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

Percentage Accurate: 95.3% → 98.0%

Time: 19.5s

Alternatives: 24

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 88.9%

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

4. Final simplification 99.6%

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

Alternative 2: 69.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-41}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a - z\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+60}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+159}:\\ \;\;\;\;z + \left(x + b \cdot \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* z (- 1.0 y))))) (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -5e+72)
     t_2
     (if (<= b 7.8e-194)
       t_1
       (if (<= b 5.6e-41)
         (- x (- (* (+ t -1.0) a) z))
         (if (<= b 2.4e+14)
           t_1
           (if (<= b 7e+60)
             (+ x (* a (- 1.0 t)))
             (if (<= b 3.6e+94)
               t_2
               (if (<= b 7e+127)
                 t_1
                 (if (<= b 2.05e+159)
                   (+ z (+ x (* b (+ t -2.0))))
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -5e+72) {
		tmp = t_2;
	} else if (b <= 7.8e-194) {
		tmp = t_1;
	} else if (b <= 5.6e-41) {
		tmp = x - (((t + -1.0) * a) - z);
	} else if (b <= 2.4e+14) {
		tmp = t_1;
	} else if (b <= 7e+60) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 3.6e+94) {
		tmp = t_2;
	} else if (b <= 7e+127) {
		tmp = t_1;
	} else if (b <= 2.05e+159) {
		tmp = z + (x + (b * (t + -2.0)));
	} 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 + (z * (1.0d0 - y)))
    t_2 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-5d+72)) then
        tmp = t_2
    else if (b <= 7.8d-194) then
        tmp = t_1
    else if (b <= 5.6d-41) then
        tmp = x - (((t + (-1.0d0)) * a) - z)
    else if (b <= 2.4d+14) then
        tmp = t_1
    else if (b <= 7d+60) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 3.6d+94) then
        tmp = t_2
    else if (b <= 7d+127) then
        tmp = t_1
    else if (b <= 2.05d+159) then
        tmp = z + (x + (b * (t + (-2.0d0))))
    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 + (z * (1.0 - y)));
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -5e+72) {
		tmp = t_2;
	} else if (b <= 7.8e-194) {
		tmp = t_1;
	} else if (b <= 5.6e-41) {
		tmp = x - (((t + -1.0) * a) - z);
	} else if (b <= 2.4e+14) {
		tmp = t_1;
	} else if (b <= 7e+60) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 3.6e+94) {
		tmp = t_2;
	} else if (b <= 7e+127) {
		tmp = t_1;
	} else if (b <= 2.05e+159) {
		tmp = z + (x + (b * (t + -2.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z * (1.0 - y)))
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -5e+72:
		tmp = t_2
	elif b <= 7.8e-194:
		tmp = t_1
	elif b <= 5.6e-41:
		tmp = x - (((t + -1.0) * a) - z)
	elif b <= 2.4e+14:
		tmp = t_1
	elif b <= 7e+60:
		tmp = x + (a * (1.0 - t))
	elif b <= 3.6e+94:
		tmp = t_2
	elif b <= 7e+127:
		tmp = t_1
	elif b <= 2.05e+159:
		tmp = z + (x + (b * (t + -2.0)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -5e+72)
		tmp = t_2;
	elseif (b <= 7.8e-194)
		tmp = t_1;
	elseif (b <= 5.6e-41)
		tmp = Float64(x - Float64(Float64(Float64(t + -1.0) * a) - z));
	elseif (b <= 2.4e+14)
		tmp = t_1;
	elseif (b <= 7e+60)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 3.6e+94)
		tmp = t_2;
	elseif (b <= 7e+127)
		tmp = t_1;
	elseif (b <= 2.05e+159)
		tmp = Float64(z + Float64(x + Float64(b * Float64(t + -2.0))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (z * (1.0 - y)));
	t_2 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -5e+72)
		tmp = t_2;
	elseif (b <= 7.8e-194)
		tmp = t_1;
	elseif (b <= 5.6e-41)
		tmp = x - (((t + -1.0) * a) - z);
	elseif (b <= 2.4e+14)
		tmp = t_1;
	elseif (b <= 7e+60)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 3.6e+94)
		tmp = t_2;
	elseif (b <= 7e+127)
		tmp = t_1;
	elseif (b <= 2.05e+159)
		tmp = z + (x + (b * (t + -2.0)));
	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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+72], t$95$2, If[LessEqual[b, 7.8e-194], t$95$1, If[LessEqual[b, 5.6e-41], N[(x - N[(N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e+14], t$95$1, If[LessEqual[b, 7e+60], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e+94], t$95$2, If[LessEqual[b, 7e+127], t$95$1, If[LessEqual[b, 2.05e+159], N[(z + N[(x + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.99999999999999992e72 or 7.0000000000000004e60 < b < 3.59999999999999992e94 or 2.05000000000000007e159 < b

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 92.4%

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

   5. Simplified 94.6%

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

   6. Taylor expanded in a around 0 84.1%

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

   if -4.99999999999999992e72 < b < 7.7999999999999997e-194 or 5.6000000000000003e-41 < b < 2.4e14 or 3.59999999999999992e94 < b < 6.99999999999999956e127

   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 87.9%

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

   4. Taylor expanded in t around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. sub-neg 75.8%

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

      3. metadata-eval 75.8%

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

      4. mul-1-neg 75.8%

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

      5. unsub-neg 75.8%

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

   6. Simplified 75.8%

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

   if 7.7999999999999997e-194 < b < 5.6000000000000003e-41

   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 b around 0 86.2%

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

   4. Taylor expanded in y around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. sub-neg 77.6%

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

      3. metadata-eval 77.6%

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

      4. fma-def 77.6%

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

      5. mul-1-neg 77.6%

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

   6. Simplified 77.6%

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

   7. Taylor expanded in a around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. sub-neg 77.6%

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

      3. metadata-eval 77.6%

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

      4. +-commutative 77.6%

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

      5. sub-neg 77.6%

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

   9. Simplified 77.6%

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

   if 2.4e14 < b < 7.0000000000000004e60

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 inf 78.6%

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

   if 6.99999999999999956e127 < b < 2.05000000000000007e159

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 86.4%

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

      1. sub-neg 86.4%

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

      2. distribute-rgt-in 86.4%

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

      3. +-commutative 86.4%

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

      4. metadata-eval 86.4%

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

   5. Applied egg-rr 86.4%

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

   6. Taylor expanded in y around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. sub-neg 74.5%

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

      3. remove-double-neg 74.5%

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

      4. +-commutative 74.5%

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

      5. *-commutative 74.5%

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

      6. distribute-lft-in 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+72}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-194}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-41}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a - z\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+60}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+94}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+127}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+159}:\\ \;\;\;\;z + \left(x + b \cdot \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ t_3 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{-66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-187}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-280}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 10500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (+ x (* a (- 1.0 t))))
        (t_3 (* (- (+ y t) 2.0) b)))
   (if (<= b -5.2e-66)
     t_3
     (if (<= b -1.6e-107)
       t_1
       (if (<= b -3.2e-114)
         t_3
         (if (<= b -6.2e-187)
           (- x (* y z))
           (if (<= b 1.2e-280)
             (+ x (+ z a))
             (if (<= b 8e-52)
               t_2
               (if (<= b 10500000000.0)
                 t_1
                 (if (<= b 1.15e+61) t_2 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (a * (1.0 - t));
	double t_3 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -5.2e-66) {
		tmp = t_3;
	} else if (b <= -1.6e-107) {
		tmp = t_1;
	} else if (b <= -3.2e-114) {
		tmp = t_3;
	} else if (b <= -6.2e-187) {
		tmp = x - (y * z);
	} else if (b <= 1.2e-280) {
		tmp = x + (z + a);
	} else if (b <= 8e-52) {
		tmp = t_2;
	} else if (b <= 10500000000.0) {
		tmp = t_1;
	} else if (b <= 1.15e+61) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = x + (a * (1.0d0 - t))
    t_3 = ((y + t) - 2.0d0) * b
    if (b <= (-5.2d-66)) then
        tmp = t_3
    else if (b <= (-1.6d-107)) then
        tmp = t_1
    else if (b <= (-3.2d-114)) then
        tmp = t_3
    else if (b <= (-6.2d-187)) then
        tmp = x - (y * z)
    else if (b <= 1.2d-280) then
        tmp = x + (z + a)
    else if (b <= 8d-52) then
        tmp = t_2
    else if (b <= 10500000000.0d0) then
        tmp = t_1
    else if (b <= 1.15d+61) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (a * (1.0 - t));
	double t_3 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -5.2e-66) {
		tmp = t_3;
	} else if (b <= -1.6e-107) {
		tmp = t_1;
	} else if (b <= -3.2e-114) {
		tmp = t_3;
	} else if (b <= -6.2e-187) {
		tmp = x - (y * z);
	} else if (b <= 1.2e-280) {
		tmp = x + (z + a);
	} else if (b <= 8e-52) {
		tmp = t_2;
	} else if (b <= 10500000000.0) {
		tmp = t_1;
	} else if (b <= 1.15e+61) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (a * (1.0 - t))
	t_3 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -5.2e-66:
		tmp = t_3
	elif b <= -1.6e-107:
		tmp = t_1
	elif b <= -3.2e-114:
		tmp = t_3
	elif b <= -6.2e-187:
		tmp = x - (y * z)
	elif b <= 1.2e-280:
		tmp = x + (z + a)
	elif b <= 8e-52:
		tmp = t_2
	elif b <= 10500000000.0:
		tmp = t_1
	elif b <= 1.15e+61:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_3 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -5.2e-66)
		tmp = t_3;
	elseif (b <= -1.6e-107)
		tmp = t_1;
	elseif (b <= -3.2e-114)
		tmp = t_3;
	elseif (b <= -6.2e-187)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= 1.2e-280)
		tmp = Float64(x + Float64(z + a));
	elseif (b <= 8e-52)
		tmp = t_2;
	elseif (b <= 10500000000.0)
		tmp = t_1;
	elseif (b <= 1.15e+61)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (a * (1.0 - t));
	t_3 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -5.2e-66)
		tmp = t_3;
	elseif (b <= -1.6e-107)
		tmp = t_1;
	elseif (b <= -3.2e-114)
		tmp = t_3;
	elseif (b <= -6.2e-187)
		tmp = x - (y * z);
	elseif (b <= 1.2e-280)
		tmp = x + (z + a);
	elseif (b <= 8e-52)
		tmp = t_2;
	elseif (b <= 10500000000.0)
		tmp = t_1;
	elseif (b <= 1.15e+61)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5.2e-66], t$95$3, If[LessEqual[b, -1.6e-107], t$95$1, If[LessEqual[b, -3.2e-114], t$95$3, If[LessEqual[b, -6.2e-187], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-280], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-52], t$95$2, If[LessEqual[b, 10500000000.0], t$95$1, If[LessEqual[b, 1.15e+61], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.1999999999999998e-66 or -1.60000000000000006e-107 < b < -3.2000000000000002e-114 or 1.15e61 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in b around inf 66.4%

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

   if -5.1999999999999998e-66 < b < -1.60000000000000006e-107 or 8.0000000000000001e-52 < b < 1.05e10

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 69.2%

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

   if -3.2000000000000002e-114 < b < -6.20000000000000039e-187

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 95.0%

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

   4. Taylor expanded in y around inf 60.7%

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

   if -6.20000000000000039e-187 < b < 1.1999999999999999e-280

   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 t around 0 94.1%

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

      1. +-commutative 94.1%

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

      2. sub-neg 94.1%

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

      3. metadata-eval 94.1%

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

      4. mul-1-neg 94.1%

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

      5. unsub-neg 94.1%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in y around 0 70.2%

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

      1. neg-mul-1 70.2%

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

   9. Simplified 70.2%

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

   if 1.1999999999999999e-280 < b < 8.0000000000000001e-52 or 1.05e10 < b < 1.15e61

   1. Initial program 96.0%

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

   3. Taylor expanded in b around 0 91.4%

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

   4. Taylor expanded in a around inf 66.6%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-114}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-187}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-280}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-52}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 10500000000:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+61}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ t_3 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{-65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{-196}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 45000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (+ x (* z (- 1.0 y))))
        (t_3 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.3e-65)
     t_3
     (if (<= b 1.8e-302)
       t_2
       (if (<= b 6.9e-196)
         (+ x (- a (* y z)))
         (if (<= b 5.7e-86)
           t_1
           (if (<= b 45000000000000.0) t_2 (if (<= b 1.3e+60) t_1 t_3))))))))

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 = x + (z * (1.0 - y));
	double t_3 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.3e-65) {
		tmp = t_3;
	} else if (b <= 1.8e-302) {
		tmp = t_2;
	} else if (b <= 6.9e-196) {
		tmp = x + (a - (y * z));
	} else if (b <= 5.7e-86) {
		tmp = t_1;
	} else if (b <= 45000000000000.0) {
		tmp = t_2;
	} else if (b <= 1.3e+60) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = x + (z * (1.0d0 - y))
    t_3 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-1.3d-65)) then
        tmp = t_3
    else if (b <= 1.8d-302) then
        tmp = t_2
    else if (b <= 6.9d-196) then
        tmp = x + (a - (y * z))
    else if (b <= 5.7d-86) then
        tmp = t_1
    else if (b <= 45000000000000.0d0) then
        tmp = t_2
    else if (b <= 1.3d+60) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (z * (1.0 - y));
	double t_3 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.3e-65) {
		tmp = t_3;
	} else if (b <= 1.8e-302) {
		tmp = t_2;
	} else if (b <= 6.9e-196) {
		tmp = x + (a - (y * z));
	} else if (b <= 5.7e-86) {
		tmp = t_1;
	} else if (b <= 45000000000000.0) {
		tmp = t_2;
	} else if (b <= 1.3e+60) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x + (z * (1.0 - y))
	t_3 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -1.3e-65:
		tmp = t_3
	elif b <= 1.8e-302:
		tmp = t_2
	elif b <= 6.9e-196:
		tmp = x + (a - (y * z))
	elif b <= 5.7e-86:
		tmp = t_1
	elif b <= 45000000000000.0:
		tmp = t_2
	elif b <= 1.3e+60:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_3 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.3e-65)
		tmp = t_3;
	elseif (b <= 1.8e-302)
		tmp = t_2;
	elseif (b <= 6.9e-196)
		tmp = Float64(x + Float64(a - Float64(y * z)));
	elseif (b <= 5.7e-86)
		tmp = t_1;
	elseif (b <= 45000000000000.0)
		tmp = t_2;
	elseif (b <= 1.3e+60)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = x + (z * (1.0 - y));
	t_3 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -1.3e-65)
		tmp = t_3;
	elseif (b <= 1.8e-302)
		tmp = t_2;
	elseif (b <= 6.9e-196)
		tmp = x + (a - (y * z));
	elseif (b <= 5.7e-86)
		tmp = t_1;
	elseif (b <= 45000000000000.0)
		tmp = t_2;
	elseif (b <= 1.3e+60)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e-65], t$95$3, If[LessEqual[b, 1.8e-302], t$95$2, If[LessEqual[b, 6.9e-196], N[(x + N[(a - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.7e-86], t$95$1, If[LessEqual[b, 45000000000000.0], t$95$2, If[LessEqual[b, 1.3e+60], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.30000000000000005e-65 or 1.30000000000000004e60 < b

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 85.1%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in a around 0 72.4%

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

   if -1.30000000000000005e-65 < b < 1.8e-302 or 5.7000000000000004e-86 < b < 4.5e13

   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 90.3%

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

   4. Taylor expanded in a around 0 69.5%

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

   if 1.8e-302 < b < 6.89999999999999958e-196

   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 t around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. sub-neg 90.5%

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

      3. metadata-eval 90.5%

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

      4. mul-1-neg 90.5%

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

      5. unsub-neg 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in y around inf 85.7%

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

   if 6.89999999999999958e-196 < b < 5.7000000000000004e-86 or 4.5e13 < b < 1.30000000000000004e60

   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 b around 0 90.4%

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

   4. Taylor expanded in a around inf 71.5%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-65}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-302}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{-196}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 45000000000000:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+60}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ t_2 := z + \left(x + \left(\left(y + t\right) - 2\right) \cdot b\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{-40}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a - z\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+60}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* z (- 1.0 y)))))
        (t_2 (+ z (+ x (* (- (+ y t) 2.0) b)))))
   (if (<= b -2.5e+68)
     t_2
     (if (<= b 2.05e-195)
       t_1
       (if (<= b 6.9e-40)
         (- x (- (* (+ t -1.0) a) z))
         (if (<= b 2.5e+14)
           t_1
           (if (<= b 1.2e+60) (+ x (* a (- 1.0 t))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = z + (x + (((y + t) - 2.0) * b));
	double tmp;
	if (b <= -2.5e+68) {
		tmp = t_2;
	} else if (b <= 2.05e-195) {
		tmp = t_1;
	} else if (b <= 6.9e-40) {
		tmp = x - (((t + -1.0) * a) - z);
	} else if (b <= 2.5e+14) {
		tmp = t_1;
	} else if (b <= 1.2e+60) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a + (z * (1.0d0 - y)))
    t_2 = z + (x + (((y + t) - 2.0d0) * b))
    if (b <= (-2.5d+68)) then
        tmp = t_2
    else if (b <= 2.05d-195) then
        tmp = t_1
    else if (b <= 6.9d-40) then
        tmp = x - (((t + (-1.0d0)) * a) - z)
    else if (b <= 2.5d+14) then
        tmp = t_1
    else if (b <= 1.2d+60) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = z + (x + (((y + t) - 2.0) * b));
	double tmp;
	if (b <= -2.5e+68) {
		tmp = t_2;
	} else if (b <= 2.05e-195) {
		tmp = t_1;
	} else if (b <= 6.9e-40) {
		tmp = x - (((t + -1.0) * a) - z);
	} else if (b <= 2.5e+14) {
		tmp = t_1;
	} else if (b <= 1.2e+60) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z * (1.0 - y)))
	t_2 = z + (x + (((y + t) - 2.0) * b))
	tmp = 0
	if b <= -2.5e+68:
		tmp = t_2
	elif b <= 2.05e-195:
		tmp = t_1
	elif b <= 6.9e-40:
		tmp = x - (((t + -1.0) * a) - z)
	elif b <= 2.5e+14:
		tmp = t_1
	elif b <= 1.2e+60:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(z + Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)))
	tmp = 0.0
	if (b <= -2.5e+68)
		tmp = t_2;
	elseif (b <= 2.05e-195)
		tmp = t_1;
	elseif (b <= 6.9e-40)
		tmp = Float64(x - Float64(Float64(Float64(t + -1.0) * a) - z));
	elseif (b <= 2.5e+14)
		tmp = t_1;
	elseif (b <= 1.2e+60)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (z * (1.0 - y)));
	t_2 = z + (x + (((y + t) - 2.0) * b));
	tmp = 0.0;
	if (b <= -2.5e+68)
		tmp = t_2;
	elseif (b <= 2.05e-195)
		tmp = t_1;
	elseif (b <= 6.9e-40)
		tmp = x - (((t + -1.0) * a) - z);
	elseif (b <= 2.5e+14)
		tmp = t_1;
	elseif (b <= 1.2e+60)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+68], t$95$2, If[LessEqual[b, 2.05e-195], t$95$1, If[LessEqual[b, 6.9e-40], N[(x - N[(N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+14], t$95$1, If[LessEqual[b, 1.2e+60], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.5000000000000002e68 or 1.2e60 < b

   1. Initial program 94.2%

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

   3. Taylor expanded in a around 0 84.9%

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

   4. Taylor expanded in y around 0 85.4%

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

      1. mul-1-neg 85.4%

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

   6. Simplified 85.4%

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

   if -2.5000000000000002e68 < b < 2.05000000000000006e-195 or 6.8999999999999996e-40 < b < 2.5e14

   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 87.1%

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

   4. Taylor expanded in t around 0 74.3%

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

      1. +-commutative 74.3%

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

      2. sub-neg 74.3%

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

      3. metadata-eval 74.3%

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

      4. mul-1-neg 74.3%

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

      5. unsub-neg 74.3%

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

   6. Simplified 74.3%

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

   if 2.05000000000000006e-195 < b < 6.8999999999999996e-40

   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 b around 0 86.2%

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

   4. Taylor expanded in y around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. sub-neg 77.6%

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

      3. metadata-eval 77.6%

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

      4. fma-def 77.6%

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

      5. mul-1-neg 77.6%

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

   6. Simplified 77.6%

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

   7. Taylor expanded in a around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. sub-neg 77.6%

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

      3. metadata-eval 77.6%

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

      4. +-commutative 77.6%

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

      5. sub-neg 77.6%

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

   9. Simplified 77.6%

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

   if 2.5e14 < b < 1.2e60

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 inf 78.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+68}:\\ \;\;\;\;z + \left(x + \left(\left(y + t\right) - 2\right) \cdot b\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-195}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{-40}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a - z\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+14}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+60}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \left(\left(y + t\right) - 2\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-67}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y))))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ x (* a (- 1.0 t)))))
   (if (<= b -1.3e-65)
     t_2
     (if (<= b 9e-300)
       t_1
       (if (<= b 5.5e-67)
         t_3
         (if (<= b 4500000000.0) t_1 (if (<= b 1.3e+61) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -1.3e-65) {
		tmp = t_2;
	} else if (b <= 9e-300) {
		tmp = t_1;
	} else if (b <= 5.5e-67) {
		tmp = t_3;
	} else if (b <= 4500000000.0) {
		tmp = t_1;
	} else if (b <= 1.3e+61) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = x + (a * (1.0d0 - t))
    if (b <= (-1.3d-65)) then
        tmp = t_2
    else if (b <= 9d-300) then
        tmp = t_1
    else if (b <= 5.5d-67) then
        tmp = t_3
    else if (b <= 4500000000.0d0) then
        tmp = t_1
    else if (b <= 1.3d+61) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -1.3e-65) {
		tmp = t_2;
	} else if (b <= 9e-300) {
		tmp = t_1;
	} else if (b <= 5.5e-67) {
		tmp = t_3;
	} else if (b <= 4500000000.0) {
		tmp = t_1;
	} else if (b <= 1.3e+61) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = ((y + t) - 2.0) * b
	t_3 = x + (a * (1.0 - t))
	tmp = 0
	if b <= -1.3e-65:
		tmp = t_2
	elif b <= 9e-300:
		tmp = t_1
	elif b <= 5.5e-67:
		tmp = t_3
	elif b <= 4500000000.0:
		tmp = t_1
	elif b <= 1.3e+61:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (b <= -1.3e-65)
		tmp = t_2;
	elseif (b <= 9e-300)
		tmp = t_1;
	elseif (b <= 5.5e-67)
		tmp = t_3;
	elseif (b <= 4500000000.0)
		tmp = t_1;
	elseif (b <= 1.3e+61)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = ((y + t) - 2.0) * b;
	t_3 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (b <= -1.3e-65)
		tmp = t_2;
	elseif (b <= 9e-300)
		tmp = t_1;
	elseif (b <= 5.5e-67)
		tmp = t_3;
	elseif (b <= 4500000000.0)
		tmp = t_1;
	elseif (b <= 1.3e+61)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e-65], t$95$2, If[LessEqual[b, 9e-300], t$95$1, If[LessEqual[b, 5.5e-67], t$95$3, If[LessEqual[b, 4500000000.0], t$95$1, If[LessEqual[b, 1.3e+61], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.30000000000000005e-65 or 1.29999999999999986e61 < b

   1. Initial program 94.5%

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

   3. Taylor expanded in b around inf 65.6%

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

   if -1.30000000000000005e-65 < b < 9.0000000000000001e-300 or 5.5000000000000003e-67 < b < 4.5e9

   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 90.3%

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

   4. Taylor expanded in a around 0 69.5%

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

   if 9.0000000000000001e-300 < b < 5.5000000000000003e-67 or 4.5e9 < b < 1.29999999999999986e61

   1. Initial program 96.4%

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

   3. Taylor expanded in b around 0 93.9%

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

   4. Taylor expanded in a around inf 67.8%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-65}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-300}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-67}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4500000000:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+61}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-154}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-91}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-87}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 130000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -5e+20)
     t_1
     (if (<= y 1.65e-154)
       (+ x (+ z a))
       (if (<= y 6.8e-91)
         (* (- (+ y t) 2.0) b)
         (if (<= y 2.3e-87) z (if (<= y 130000000.0) (* t (- b a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -5e+20) {
		tmp = t_1;
	} else if (y <= 1.65e-154) {
		tmp = x + (z + a);
	} else if (y <= 6.8e-91) {
		tmp = ((y + t) - 2.0) * b;
	} else if (y <= 2.3e-87) {
		tmp = z;
	} else if (y <= 130000000.0) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-5d+20)) then
        tmp = t_1
    else if (y <= 1.65d-154) then
        tmp = x + (z + a)
    else if (y <= 6.8d-91) then
        tmp = ((y + t) - 2.0d0) * b
    else if (y <= 2.3d-87) then
        tmp = z
    else if (y <= 130000000.0d0) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -5e+20) {
		tmp = t_1;
	} else if (y <= 1.65e-154) {
		tmp = x + (z + a);
	} else if (y <= 6.8e-91) {
		tmp = ((y + t) - 2.0) * b;
	} else if (y <= 2.3e-87) {
		tmp = z;
	} else if (y <= 130000000.0) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -5e+20:
		tmp = t_1
	elif y <= 1.65e-154:
		tmp = x + (z + a)
	elif y <= 6.8e-91:
		tmp = ((y + t) - 2.0) * b
	elif y <= 2.3e-87:
		tmp = z
	elif y <= 130000000.0:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -5e+20)
		tmp = t_1;
	elseif (y <= 1.65e-154)
		tmp = Float64(x + Float64(z + a));
	elseif (y <= 6.8e-91)
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	elseif (y <= 2.3e-87)
		tmp = z;
	elseif (y <= 130000000.0)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -5e+20)
		tmp = t_1;
	elseif (y <= 1.65e-154)
		tmp = x + (z + a);
	elseif (y <= 6.8e-91)
		tmp = ((y + t) - 2.0) * b;
	elseif (y <= 2.3e-87)
		tmp = z;
	elseif (y <= 130000000.0)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+20], t$95$1, If[LessEqual[y, 1.65e-154], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-91], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[y, 2.3e-87], z, If[LessEqual[y, 130000000.0], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5e20 or 1.3e8 < y

   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 y around inf 70.7%

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

   if -5e20 < y < 1.65000000000000014e-154

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 72.6%

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

   4. Taylor expanded in t around 0 54.9%

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

      1. +-commutative 54.9%

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

      2. sub-neg 54.9%

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

      3. metadata-eval 54.9%

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

      4. mul-1-neg 54.9%

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

      5. unsub-neg 54.9%

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

   6. Simplified 54.9%

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

   7. Taylor expanded in y around 0 54.9%

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

      1. neg-mul-1 54.9%

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

   9. Simplified 54.9%

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

   if 1.65000000000000014e-154 < y < 6.80000000000000053e-91

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 65.3%

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

   if 6.80000000000000053e-91 < y < 2.3000000000000001e-87

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   if 2.3000000000000001e-87 < y < 1.3e8

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 64.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-154}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-91}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-87}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 130000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - y \cdot z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-239}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 140000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- a (* y z)))) (t_2 (* t (- b a))))
   (if (<= t -2.6e+49)
     t_2
     (if (<= t -2.4e-130)
       t_1
       (if (<= t -1.2e-239)
         (* (- (+ y t) 2.0) b)
         (if (<= t 140000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (y * z));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.6e+49) {
		tmp = t_2;
	} else if (t <= -2.4e-130) {
		tmp = t_1;
	} else if (t <= -1.2e-239) {
		tmp = ((y + t) - 2.0) * b;
	} else if (t <= 140000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a - (y * z))
    t_2 = t * (b - a)
    if (t <= (-2.6d+49)) then
        tmp = t_2
    else if (t <= (-2.4d-130)) then
        tmp = t_1
    else if (t <= (-1.2d-239)) then
        tmp = ((y + t) - 2.0d0) * b
    else if (t <= 140000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (y * z));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.6e+49) {
		tmp = t_2;
	} else if (t <= -2.4e-130) {
		tmp = t_1;
	} else if (t <= -1.2e-239) {
		tmp = ((y + t) - 2.0) * b;
	} else if (t <= 140000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a - (y * z))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -2.6e+49:
		tmp = t_2
	elif t <= -2.4e-130:
		tmp = t_1
	elif t <= -1.2e-239:
		tmp = ((y + t) - 2.0) * b
	elif t <= 140000000000.0:
		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(y * z)))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.6e+49)
		tmp = t_2;
	elseif (t <= -2.4e-130)
		tmp = t_1;
	elseif (t <= -1.2e-239)
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	elseif (t <= 140000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a - (y * z));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.6e+49)
		tmp = t_2;
	elseif (t <= -2.4e-130)
		tmp = t_1;
	elseif (t <= -1.2e-239)
		tmp = ((y + t) - 2.0) * b;
	elseif (t <= 140000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+49], t$95$2, If[LessEqual[t, -2.4e-130], t$95$1, If[LessEqual[t, -1.2e-239], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 140000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.59999999999999989e49 or 1.4e11 < t

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf 67.1%

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

   if -2.59999999999999989e49 < t < -2.39999999999999997e-130 or -1.19999999999999996e-239 < t < 1.4e11

   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 78.6%

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

   4. Taylor expanded in t around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. sub-neg 76.9%

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

      3. metadata-eval 76.9%

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

      4. mul-1-neg 76.9%

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

      5. unsub-neg 76.9%

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

   6. Simplified 76.9%

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

   7. Taylor expanded in y around inf 67.5%

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

   if -2.39999999999999997e-130 < t < -1.19999999999999996e-239

   1. Initial program 95.5%

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

   3. Taylor expanded in b around inf 64.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-130}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-239}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 140000000000:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-82}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-86}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 140000000000:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2.1e+59)
     t_1
     (if (<= t -2.9e-82)
       (+ x (* z (- 1.0 y)))
       (if (<= t 6.4e-86)
         (+ x (+ a (* b (+ y -2.0))))
         (if (<= t 140000000000.0) (+ x (- a (* y z))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.1e+59) {
		tmp = t_1;
	} else if (t <= -2.9e-82) {
		tmp = x + (z * (1.0 - y));
	} else if (t <= 6.4e-86) {
		tmp = x + (a + (b * (y + -2.0)));
	} else if (t <= 140000000000.0) {
		tmp = x + (a - (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-2.1d+59)) then
        tmp = t_1
    else if (t <= (-2.9d-82)) then
        tmp = x + (z * (1.0d0 - y))
    else if (t <= 6.4d-86) then
        tmp = x + (a + (b * (y + (-2.0d0))))
    else if (t <= 140000000000.0d0) then
        tmp = x + (a - (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.1e+59) {
		tmp = t_1;
	} else if (t <= -2.9e-82) {
		tmp = x + (z * (1.0 - y));
	} else if (t <= 6.4e-86) {
		tmp = x + (a + (b * (y + -2.0)));
	} else if (t <= 140000000000.0) {
		tmp = x + (a - (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2.1e+59:
		tmp = t_1
	elif t <= -2.9e-82:
		tmp = x + (z * (1.0 - y))
	elif t <= 6.4e-86:
		tmp = x + (a + (b * (y + -2.0)))
	elif t <= 140000000000.0:
		tmp = x + (a - (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.1e+59)
		tmp = t_1;
	elseif (t <= -2.9e-82)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (t <= 6.4e-86)
		tmp = Float64(x + Float64(a + Float64(b * Float64(y + -2.0))));
	elseif (t <= 140000000000.0)
		tmp = Float64(x + Float64(a - Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.1e+59)
		tmp = t_1;
	elseif (t <= -2.9e-82)
		tmp = x + (z * (1.0 - y));
	elseif (t <= 6.4e-86)
		tmp = x + (a + (b * (y + -2.0)));
	elseif (t <= 140000000000.0)
		tmp = x + (a - (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+59], t$95$1, If[LessEqual[t, -2.9e-82], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e-86], N[(x + N[(a + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 140000000000.0], N[(x + N[(a - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.09999999999999984e59 or 1.4e11 < t

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf 67.1%

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

   if -2.09999999999999984e59 < t < -2.89999999999999977e-82

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 76.4%

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

   4. Taylor expanded in a around 0 70.4%

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

   if -2.89999999999999977e-82 < t < 6.40000000000000011e-86

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in t around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. sub-neg 75.5%

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

      3. metadata-eval 75.5%

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

   8. Simplified 75.5%

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

   if 6.40000000000000011e-86 < t < 1.4e11

   1. Initial program 96.0%

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

   3. Taylor expanded in b around 0 94.1%

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

   4. Taylor expanded in t around 0 88.0%

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

      1. +-commutative 88.0%

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

      2. sub-neg 88.0%

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

      3. metadata-eval 88.0%

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

      4. mul-1-neg 88.0%

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

      5. unsub-neg 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in y around inf 84.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-82}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-86}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 140000000000:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-155}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 10500000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* y (- z))))
   (if (<= y -1.16e+104)
     t_2
     (if (<= y -2.25e-185)
       t_1
       (if (<= y 2.1e-155) (+ x z) (if (<= y 10500000000000.0) 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 = y * -z;
	double tmp;
	if (y <= -1.16e+104) {
		tmp = t_2;
	} else if (y <= -2.25e-185) {
		tmp = t_1;
	} else if (y <= 2.1e-155) {
		tmp = x + z;
	} else if (y <= 10500000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = y * -z
    if (y <= (-1.16d+104)) then
        tmp = t_2
    else if (y <= (-2.25d-185)) then
        tmp = t_1
    else if (y <= 2.1d-155) then
        tmp = x + z
    else if (y <= 10500000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = y * -z;
	double tmp;
	if (y <= -1.16e+104) {
		tmp = t_2;
	} else if (y <= -2.25e-185) {
		tmp = t_1;
	} else if (y <= 2.1e-155) {
		tmp = x + z;
	} else if (y <= 10500000000000.0) {
		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 = y * -z
	tmp = 0
	if y <= -1.16e+104:
		tmp = t_2
	elif y <= -2.25e-185:
		tmp = t_1
	elif y <= 2.1e-155:
		tmp = x + z
	elif y <= 10500000000000.0:
		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(y * Float64(-z))
	tmp = 0.0
	if (y <= -1.16e+104)
		tmp = t_2;
	elseif (y <= -2.25e-185)
		tmp = t_1;
	elseif (y <= 2.1e-155)
		tmp = Float64(x + z);
	elseif (y <= 10500000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = y * -z;
	tmp = 0.0;
	if (y <= -1.16e+104)
		tmp = t_2;
	elseif (y <= -2.25e-185)
		tmp = t_1;
	elseif (y <= 2.1e-155)
		tmp = x + z;
	elseif (y <= 10500000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.16e+104], t$95$2, If[LessEqual[y, -2.25e-185], t$95$1, If[LessEqual[y, 2.1e-155], N[(x + z), $MachinePrecision], If[LessEqual[y, 10500000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1599999999999999e104 or 1.05e13 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in z around inf 49.0%

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

   4. Taylor expanded in y around inf 48.9%

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

      1. mul-1-neg 48.9%

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

      2. distribute-rgt-neg-in 48.9%

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

   6. Simplified 48.9%

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

   if -1.1599999999999999e104 < y < -2.2500000000000001e-185 or 2.1000000000000002e-155 < y < 1.05e13

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 41.0%

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

   if -2.2500000000000001e-185 < y < 2.1000000000000002e-155

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 76.2%

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

   4. Taylor expanded in y around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. sub-neg 76.2%

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

      3. metadata-eval 76.2%

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

      4. fma-def 76.2%

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

      5. mul-1-neg 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in a around 0 45.0%

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

      1. mul-1-neg 45.0%

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

   9. Simplified 45.0%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-155}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 10500000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-154}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 190000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -4.3e+103)
     t_1
     (if (<= y -2.2e-185)
       (* a (- 1.0 t))
       (if (<= y 1.5e-154)
         (+ x z)
         (if (<= y 190000000.0) (* t (- b a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.3e+103) {
		tmp = t_1;
	} else if (y <= -2.2e-185) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.5e-154) {
		tmp = x + z;
	} else if (y <= 190000000.0) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-4.3d+103)) then
        tmp = t_1
    else if (y <= (-2.2d-185)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 1.5d-154) then
        tmp = x + z
    else if (y <= 190000000.0d0) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.3e+103) {
		tmp = t_1;
	} else if (y <= -2.2e-185) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.5e-154) {
		tmp = x + z;
	} else if (y <= 190000000.0) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -4.3e+103:
		tmp = t_1
	elif y <= -2.2e-185:
		tmp = a * (1.0 - t)
	elif y <= 1.5e-154:
		tmp = x + z
	elif y <= 190000000.0:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4.3e+103)
		tmp = t_1;
	elseif (y <= -2.2e-185)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 1.5e-154)
		tmp = Float64(x + z);
	elseif (y <= 190000000.0)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -4.3e+103)
		tmp = t_1;
	elseif (y <= -2.2e-185)
		tmp = a * (1.0 - t);
	elseif (y <= 1.5e-154)
		tmp = x + z;
	elseif (y <= 190000000.0)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+103], t$95$1, If[LessEqual[y, -2.2e-185], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-154], N[(x + z), $MachinePrecision], If[LessEqual[y, 190000000.0], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.29999999999999969e103 or 1.9e8 < y

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 75.1%

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

   if -4.29999999999999969e103 < y < -2.2e-185

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 42.9%

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

   if -2.2e-185 < y < 1.5000000000000001e-154

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 76.6%

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

   4. Taylor expanded in y around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. sub-neg 76.6%

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

      3. metadata-eval 76.6%

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

      4. fma-def 76.7%

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

      5. mul-1-neg 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in a around 0 44.2%

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

      1. mul-1-neg 44.2%

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

   9. Simplified 44.2%

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

   if 1.5000000000000001e-154 < y < 1.9e8

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 56.2%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+103}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-154}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 190000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -3.65 \cdot 10^{-32}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+62}:\\ \;\;\;\;x + \left(t_3 + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (+ x (* (- (+ y t) 2.0) b)))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -3.65e-32)
     (+ t_2 t_1)
     (if (<= b 4.5e+62) (+ x (+ t_3 t_1)) (+ t_2 t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (((y + t) - 2.0) * b);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -3.65e-32) {
		tmp = t_2 + t_1;
	} else if (b <= 4.5e+62) {
		tmp = x + (t_3 + t_1);
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (((y + t) - 2.0d0) * b)
    t_3 = z * (1.0d0 - y)
    if (b <= (-3.65d-32)) then
        tmp = t_2 + t_1
    else if (b <= 4.5d+62) then
        tmp = x + (t_3 + t_1)
    else
        tmp = t_2 + t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (((y + t) - 2.0) * b);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -3.65e-32) {
		tmp = t_2 + t_1;
	} else if (b <= 4.5e+62) {
		tmp = x + (t_3 + t_1);
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (((y + t) - 2.0) * b)
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -3.65e-32:
		tmp = t_2 + t_1
	elif b <= 4.5e+62:
		tmp = x + (t_3 + t_1)
	else:
		tmp = t_2 + t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -3.65e-32)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 4.5e+62)
		tmp = Float64(x + Float64(t_3 + t_1));
	else
		tmp = Float64(t_2 + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (((y + t) - 2.0) * b);
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -3.65e-32)
		tmp = t_2 + t_1;
	elseif (b <= 4.5e+62)
		tmp = x + (t_3 + t_1);
	else
		tmp = t_2 + t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.65e-32], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 4.5e+62], N[(x + N[(t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.65000000000000024e-32

   1. Initial program 92.4%

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

   3. Taylor expanded in z around 0 84.9%

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

   if -3.65000000000000024e-32 < b < 4.49999999999999999e62

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 91.4%

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

   if 4.49999999999999999e62 < b

   1. Initial program 96.5%

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

   3. Taylor expanded in a around 0 91.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.65 \cdot 10^{-32}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+62}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 34.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-24}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 170000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= t -9.5e+58)
     (* t b)
     (if (<= t -9e-83)
       t_1
       (if (<= t 3.1e-24) (+ x a) (if (<= t 170000000000.0) t_1 (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (t <= -9.5e+58) {
		tmp = t * b;
	} else if (t <= -9e-83) {
		tmp = t_1;
	} else if (t <= 3.1e-24) {
		tmp = x + a;
	} else if (t <= 170000000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (t <= (-9.5d+58)) then
        tmp = t * b
    else if (t <= (-9d-83)) then
        tmp = t_1
    else if (t <= 3.1d-24) then
        tmp = x + a
    else if (t <= 170000000000.0d0) then
        tmp = t_1
    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 t_1 = y * -z;
	double tmp;
	if (t <= -9.5e+58) {
		tmp = t * b;
	} else if (t <= -9e-83) {
		tmp = t_1;
	} else if (t <= 3.1e-24) {
		tmp = x + a;
	} else if (t <= 170000000000.0) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if t <= -9.5e+58:
		tmp = t * b
	elif t <= -9e-83:
		tmp = t_1
	elif t <= 3.1e-24:
		tmp = x + a
	elif t <= 170000000000.0:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (t <= -9.5e+58)
		tmp = Float64(t * b);
	elseif (t <= -9e-83)
		tmp = t_1;
	elseif (t <= 3.1e-24)
		tmp = Float64(x + a);
	elseif (t <= 170000000000.0)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (t <= -9.5e+58)
		tmp = t * b;
	elseif (t <= -9e-83)
		tmp = t_1;
	elseif (t <= 3.1e-24)
		tmp = x + a;
	elseif (t <= 170000000000.0)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[t, -9.5e+58], N[(t * b), $MachinePrecision], If[LessEqual[t, -9e-83], t$95$1, If[LessEqual[t, 3.1e-24], N[(x + a), $MachinePrecision], If[LessEqual[t, 170000000000.0], t$95$1, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5000000000000002e58 or 1.7e11 < t

   1. Initial program 93.7%

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

   3. Taylor expanded in a around 0 66.2%

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

      1. sub-neg 66.2%

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

      2. distribute-rgt-in 66.2%

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

      3. +-commutative 66.2%

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

      4. metadata-eval 66.2%

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

   5. Applied egg-rr 66.2%

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

   6. Taylor expanded in t around inf 35.9%

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

   if -9.5000000000000002e58 < t < -8.99999999999999995e-83 or 3.1e-24 < t < 1.7e11

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 60.8%

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

   4. Taylor expanded in y around inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. distribute-rgt-neg-in 54.5%

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

   6. Simplified 54.5%

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

   if -8.99999999999999995e-83 < t < 3.1e-24

   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 z around 0 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in t around 0 74.3%

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

      1. +-commutative 74.3%

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

      2. sub-neg 74.3%

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

      3. metadata-eval 74.3%

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

   8. Simplified 74.3%

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

   9. Taylor expanded in b around 0 41.3%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-24}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 170000000000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-24}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;y \leq 3850000000:\\ \;\;\;\;z + \left(x + b \cdot \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.9e+110)
     t_1
     (if (<= y -4.5e-24)
       (+ x (- a (* y z)))
       (if (<= y 3850000000.0) (+ z (+ x (* b (+ t -2.0)))) 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 <= -2.9e+110) {
		tmp = t_1;
	} else if (y <= -4.5e-24) {
		tmp = x + (a - (y * z));
	} else if (y <= 3850000000.0) {
		tmp = z + (x + (b * (t + -2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-2.9d+110)) then
        tmp = t_1
    else if (y <= (-4.5d-24)) then
        tmp = x + (a - (y * z))
    else if (y <= 3850000000.0d0) then
        tmp = z + (x + (b * (t + (-2.0d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.9e+110) {
		tmp = t_1;
	} else if (y <= -4.5e-24) {
		tmp = x + (a - (y * z));
	} else if (y <= 3850000000.0) {
		tmp = z + (x + (b * (t + -2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2.9e+110:
		tmp = t_1
	elif y <= -4.5e-24:
		tmp = x + (a - (y * z))
	elif y <= 3850000000.0:
		tmp = z + (x + (b * (t + -2.0)))
	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 <= -2.9e+110)
		tmp = t_1;
	elseif (y <= -4.5e-24)
		tmp = Float64(x + Float64(a - Float64(y * z)));
	elseif (y <= 3850000000.0)
		tmp = Float64(z + Float64(x + Float64(b * Float64(t + -2.0))));
	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 <= -2.9e+110)
		tmp = t_1;
	elseif (y <= -4.5e-24)
		tmp = x + (a - (y * z));
	elseif (y <= 3850000000.0)
		tmp = z + (x + (b * (t + -2.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+110], t$95$1, If[LessEqual[y, -4.5e-24], N[(x + N[(a - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3850000000.0], N[(z + N[(x + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9e110 or 3.85e9 < y

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 76.2%

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

   if -2.9e110 < y < -4.4999999999999997e-24

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 88.1%

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

   4. Taylor expanded in t around 0 66.6%

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

      1. +-commutative 66.6%

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

      2. sub-neg 66.6%

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

      3. metadata-eval 66.6%

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

      4. mul-1-neg 66.6%

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

      5. unsub-neg 66.6%

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

   6. Simplified 66.6%

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

   7. Taylor expanded in y around inf 66.6%

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

   if -4.4999999999999997e-24 < y < 3.85e9

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 65.9%

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

      1. sub-neg 65.9%

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

      2. distribute-rgt-in 65.9%

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

      3. +-commutative 65.9%

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

      4. metadata-eval 65.9%

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

   5. Applied egg-rr 65.9%

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

   6. Taylor expanded in y around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. sub-neg 64.8%

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

      3. remove-double-neg 64.8%

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

      4. +-commutative 64.8%

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

      5. *-commutative 64.8%

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

      6. distribute-lft-in 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-24}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;y \leq 3850000000:\\ \;\;\;\;z + \left(x + b \cdot \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-278}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+61}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.3e-65)
     t_1
     (if (<= b -5.1e-278)
       (+ x (* z (- 1.0 y)))
       (if (<= b 3e+61) (- x (- (* (+ t -1.0) a) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.3e-65) {
		tmp = t_1;
	} else if (b <= -5.1e-278) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 3e+61) {
		tmp = x - (((t + -1.0) * a) - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-1.3d-65)) then
        tmp = t_1
    else if (b <= (-5.1d-278)) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 3d+61) then
        tmp = x - (((t + (-1.0d0)) * a) - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.3e-65) {
		tmp = t_1;
	} else if (b <= -5.1e-278) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 3e+61) {
		tmp = x - (((t + -1.0) * a) - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -1.3e-65:
		tmp = t_1
	elif b <= -5.1e-278:
		tmp = x + (z * (1.0 - y))
	elif b <= 3e+61:
		tmp = x - (((t + -1.0) * a) - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.3e-65)
		tmp = t_1;
	elseif (b <= -5.1e-278)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 3e+61)
		tmp = Float64(x - Float64(Float64(Float64(t + -1.0) * a) - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -1.3e-65)
		tmp = t_1;
	elseif (b <= -5.1e-278)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 3e+61)
		tmp = x - (((t + -1.0) * a) - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e-65], t$95$1, If[LessEqual[b, -5.1e-278], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+61], N[(x - N[(N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.30000000000000005e-65 or 3e61 < b

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 85.1%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in a around 0 72.4%

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

   if -1.30000000000000005e-65 < b < -5.10000000000000011e-278

   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 91.8%

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

   4. Taylor expanded in a around 0 70.2%

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

   if -5.10000000000000011e-278 < b < 3e61

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0 91.9%

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

   4. Taylor expanded in y around 0 70.6%

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

      1. +-commutative 70.6%

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

      2. sub-neg 70.6%

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

      3. metadata-eval 70.6%

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

      4. fma-def 70.6%

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

      5. mul-1-neg 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in a around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. sub-neg 70.6%

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

      3. metadata-eval 70.6%

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

      4. +-commutative 70.6%

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

      5. sub-neg 70.6%

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

   9. Simplified 70.6%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-65}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-278}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+61}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 85.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+72} \lor \neg \left(b \leq 6.5 \cdot 10^{+63}\right):\\ \;\;\;\;z + \left(x + \left(\left(y + t\right) - 2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.3e+72) (not (<= b 6.5e+63)))
   (+ z (+ x (* (- (+ y t) 2.0) b)))
   (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e+72) || !(b <= 6.5e+63)) {
		tmp = z + (x + (((y + t) - 2.0) * b));
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.3d+72)) .or. (.not. (b <= 6.5d+63))) then
        tmp = z + (x + (((y + t) - 2.0d0) * b))
    else
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e+72) || !(b <= 6.5e+63)) {
		tmp = z + (x + (((y + t) - 2.0) * b));
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.3e+72) or not (b <= 6.5e+63):
		tmp = z + (x + (((y + t) - 2.0) * b))
	else:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.3e+72) || !(b <= 6.5e+63))
		tmp = Float64(z + Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.3e+72) || ~((b <= 6.5e+63)))
		tmp = z + (x + (((y + t) - 2.0) * b));
	else
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.3e+72], N[Not[LessEqual[b, 6.5e+63]], $MachinePrecision]], N[(z + N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.29999999999999991e72 or 6.49999999999999992e63 < b

   1. Initial program 94.2%

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

   3. Taylor expanded in a around 0 84.9%

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

   4. Taylor expanded in y around 0 85.4%

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

      1. mul-1-neg 85.4%

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

   6. Simplified 85.4%

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

   if -1.29999999999999991e72 < b < 6.49999999999999992e63

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0 87.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+72} \lor \neg \left(b \leq 6.5 \cdot 10^{+63}\right):\\ \;\;\;\;z + \left(x + \left(\left(y + t\right) - 2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 86.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.32 \cdot 10^{-32}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+62}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;z + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -2.32e-32)
     (+ t_2 t_1)
     (if (<= b 1.25e+62) (+ x (+ (* z (- 1.0 y)) t_1)) (+ z t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.32e-32) {
		tmp = t_2 + t_1;
	} else if (b <= 1.25e+62) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = z + 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 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-2.32d-32)) then
        tmp = t_2 + t_1
    else if (b <= 1.25d+62) then
        tmp = x + ((z * (1.0d0 - y)) + t_1)
    else
        tmp = z + 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 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.32e-32) {
		tmp = t_2 + t_1;
	} else if (b <= 1.25e+62) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = z + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -2.32e-32:
		tmp = t_2 + t_1
	elif b <= 1.25e+62:
		tmp = x + ((z * (1.0 - y)) + t_1)
	else:
		tmp = z + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -2.32e-32)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 1.25e+62)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	else
		tmp = Float64(z + 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 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -2.32e-32)
		tmp = t_2 + t_1;
	elseif (b <= 1.25e+62)
		tmp = x + ((z * (1.0 - y)) + t_1);
	else
		tmp = z + 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[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.32e-32], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 1.25e+62], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(z + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.32000000000000002e-32

   1. Initial program 92.4%

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

   3. Taylor expanded in z around 0 84.9%

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

   if -2.32000000000000002e-32 < b < 1.25000000000000007e62

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 91.4%

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

   if 1.25000000000000007e62 < b

   1. Initial program 96.5%

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

   3. Taylor expanded in a around 0 91.3%

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

   4. Taylor expanded in y around 0 90.3%

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

      1. mul-1-neg 90.3%

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

   6. Simplified 90.3%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.32 \cdot 10^{-32}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+62}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \left(\left(y + t\right) - 2\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 690:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2.3e+48)
     t_1
     (if (<= t -6e-83) (* y (- z)) (if (<= t 690.0) (+ x a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.3e+48) {
		tmp = t_1;
	} else if (t <= -6e-83) {
		tmp = y * -z;
	} else if (t <= 690.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-2.3d+48)) then
        tmp = t_1
    else if (t <= (-6d-83)) then
        tmp = y * -z
    else if (t <= 690.0d0) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.3e+48) {
		tmp = t_1;
	} else if (t <= -6e-83) {
		tmp = y * -z;
	} else if (t <= 690.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2.3e+48:
		tmp = t_1
	elif t <= -6e-83:
		tmp = y * -z
	elif t <= 690.0:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.3e+48)
		tmp = t_1;
	elseif (t <= -6e-83)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 690.0)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.3e+48)
		tmp = t_1;
	elseif (t <= -6e-83)
		tmp = y * -z;
	elseif (t <= 690.0)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+48], t$95$1, If[LessEqual[t, -6e-83], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 690.0], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e48 or 690 < t

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf 66.5%

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

   if -2.3e48 < t < -6.00000000000000021e-83

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 58.5%

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

   4. Taylor expanded in y around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. distribute-rgt-neg-in 50.1%

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

   6. Simplified 50.1%

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

   if -6.00000000000000021e-83 < t < 690

   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 z around 0 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in t around 0 72.1%

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

      1. +-commutative 72.1%

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

      2. sub-neg 72.1%

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

      3. metadata-eval 72.1%

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

   8. Simplified 72.1%

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

   9. Taylor expanded in b around 0 40.3%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 690:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 55.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-154}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 44000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -3.2e+20)
     t_1
     (if (<= y 1.15e-154)
       (+ x (+ z a))
       (if (<= y 44000000.0) (* t (- b a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -3.2e+20) {
		tmp = t_1;
	} else if (y <= 1.15e-154) {
		tmp = x + (z + a);
	} else if (y <= 44000000.0) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-3.2d+20)) then
        tmp = t_1
    else if (y <= 1.15d-154) then
        tmp = x + (z + a)
    else if (y <= 44000000.0d0) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -3.2e+20) {
		tmp = t_1;
	} else if (y <= 1.15e-154) {
		tmp = x + (z + a);
	} else if (y <= 44000000.0) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -3.2e+20:
		tmp = t_1
	elif y <= 1.15e-154:
		tmp = x + (z + a)
	elif y <= 44000000.0:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -3.2e+20)
		tmp = t_1;
	elseif (y <= 1.15e-154)
		tmp = Float64(x + Float64(z + a));
	elseif (y <= 44000000.0)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -3.2e+20)
		tmp = t_1;
	elseif (y <= 1.15e-154)
		tmp = x + (z + a);
	elseif (y <= 44000000.0)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+20], t$95$1, If[LessEqual[y, 1.15e-154], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 44000000.0], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e20 or 4.4e7 < y

   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 y around inf 70.7%

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

   if -3.2e20 < y < 1.15e-154

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 72.6%

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

   4. Taylor expanded in t around 0 54.9%

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

      1. +-commutative 54.9%

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

      2. sub-neg 54.9%

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

      3. metadata-eval 54.9%

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

      4. mul-1-neg 54.9%

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

      5. unsub-neg 54.9%

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

   6. Simplified 54.9%

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

   7. Taylor expanded in y around 0 54.9%

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

      1. neg-mul-1 54.9%

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

   9. Simplified 54.9%

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

   if 1.15e-154 < y < 4.4e7

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 56.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-154}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 44000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 18.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+146}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-271}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.6e+146) a (if (<= a 5.2e-271) z (if (<= a 4.8e+62) x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.6e+146) {
		tmp = a;
	} else if (a <= 5.2e-271) {
		tmp = z;
	} else if (a <= 4.8e+62) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.6d+146)) then
        tmp = a
    else if (a <= 5.2d-271) then
        tmp = z
    else if (a <= 4.8d+62) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.6e+146) {
		tmp = a;
	} else if (a <= 5.2e-271) {
		tmp = z;
	} else if (a <= 4.8e+62) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.6e+146:
		tmp = a
	elif a <= 5.2e-271:
		tmp = z
	elif a <= 4.8e+62:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.6e+146)
		tmp = a;
	elseif (a <= 5.2e-271)
		tmp = z;
	elseif (a <= 4.8e+62)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.6e+146)
		tmp = a;
	elseif (a <= 5.2e-271)
		tmp = z;
	elseif (a <= 4.8e+62)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.6e+146], a, If[LessEqual[a, 5.2e-271], z, If[LessEqual[a, 4.8e+62], x, a]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6e146 or 4.8e62 < a

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 59.0%

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

   4. Taylor expanded in t around 0 30.4%

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

   if -1.6e146 < a < 5.2e-271

   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 z around inf 40.9%

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

   4. Taylor expanded in y around 0 16.7%

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

   if 5.2e-271 < a < 4.8e62

   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 20.7%

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

4. Final simplification 22.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+146}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-271}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 25.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-43} \lor \neg \left(t \leq 0.00135\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.6e-43) (not (<= t 0.00135))) (* t b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e-43) || !(t <= 0.00135)) {
		tmp = t * b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.6d-43)) .or. (.not. (t <= 0.00135d0))) then
        tmp = t * b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e-43) || !(t <= 0.00135)) {
		tmp = t * b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.6e-43) or not (t <= 0.00135):
		tmp = t * b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.6e-43) || !(t <= 0.00135))
		tmp = Float64(t * b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.6e-43) || ~((t <= 0.00135)))
		tmp = t * b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.6e-43], N[Not[LessEqual[t, 0.00135]], $MachinePrecision]], N[(t * b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if t < -2.6e-43 or 0.0013500000000000001 < t

   1. Initial program 94.7%

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

   3. Taylor expanded in a around 0 70.0%

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

      1. sub-neg 70.0%

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

      2. distribute-rgt-in 70.0%

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

      3. +-commutative 70.0%

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

      4. metadata-eval 70.0%

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

   5. Applied egg-rr 70.0%

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

   6. Taylor expanded in t around inf 31.4%

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

   if -2.6e-43 < t < 0.0013500000000000001

   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 a around inf 25.7%

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

   4. Taylor expanded in t around 0 25.2%

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

4. Final simplification 28.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-43} \lor \neg \left(t \leq 0.00135\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 35.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5200000000000 \lor \neg \left(t \leq 3950000\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5200000000000.0) (not (<= t 3950000.0))) (* t b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5200000000000.0) || !(t <= 3950000.0)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5200000000000.0d0)) .or. (.not. (t <= 3950000.0d0))) then
        tmp = t * b
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5200000000000.0) || !(t <= 3950000.0)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5200000000000.0) or not (t <= 3950000.0):
		tmp = t * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5200000000000.0) || !(t <= 3950000.0))
		tmp = Float64(t * b);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5200000000000.0) || ~((t <= 3950000.0)))
		tmp = t * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5200000000000.0], N[Not[LessEqual[t, 3950000.0]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2e12 or 3.95e6 < t

   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 0 66.5%

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

      1. sub-neg 66.5%

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

      2. distribute-rgt-in 66.5%

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

      3. +-commutative 66.5%

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

      4. metadata-eval 66.5%

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

   5. Applied egg-rr 66.5%

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

   6. Taylor expanded in t around inf 34.6%

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

   if -5.2e12 < t < 3.95e6

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in t around 0 69.2%

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

      1. +-commutative 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in b around 0 37.5%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5200000000000 \lor \neg \left(t \leq 3950000\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 20.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+103}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.6e+103) a (if (<= a 5.6e+64) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.6e+103) {
		tmp = a;
	} else if (a <= 5.6e+64) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.6d+103)) then
        tmp = a
    else if (a <= 5.6d+64) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.6e+103) {
		tmp = a;
	} else if (a <= 5.6e+64) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.6e+103:
		tmp = a
	elif a <= 5.6e+64:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.6e+103)
		tmp = a;
	elseif (a <= 5.6e+64)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.6e+103)
		tmp = a;
	elseif (a <= 5.6e+64)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.6e+103], a, If[LessEqual[a, 5.6e+64], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.6000000000000002e103 or 5.60000000000000047e64 < a

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 56.1%

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

   4. Taylor expanded in t around 0 27.5%

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

   if -2.6000000000000002e103 < a < 5.60000000000000047e64

   1. Initial program 98.7%

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

   3. Taylor expanded in x around inf 15.1%

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

4. Final simplification 20.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+103}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 10.8% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

3. Taylor expanded in a around inf 29.3%

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

4. Taylor expanded in t around 0 13.3%

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

5. Final simplification 13.3%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(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)))