not[LessEqual[t, 3500.0]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(a + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.5e5 or 3500 < t

   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 t around inf 65.8%

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

   if -9.5e5 < t < 3500

   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 a around inf 81.7%

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

   4. Taylor expanded in a around inf 55.9%

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

   5. Taylor expanded in t around 0 54.5%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -950000 \lor \neg \left(t \leq 3500\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 26.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \lor \neg \left(t \leq 9.5 \cdot 10^{+61}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.7) (not (<= t 9.5e+61))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.7) || !(t <= 9.5e+61)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.7d0)) .or. (.not. (t <= 9.5d+61))) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.7) || !(t <= 9.5e+61)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.7) or not (t <= 9.5e+61):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.7) || !(t <= 9.5e+61))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.7) || ~((t <= 9.5e+61)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.7], N[Not[LessEqual[t, 9.5e+61]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.69999999999999996 or 9.49999999999999959e61 < t

   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 t around inf 67.3%

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

   4. Taylor expanded in b around inf 27.4%

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

      1. *-commutative 27.4%

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

   6. Simplified 27.4%

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

   if -1.69999999999999996 < t < 9.49999999999999959e61

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 21.3%

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

4. Final simplification 24.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \lor \neg \left(t \leq 9.5 \cdot 10^{+61}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 34.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+82} \lor \neg \left(y \leq 2.2 \cdot 10^{+89}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.4e+82) (not (<= y 2.2e+89))) (* y b) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.4e+82) || !(y <= 2.2e+89)) {
		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 <= (-3.4d+82)) .or. (.not. (y <= 2.2d+89))) 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 <= -3.4e+82) || !(y <= 2.2e+89)) {
		tmp = y * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.4e+82) or not (y <= 2.2e+89):
		tmp = y * b
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.4e+82) || !(y <= 2.2e+89))
		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 <= -3.4e+82) || ~((y <= 2.2e+89)))
		tmp = y * b;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.4e+82], N[Not[LessEqual[y, 2.2e+89]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999994e82 or 2.2e89 < y

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 63.1%

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

   4. Taylor expanded in b around inf 34.3%

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

      1. *-commutative 34.3%

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

   6. Simplified 34.3%

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

   if -3.39999999999999994e82 < y < 2.2e89

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0 75.7%

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

   4. Taylor expanded in a around 0 35.7%

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

   5. Taylor expanded in y around 0 29.5%

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

      1. cancel-sign-sub-inv 29.5%

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

      2. metadata-eval 29.5%

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

      3. *-lft-identity 29.5%

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

   7. Simplified 29.5%

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

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+82} \lor \neg \left(y \leq 2.2 \cdot 10^{+89}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 17.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 2.7e+34) x (* -2.0 b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.7e+34) {
		tmp = x;
	} else {
		tmp = -2.0 * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.7d+34) then
        tmp = x
    else
        tmp = (-2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.7e+34) {
		tmp = x;
	} else {
		tmp = -2.0 * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.7e+34:
		tmp = x
	else:
		tmp = -2.0 * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.7e+34)
		tmp = x;
	else
		tmp = Float64(-2.0 * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.7e+34)
		tmp = x;
	else
		tmp = -2.0 * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.7e+34], x, N[(-2.0 * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.7e34

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 16.8%

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

   if 2.7e34 < b

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-rgt-neg-in 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around 0 47.8%

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

   7. Taylor expanded in y around 0 20.0%

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

      1. *-commutative 20.0%

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

   9. Simplified 20.0%

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

4. Final simplification 17.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 16.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

3. Taylor expanded in x around inf 14.3%

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

4. Final simplification 14.3%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024066 
(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)))