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

Percentage Accurate: 95.4% → 98.2%

Time: 17.0s

Alternatives: 28

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.4% 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: 98.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = 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))) + (b * ((y + t) - 2.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a * Float64(1.0 - t))) + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(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))) + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 67.1%

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

4. Final simplification 98.4%

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

Alternative 2: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. +-commutative 95.3%

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

   2. fma-def 97.2%

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

   3. associate--l+ 97.2%

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

   4. sub-neg 97.2%

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

   5. metadata-eval 97.2%

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

   6. sub-neg 97.2%

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

   7. associate-+l- 97.2%

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

   8. fma-neg 97.6%

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

   9. sub-neg 97.6%

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

   10. metadata-eval 97.6%

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

   11. remove-double-neg 97.6%

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

   12. sub-neg 97.6%

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

   13. metadata-eval 97.6%

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

3. Simplified 97.6%

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

4. Final simplification 97.6%

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

Alternative 3: 52.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -10000000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -3900:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4300000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z a))) (t_2 (* t (- b a))) (t_3 (* b (- y 2.0))))
   (if (<= t -1e+59)
     t_2
     (if (<= t -10000000000.0)
       (- x (* y z))
       (if (<= t -3900.0)
         (- x (* t a))
         (if (<= t -9e-62)
           t_3
           (if (<= t -3.4e-166)
             (* y (- b z))
             (if (<= t 1.25e-174)
               t_1
               (if (<= t 3.7e-60)
                 t_3
                 (if (<= t 4300000000000.0) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = t * (b - a);
	double t_3 = b * (y - 2.0);
	double tmp;
	if (t <= -1e+59) {
		tmp = t_2;
	} else if (t <= -10000000000.0) {
		tmp = x - (y * z);
	} else if (t <= -3900.0) {
		tmp = x - (t * a);
	} else if (t <= -9e-62) {
		tmp = t_3;
	} else if (t <= -3.4e-166) {
		tmp = y * (b - z);
	} else if (t <= 1.25e-174) {
		tmp = t_1;
	} else if (t <= 3.7e-60) {
		tmp = t_3;
	} else if (t <= 4300000000000.0) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x + (z + a)
    t_2 = t * (b - a)
    t_3 = b * (y - 2.0d0)
    if (t <= (-1d+59)) then
        tmp = t_2
    else if (t <= (-10000000000.0d0)) then
        tmp = x - (y * z)
    else if (t <= (-3900.0d0)) then
        tmp = x - (t * a)
    else if (t <= (-9d-62)) then
        tmp = t_3
    else if (t <= (-3.4d-166)) then
        tmp = y * (b - z)
    else if (t <= 1.25d-174) then
        tmp = t_1
    else if (t <= 3.7d-60) then
        tmp = t_3
    else if (t <= 4300000000000.0d0) 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 + (z + a);
	double t_2 = t * (b - a);
	double t_3 = b * (y - 2.0);
	double tmp;
	if (t <= -1e+59) {
		tmp = t_2;
	} else if (t <= -10000000000.0) {
		tmp = x - (y * z);
	} else if (t <= -3900.0) {
		tmp = x - (t * a);
	} else if (t <= -9e-62) {
		tmp = t_3;
	} else if (t <= -3.4e-166) {
		tmp = y * (b - z);
	} else if (t <= 1.25e-174) {
		tmp = t_1;
	} else if (t <= 3.7e-60) {
		tmp = t_3;
	} else if (t <= 4300000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + a)
	t_2 = t * (b - a)
	t_3 = b * (y - 2.0)
	tmp = 0
	if t <= -1e+59:
		tmp = t_2
	elif t <= -10000000000.0:
		tmp = x - (y * z)
	elif t <= -3900.0:
		tmp = x - (t * a)
	elif t <= -9e-62:
		tmp = t_3
	elif t <= -3.4e-166:
		tmp = y * (b - z)
	elif t <= 1.25e-174:
		tmp = t_1
	elif t <= 3.7e-60:
		tmp = t_3
	elif t <= 4300000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + a))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (t <= -1e+59)
		tmp = t_2;
	elseif (t <= -10000000000.0)
		tmp = Float64(x - Float64(y * z));
	elseif (t <= -3900.0)
		tmp = Float64(x - Float64(t * a));
	elseif (t <= -9e-62)
		tmp = t_3;
	elseif (t <= -3.4e-166)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 1.25e-174)
		tmp = t_1;
	elseif (t <= 3.7e-60)
		tmp = t_3;
	elseif (t <= 4300000000000.0)
		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 + (z + a);
	t_2 = t * (b - a);
	t_3 = b * (y - 2.0);
	tmp = 0.0;
	if (t <= -1e+59)
		tmp = t_2;
	elseif (t <= -10000000000.0)
		tmp = x - (y * z);
	elseif (t <= -3900.0)
		tmp = x - (t * a);
	elseif (t <= -9e-62)
		tmp = t_3;
	elseif (t <= -3.4e-166)
		tmp = y * (b - z);
	elseif (t <= 1.25e-174)
		tmp = t_1;
	elseif (t <= 3.7e-60)
		tmp = t_3;
	elseif (t <= 4300000000000.0)
		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[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+59], t$95$2, If[LessEqual[t, -10000000000.0], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3900.0], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-62], t$95$3, If[LessEqual[t, -3.4e-166], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-174], t$95$1, If[LessEqual[t, 3.7e-60], t$95$3, If[LessEqual[t, 4300000000000.0], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -9.99999999999999972e58 or 4.3e12 < t

   1. Initial program 91.6%

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

   2. Taylor expanded in t around inf 69.3%

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

   if -9.99999999999999972e58 < t < -1e10

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 82.2%

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

   3. Taylor expanded in y around inf 61.5%

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

   if -1e10 < t < -3900

   1. Initial program 100.0%

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

   2. Taylor expanded in b around 0 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in t around inf 69.1%

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

      1. *-commutative 69.1%

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

   6. Simplified 69.1%

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

   if -3900 < t < -9.00000000000000036e-62 or 1.2500000000000001e-174 < t < 3.70000000000000025e-60

   1. Initial program 97.6%

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

   2. Taylor expanded in b around inf 55.5%

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

   3. Taylor expanded in t around 0 54.8%

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

   if -9.00000000000000036e-62 < t < -3.3999999999999997e-166

   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. Taylor expanded in y around inf 67.4%

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

   if -3.3999999999999997e-166 < t < 1.2500000000000001e-174 or 3.70000000000000025e-60 < t < 4.3e12

   1. Initial program 100.0%

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

   2. Taylor expanded in b around 0 79.9%

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

   3. Taylor expanded in y around 0 60.4%

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

   4. Taylor expanded in t around 0 58.9%

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

      1. neg-mul-1 58.9%

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

      2. unsub-neg 58.9%

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

      3. mul-1-neg 58.9%

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

   6. Simplified 58.9%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -10000000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -3900:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-174}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 4300000000000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 4: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + \left(z - y \cdot z\right)\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := \left(x + a\right) - t \cdot a\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{-269}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (- z (* y z)))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (- (+ x a) (* t a))))
   (if (<= b -2.2e+126)
     t_2
     (if (<= b -1.22e-164)
       t_1
       (if (<= b -1.46e-269)
         t_3
         (if (<= b 5.6e-157)
           t_1
           (if (<= b 2.6e-76) t_3 (if (<= b 4.4e+32) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z - (y * z)));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = (x + a) - (t * a);
	double tmp;
	if (b <= -2.2e+126) {
		tmp = t_2;
	} else if (b <= -1.22e-164) {
		tmp = t_1;
	} else if (b <= -1.46e-269) {
		tmp = t_3;
	} else if (b <= 5.6e-157) {
		tmp = t_1;
	} else if (b <= 2.6e-76) {
		tmp = t_3;
	} else if (b <= 4.4e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a + (z - (y * z)))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = (x + a) - (t * a)
    if (b <= (-2.2d+126)) then
        tmp = t_2
    else if (b <= (-1.22d-164)) then
        tmp = t_1
    else if (b <= (-1.46d-269)) then
        tmp = t_3
    else if (b <= 5.6d-157) then
        tmp = t_1
    else if (b <= 2.6d-76) then
        tmp = t_3
    else if (b <= 4.4d+32) 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 + (z - (y * z)));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = (x + a) - (t * a);
	double tmp;
	if (b <= -2.2e+126) {
		tmp = t_2;
	} else if (b <= -1.22e-164) {
		tmp = t_1;
	} else if (b <= -1.46e-269) {
		tmp = t_3;
	} else if (b <= 5.6e-157) {
		tmp = t_1;
	} else if (b <= 2.6e-76) {
		tmp = t_3;
	} else if (b <= 4.4e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z - (y * z)))
	t_2 = b * ((y + t) - 2.0)
	t_3 = (x + a) - (t * a)
	tmp = 0
	if b <= -2.2e+126:
		tmp = t_2
	elif b <= -1.22e-164:
		tmp = t_1
	elif b <= -1.46e-269:
		tmp = t_3
	elif b <= 5.6e-157:
		tmp = t_1
	elif b <= 2.6e-76:
		tmp = t_3
	elif b <= 4.4e+32:
		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(z - Float64(y * z))))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(Float64(x + a) - Float64(t * a))
	tmp = 0.0
	if (b <= -2.2e+126)
		tmp = t_2;
	elseif (b <= -1.22e-164)
		tmp = t_1;
	elseif (b <= -1.46e-269)
		tmp = t_3;
	elseif (b <= 5.6e-157)
		tmp = t_1;
	elseif (b <= 2.6e-76)
		tmp = t_3;
	elseif (b <= 4.4e+32)
		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 + (z - (y * z)));
	t_2 = b * ((y + t) - 2.0);
	t_3 = (x + a) - (t * a);
	tmp = 0.0;
	if (b <= -2.2e+126)
		tmp = t_2;
	elseif (b <= -1.22e-164)
		tmp = t_1;
	elseif (b <= -1.46e-269)
		tmp = t_3;
	elseif (b <= 5.6e-157)
		tmp = t_1;
	elseif (b <= 2.6e-76)
		tmp = t_3;
	elseif (b <= 4.4e+32)
		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[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + a), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+126], t$95$2, If[LessEqual[b, -1.22e-164], t$95$1, If[LessEqual[b, -1.46e-269], t$95$3, If[LessEqual[b, 5.6e-157], t$95$1, If[LessEqual[b, 2.6e-76], t$95$3, If[LessEqual[b, 4.4e+32], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.19999999999999999e126 or 4.40000000000000002e32 < b

   1. Initial program 91.2%

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

   2. Taylor expanded in b around inf 79.7%

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

   if -2.19999999999999999e126 < b < -1.2199999999999999e-164 or -1.45999999999999999e-269 < b < 5.6000000000000002e-157 or 2.6e-76 < b < 4.40000000000000002e32

   1. Initial program 97.6%

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

   2. Taylor expanded in b around 0 86.6%

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

   3. Taylor expanded in t around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. sub-neg 72.4%

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

      3. metadata-eval 72.4%

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

      4. mul-1-neg 72.4%

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

      5. unsub-neg 72.4%

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

      6. distribute-rgt-in 72.4%

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

      7. neg-mul-1 72.4%

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

      8. unsub-neg 72.4%

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

   5. Simplified 72.4%

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

   if -1.2199999999999999e-164 < b < -1.45999999999999999e-269 or 5.6000000000000002e-157 < b < 2.6e-76

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 97.4%

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

   3. Taylor expanded in z around 0 75.4%

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

      1. associate--l+ 75.4%

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

      2. sub-neg 75.4%

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

      3. metadata-eval 75.4%

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

      4. distribute-lft-out 75.4%

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

      5. sub-neg 75.4%

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

      6. metadata-eval 75.4%

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

      7. fma-neg 75.4%

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

      8. associate-+r+ 75.4%

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

      9. +-commutative 75.4%

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

      10. associate-+l+ 75.4%

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

      11. distribute-rgt-in 75.4%

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

      12. *-commutative 75.4%

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

      13. +-commutative 75.4%

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

      14. distribute-neg-in 75.4%

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

      15. mul-1-neg 75.4%

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

      16. remove-double-neg 75.4%

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

      17. unsub-neg 75.4%

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

      18. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in b around 0 72.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+126}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-164}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{-269}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-157}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-76}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+32}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 5: 65.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1200000000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -5400:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 820000:\\ \;\;\;\;\left(x + a\right) + b \cdot \left(y + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -9.5e+58)
     t_1
     (if (<= t -1200000000000.0)
       (- x (* y z))
       (if (<= t -5400.0)
         (- (+ x a) (* t a))
         (if (<= t -1.05e-38)
           (* y (- b z))
           (if (<= t 820000.0) (+ (+ x a) (* b (+ y -2.0))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -9.5e+58) {
		tmp = t_1;
	} else if (t <= -1200000000000.0) {
		tmp = x - (y * z);
	} else if (t <= -5400.0) {
		tmp = (x + a) - (t * a);
	} else if (t <= -1.05e-38) {
		tmp = y * (b - z);
	} else if (t <= 820000.0) {
		tmp = (x + a) + (b * (y + -2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-9.5d+58)) then
        tmp = t_1
    else if (t <= (-1200000000000.0d0)) then
        tmp = x - (y * z)
    else if (t <= (-5400.0d0)) then
        tmp = (x + a) - (t * a)
    else if (t <= (-1.05d-38)) then
        tmp = y * (b - z)
    else if (t <= 820000.0d0) then
        tmp = (x + a) + (b * (y + (-2.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -9.5e+58) {
		tmp = t_1;
	} else if (t <= -1200000000000.0) {
		tmp = x - (y * z);
	} else if (t <= -5400.0) {
		tmp = (x + a) - (t * a);
	} else if (t <= -1.05e-38) {
		tmp = y * (b - z);
	} else if (t <= 820000.0) {
		tmp = (x + a) + (b * (y + -2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -9.5e+58:
		tmp = t_1
	elif t <= -1200000000000.0:
		tmp = x - (y * z)
	elif t <= -5400.0:
		tmp = (x + a) - (t * a)
	elif t <= -1.05e-38:
		tmp = y * (b - z)
	elif t <= 820000.0:
		tmp = (x + a) + (b * (y + -2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -9.5e+58)
		tmp = t_1;
	elseif (t <= -1200000000000.0)
		tmp = Float64(x - Float64(y * z));
	elseif (t <= -5400.0)
		tmp = Float64(Float64(x + a) - Float64(t * a));
	elseif (t <= -1.05e-38)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 820000.0)
		tmp = Float64(Float64(x + a) + Float64(b * Float64(y + -2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -9.5e+58)
		tmp = t_1;
	elseif (t <= -1200000000000.0)
		tmp = x - (y * z);
	elseif (t <= -5400.0)
		tmp = (x + a) - (t * a);
	elseif (t <= -1.05e-38)
		tmp = y * (b - z);
	elseif (t <= 820000.0)
		tmp = (x + a) + (b * (y + -2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+58], t$95$1, If[LessEqual[t, -1200000000000.0], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5400.0], N[(N[(x + a), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e-38], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 820000.0], N[(N[(x + a), $MachinePrecision] + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.5000000000000002e58 or 8.2e5 < t

   1. Initial program 91.7%

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

   2. Taylor expanded in t around inf 68.6%

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

   if -9.5000000000000002e58 < t < -1.2e12

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 82.2%

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

   3. Taylor expanded in y around inf 61.5%

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

   if -1.2e12 < t < -5400

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. distribute-lft-out 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. fma-neg 100.0%

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

      8. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. associate-+l+ 100.0%

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

      11. distribute-rgt-in 100.0%

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

      12. *-commutative 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-neg-in 100.0%

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

      15. mul-1-neg 100.0%

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

      16. remove-double-neg 100.0%

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

      17. unsub-neg 100.0%

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

      18. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in b around 0 100.0%

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

   if -5400 < t < -1.05000000000000006e-38

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 67.7%

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

   if -1.05000000000000006e-38 < t < 8.2e5

   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. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in z around 0 72.4%

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

      1. associate--l+ 72.4%

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

      2. sub-neg 72.4%

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

      3. metadata-eval 72.4%

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

      4. distribute-lft-out 72.4%

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

      5. sub-neg 72.4%

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

      6. metadata-eval 72.4%

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

      7. fma-neg 72.4%

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

      8. associate-+r+ 72.4%

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

      9. +-commutative 72.4%

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

      10. associate-+l+ 72.4%

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

      11. distribute-rgt-in 72.4%

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

      12. *-commutative 72.4%

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

      13. +-commutative 72.4%

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

      14. distribute-neg-in 72.4%

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

      15. mul-1-neg 72.4%

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

      16. remove-double-neg 72.4%

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

      17. unsub-neg 72.4%

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

      18. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in t around 0 72.4%

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

      1. associate-+r+ 72.4%

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

      2. sub-neg 72.4%

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

      3. metadata-eval 72.4%

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

   8. Simplified 72.4%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1200000000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -5400:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 820000:\\ \;\;\;\;\left(x + a\right) + b \cdot \left(y + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 6: 85.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+126} \lor \neg \left(b \leq 2.9 \cdot 10^{+31}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_1 - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -2.2e+126) (not (<= b 2.9e+31)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (- t_1 (* z (+ y -1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -2.2e+126) || !(b <= 2.9e+31)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 - (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-2.2d+126)) .or. (.not. (b <= 2.9d+31))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + (t_1 - (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -2.2e+126) || !(b <= 2.9e+31)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 - (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -2.2e+126) or not (b <= 2.9e+31):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + (t_1 - (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -2.2e+126) || !(b <= 2.9e+31))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(t_1 - Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((b <= -2.2e+126) || ~((b <= 2.9e+31)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + (t_1 - (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2.2e+126], N[Not[LessEqual[b, 2.9e+31]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.19999999999999999e126 or 2.9e31 < b

   1. Initial program 91.2%

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

   2. Taylor expanded in z around 0 91.2%

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

   if -2.19999999999999999e126 < b < 2.9e31

   1. Initial program 97.6%

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

   2. Taylor expanded in b around 0 88.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+126} \lor \neg \left(b \leq 2.9 \cdot 10^{+31}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 7: 86.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{-11}:\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+32}:\\ \;\;\;\;x + \left(t_2 - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))) (t_2 (* a (- 1.0 t))))
   (if (<= b -9.5e-11)
     (+ t_1 (* z (- 1.0 y)))
     (if (<= b 4.6e+32) (+ x (- t_2 (* z (+ y -1.0)))) (+ t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double t_2 = a * (1.0 - t);
	double tmp;
	if (b <= -9.5e-11) {
		tmp = t_1 + (z * (1.0 - y));
	} else if (b <= 4.6e+32) {
		tmp = x + (t_2 - (z * (y + -1.0)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    t_2 = a * (1.0d0 - t)
    if (b <= (-9.5d-11)) then
        tmp = t_1 + (z * (1.0d0 - y))
    else if (b <= 4.6d+32) then
        tmp = x + (t_2 - (z * (y + (-1.0d0))))
    else
        tmp = t_1 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double t_2 = a * (1.0 - t);
	double tmp;
	if (b <= -9.5e-11) {
		tmp = t_1 + (z * (1.0 - y));
	} else if (b <= 4.6e+32) {
		tmp = x + (t_2 - (z * (y + -1.0)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	t_2 = a * (1.0 - t)
	tmp = 0
	if b <= -9.5e-11:
		tmp = t_1 + (z * (1.0 - y))
	elif b <= 4.6e+32:
		tmp = x + (t_2 - (z * (y + -1.0)))
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -9.5e-11)
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	elseif (b <= 4.6e+32)
		tmp = Float64(x + Float64(t_2 - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -9.5e-11)
		tmp = t_1 + (z * (1.0 - y));
	elseif (b <= 4.6e+32)
		tmp = x + (t_2 - (z * (y + -1.0)));
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.5e-11], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.6e+32], N[(x + N[(t$95$2 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.49999999999999951e-11

   1. Initial program 89.4%

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

   2. Taylor expanded in a around 0 83.3%

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

   if -9.49999999999999951e-11 < b < 4.5999999999999999e32

   1. Initial program 99.2%

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

   2. Taylor expanded in b around 0 92.3%

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

   if 4.5999999999999999e32 < b

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 93.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-11}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+32}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 8: 86.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;z + \left(x - \left(b \cdot \left(2 - t\right) - y \cdot \left(b - z\right)\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+31}:\\ \;\;\;\;x + \left(t_1 - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -2.1e-9)
     (+ z (- x (- (* b (- 2.0 t)) (* y (- b z)))))
     (if (<= b 6.5e+31)
       (+ x (- t_1 (* z (+ y -1.0))))
       (+ (+ x (* b (- (+ y t) 2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -2.1e-9) {
		tmp = z + (x - ((b * (2.0 - t)) - (y * (b - z))));
	} else if (b <= 6.5e+31) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-2.1d-9)) then
        tmp = z + (x - ((b * (2.0d0 - t)) - (y * (b - z))))
    else if (b <= 6.5d+31) then
        tmp = x + (t_1 - (z * (y + (-1.0d0))))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -2.1e-9) {
		tmp = z + (x - ((b * (2.0 - t)) - (y * (b - z))));
	} else if (b <= 6.5e+31) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -2.1e-9:
		tmp = z + (x - ((b * (2.0 - t)) - (y * (b - z))))
	elif b <= 6.5e+31:
		tmp = x + (t_1 - (z * (y + -1.0)))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -2.1e-9)
		tmp = Float64(z + Float64(x - Float64(Float64(b * Float64(2.0 - t)) - Float64(y * Float64(b - z)))));
	elseif (b <= 6.5e+31)
		tmp = Float64(x + Float64(t_1 - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -2.1e-9)
		tmp = z + (x - ((b * (2.0 - t)) - (y * (b - z))));
	elseif (b <= 6.5e+31)
		tmp = x + (t_1 - (z * (y + -1.0)));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.1e-9], N[(z + N[(x - N[(N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+31], N[(x + N[(t$95$1 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.10000000000000019e-9

   1. Initial program 89.4%

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

   2. Taylor expanded in y around 0 89.5%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. neg-mul-1 83.3%

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

   5. Simplified 83.3%

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

   if -2.10000000000000019e-9 < b < 6.5000000000000004e31

   1. Initial program 99.2%

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

   2. Taylor expanded in b around 0 92.3%

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

   if 6.5000000000000004e31 < b

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 93.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;z + \left(x - \left(b \cdot \left(2 - t\right) - y \cdot \left(b - z\right)\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+31}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 9: 49.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-115}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+53} \lor \neg \left(y \leq 3.9 \cdot 10^{+75}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -1.2e+28)
     t_2
     (if (<= y 1.12e-207)
       t_1
       (if (<= y 3.2e-115)
         z
         (if (<= y 5.8e-6)
           t_1
           (if (or (<= y 2.5e+53) (not (<= y 3.9e+75)))
             t_2
             (* a (- 1.0 t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.2e+28) {
		tmp = t_2;
	} else if (y <= 1.12e-207) {
		tmp = t_1;
	} else if (y <= 3.2e-115) {
		tmp = z;
	} else if (y <= 5.8e-6) {
		tmp = t_1;
	} else if ((y <= 2.5e+53) || !(y <= 3.9e+75)) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-1.2d+28)) then
        tmp = t_2
    else if (y <= 1.12d-207) then
        tmp = t_1
    else if (y <= 3.2d-115) then
        tmp = z
    else if (y <= 5.8d-6) then
        tmp = t_1
    else if ((y <= 2.5d+53) .or. (.not. (y <= 3.9d+75))) then
        tmp = t_2
    else
        tmp = 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 t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.2e+28) {
		tmp = t_2;
	} else if (y <= 1.12e-207) {
		tmp = t_1;
	} else if (y <= 3.2e-115) {
		tmp = z;
	} else if (y <= 5.8e-6) {
		tmp = t_1;
	} else if ((y <= 2.5e+53) || !(y <= 3.9e+75)) {
		tmp = t_2;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -1.2e+28:
		tmp = t_2
	elif y <= 1.12e-207:
		tmp = t_1
	elif y <= 3.2e-115:
		tmp = z
	elif y <= 5.8e-6:
		tmp = t_1
	elif (y <= 2.5e+53) or not (y <= 3.9e+75):
		tmp = t_2
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.2e+28)
		tmp = t_2;
	elseif (y <= 1.12e-207)
		tmp = t_1;
	elseif (y <= 3.2e-115)
		tmp = z;
	elseif (y <= 5.8e-6)
		tmp = t_1;
	elseif ((y <= 2.5e+53) || !(y <= 3.9e+75))
		tmp = t_2;
	else
		tmp = Float64(a * Float64(1.0 - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.2e+28)
		tmp = t_2;
	elseif (y <= 1.12e-207)
		tmp = t_1;
	elseif (y <= 3.2e-115)
		tmp = z;
	elseif (y <= 5.8e-6)
		tmp = t_1;
	elseif ((y <= 2.5e+53) || ~((y <= 3.9e+75)))
		tmp = t_2;
	else
		tmp = a * (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+28], t$95$2, If[LessEqual[y, 1.12e-207], t$95$1, If[LessEqual[y, 3.2e-115], z, If[LessEqual[y, 5.8e-6], t$95$1, If[Or[LessEqual[y, 2.5e+53], N[Not[LessEqual[y, 3.9e+75]], $MachinePrecision]], t$95$2, N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.19999999999999991e28 or 5.8000000000000004e-6 < y < 2.5000000000000002e53 or 3.90000000000000038e75 < y

   1. Initial program 92.2%

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

   2. Taylor expanded in y around inf 70.4%

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

   if -1.19999999999999991e28 < y < 1.12000000000000001e-207 or 3.2e-115 < y < 5.8000000000000004e-6

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 49.8%

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

   if 1.12000000000000001e-207 < y < 3.2e-115

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in z around inf 38.4%

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

      1. distribute-rgt-in 38.4%

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

      2. metadata-eval 38.4%

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

      3. associate-*r* 38.4%

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

      4. mul-1-neg 38.4%

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

      5. unsub-neg 38.4%

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

      6. metadata-eval 38.4%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 38.4%

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

   5. Simplified 38.4%

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

   6. Taylor expanded in y around 0 38.4%

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

   if 2.5000000000000002e53 < y < 3.90000000000000038e75

   1. Initial program 90.9%

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

   2. Taylor expanded in a around inf 73.2%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-115}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+53} \lor \neg \left(y \leq 3.9 \cdot 10^{+75}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 10: 49.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+53} \lor \neg \left(y \leq 1.05 \cdot 10^{+77}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -4.9e+30)
     t_2
     (if (<= y 8.5e-209)
       t_1
       (if (<= y 3.2e-115)
         (* z (- 1.0 y))
         (if (<= y 5.8e-6)
           t_1
           (if (or (<= y 2.9e+53) (not (<= y 1.05e+77)))
             t_2
             (* a (- 1.0 t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -4.9e+30) {
		tmp = t_2;
	} else if (y <= 8.5e-209) {
		tmp = t_1;
	} else if (y <= 3.2e-115) {
		tmp = z * (1.0 - y);
	} else if (y <= 5.8e-6) {
		tmp = t_1;
	} else if ((y <= 2.9e+53) || !(y <= 1.05e+77)) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-4.9d+30)) then
        tmp = t_2
    else if (y <= 8.5d-209) then
        tmp = t_1
    else if (y <= 3.2d-115) then
        tmp = z * (1.0d0 - y)
    else if (y <= 5.8d-6) then
        tmp = t_1
    else if ((y <= 2.9d+53) .or. (.not. (y <= 1.05d+77))) then
        tmp = t_2
    else
        tmp = 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 t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -4.9e+30) {
		tmp = t_2;
	} else if (y <= 8.5e-209) {
		tmp = t_1;
	} else if (y <= 3.2e-115) {
		tmp = z * (1.0 - y);
	} else if (y <= 5.8e-6) {
		tmp = t_1;
	} else if ((y <= 2.9e+53) || !(y <= 1.05e+77)) {
		tmp = t_2;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -4.9e+30:
		tmp = t_2
	elif y <= 8.5e-209:
		tmp = t_1
	elif y <= 3.2e-115:
		tmp = z * (1.0 - y)
	elif y <= 5.8e-6:
		tmp = t_1
	elif (y <= 2.9e+53) or not (y <= 1.05e+77):
		tmp = t_2
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4.9e+30)
		tmp = t_2;
	elseif (y <= 8.5e-209)
		tmp = t_1;
	elseif (y <= 3.2e-115)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= 5.8e-6)
		tmp = t_1;
	elseif ((y <= 2.9e+53) || !(y <= 1.05e+77))
		tmp = t_2;
	else
		tmp = Float64(a * Float64(1.0 - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -4.9e+30)
		tmp = t_2;
	elseif (y <= 8.5e-209)
		tmp = t_1;
	elseif (y <= 3.2e-115)
		tmp = z * (1.0 - y);
	elseif (y <= 5.8e-6)
		tmp = t_1;
	elseif ((y <= 2.9e+53) || ~((y <= 1.05e+77)))
		tmp = t_2;
	else
		tmp = a * (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.9e+30], t$95$2, If[LessEqual[y, 8.5e-209], t$95$1, If[LessEqual[y, 3.2e-115], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-6], t$95$1, If[Or[LessEqual[y, 2.9e+53], N[Not[LessEqual[y, 1.05e+77]], $MachinePrecision]], t$95$2, N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.89999999999999984e30 or 5.8000000000000004e-6 < y < 2.9000000000000002e53 or 1.0499999999999999e77 < y

   1. Initial program 92.2%

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

   2. Taylor expanded in y around inf 70.4%

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

   if -4.89999999999999984e30 < y < 8.5e-209 or 3.2e-115 < y < 5.8000000000000004e-6

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 49.8%

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

   if 8.5e-209 < y < 3.2e-115

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 38.4%

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

   if 2.9000000000000002e53 < y < 1.0499999999999999e77

   1. Initial program 90.9%

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

   2. Taylor expanded in a around inf 73.2%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-209}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+53} \lor \neg \left(y \leq 1.05 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 11: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-164}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-134}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -2.2e+126)
     t_1
     (if (<= b -7e-14)
       (- x (* y z))
       (if (<= b -1.55e-164)
         (- z (* y z))
         (if (<= b 6.5e-134)
           (- x (* t a))
           (if (<= b 1.45e+31) (* a (- 1.0 t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.2e+126) {
		tmp = t_1;
	} else if (b <= -7e-14) {
		tmp = x - (y * z);
	} else if (b <= -1.55e-164) {
		tmp = z - (y * z);
	} else if (b <= 6.5e-134) {
		tmp = x - (t * a);
	} else if (b <= 1.45e+31) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-2.2d+126)) then
        tmp = t_1
    else if (b <= (-7d-14)) then
        tmp = x - (y * z)
    else if (b <= (-1.55d-164)) then
        tmp = z - (y * z)
    else if (b <= 6.5d-134) then
        tmp = x - (t * a)
    else if (b <= 1.45d+31) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.2e+126) {
		tmp = t_1;
	} else if (b <= -7e-14) {
		tmp = x - (y * z);
	} else if (b <= -1.55e-164) {
		tmp = z - (y * z);
	} else if (b <= 6.5e-134) {
		tmp = x - (t * a);
	} else if (b <= 1.45e+31) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2.2e+126:
		tmp = t_1
	elif b <= -7e-14:
		tmp = x - (y * z)
	elif b <= -1.55e-164:
		tmp = z - (y * z)
	elif b <= 6.5e-134:
		tmp = x - (t * a)
	elif b <= 1.45e+31:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2.2e+126)
		tmp = t_1;
	elseif (b <= -7e-14)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= -1.55e-164)
		tmp = Float64(z - Float64(y * z));
	elseif (b <= 6.5e-134)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 1.45e+31)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.2e+126)
		tmp = t_1;
	elseif (b <= -7e-14)
		tmp = x - (y * z);
	elseif (b <= -1.55e-164)
		tmp = z - (y * z);
	elseif (b <= 6.5e-134)
		tmp = x - (t * a);
	elseif (b <= 1.45e+31)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+126], t$95$1, If[LessEqual[b, -7e-14], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.55e-164], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e-134], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e+31], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.19999999999999999e126 or 1.45e31 < b

   1. Initial program 91.2%

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

   2. Taylor expanded in b around inf 79.7%

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

   if -2.19999999999999999e126 < b < -7.0000000000000005e-14

   1. Initial program 90.3%

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

   2. Taylor expanded in b around 0 73.2%

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

   3. Taylor expanded in y around inf 51.6%

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

   if -7.0000000000000005e-14 < b < -1.55e-164

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

   3. Taylor expanded in z around inf 58.9%

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

      1. distribute-rgt-in 58.9%

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

      2. metadata-eval 58.9%

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

      3. associate-*r* 58.9%

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

      4. mul-1-neg 58.9%

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

      5. unsub-neg 58.9%

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

      6. metadata-eval 58.9%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 58.9%

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

   5. Simplified 58.9%

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

   if -1.55e-164 < b < 6.4999999999999998e-134

   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. Taylor expanded in b around 0 96.7%

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

   3. Taylor expanded in y around 0 76.3%

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

   4. Taylor expanded in t around inf 59.8%

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

      1. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if 6.4999999999999998e-134 < b < 1.45e31

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 55.9%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+126}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-164}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-134}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 12: 67.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-164}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-22}:\\ \;\;\;\;x + \left(z - a \cdot \left(t + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -2.2e+126)
     t_1
     (if (<= b -1.05e-164)
       (+ x (+ a (- z (* y z))))
       (if (<= b 3.1e-22) (+ x (- z (* a (+ t -1.0)))) (- t_1 (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.2e+126) {
		tmp = t_1;
	} else if (b <= -1.05e-164) {
		tmp = x + (a + (z - (y * z)));
	} else if (b <= 3.1e-22) {
		tmp = x + (z - (a * (t + -1.0)));
	} else {
		tmp = t_1 - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-2.2d+126)) then
        tmp = t_1
    else if (b <= (-1.05d-164)) then
        tmp = x + (a + (z - (y * z)))
    else if (b <= 3.1d-22) then
        tmp = x + (z - (a * (t + (-1.0d0))))
    else
        tmp = t_1 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.2e+126) {
		tmp = t_1;
	} else if (b <= -1.05e-164) {
		tmp = x + (a + (z - (y * z)));
	} else if (b <= 3.1e-22) {
		tmp = x + (z - (a * (t + -1.0)));
	} else {
		tmp = t_1 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2.2e+126:
		tmp = t_1
	elif b <= -1.05e-164:
		tmp = x + (a + (z - (y * z)))
	elif b <= 3.1e-22:
		tmp = x + (z - (a * (t + -1.0)))
	else:
		tmp = t_1 - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2.2e+126)
		tmp = t_1;
	elseif (b <= -1.05e-164)
		tmp = Float64(x + Float64(a + Float64(z - Float64(y * z))));
	elseif (b <= 3.1e-22)
		tmp = Float64(x + Float64(z - Float64(a * Float64(t + -1.0))));
	else
		tmp = Float64(t_1 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.2e+126)
		tmp = t_1;
	elseif (b <= -1.05e-164)
		tmp = x + (a + (z - (y * z)));
	elseif (b <= 3.1e-22)
		tmp = x + (z - (a * (t + -1.0)));
	else
		tmp = t_1 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+126], t$95$1, If[LessEqual[b, -1.05e-164], N[(x + N[(a + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-22], N[(x + N[(z - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.19999999999999999e126

   1. Initial program 89.0%

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

   2. Taylor expanded in b around inf 83.0%

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

   if -2.19999999999999999e126 < b < -1.04999999999999995e-164

   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. Taylor expanded in b around 0 80.7%

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

   3. Taylor expanded in t around 0 68.3%

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

      1. +-commutative 68.3%

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

      2. sub-neg 68.3%

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

      3. metadata-eval 68.3%

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

      4. mul-1-neg 68.3%

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

      5. unsub-neg 68.3%

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

      6. distribute-rgt-in 68.3%

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

      7. neg-mul-1 68.3%

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

      8. unsub-neg 68.3%

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

   5. Simplified 68.3%

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

   if -1.04999999999999995e-164 < b < 3.10000000000000013e-22

   1. Initial program 98.7%

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

   2. Taylor expanded in b around 0 97.5%

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

   3. Taylor expanded in y around 0 76.8%

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

   if 3.10000000000000013e-22 < b

   1. Initial program 94.9%

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

   2. Taylor expanded in y around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-rgt-neg-in 73.4%

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

   4. Simplified 73.4%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+126}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-164}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-22}:\\ \;\;\;\;x + \left(z - a \cdot \left(t + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \end{array} \]

Alternative 13: 80.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -5.5e+126)
     t_1
     (if (<= b 1.3e+31)
       (+ x (- (* a (- 1.0 t)) (* z (+ y -1.0))))
       (- t_1 (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -5.5e+126) {
		tmp = t_1;
	} else if (b <= 1.3e+31) {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	} else {
		tmp = t_1 - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-5.5d+126)) then
        tmp = t_1
    else if (b <= 1.3d+31) then
        tmp = x + ((a * (1.0d0 - t)) - (z * (y + (-1.0d0))))
    else
        tmp = t_1 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -5.5e+126) {
		tmp = t_1;
	} else if (b <= 1.3e+31) {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	} else {
		tmp = t_1 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -5.5e+126:
		tmp = t_1
	elif b <= 1.3e+31:
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)))
	else:
		tmp = t_1 - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -5.5e+126)
		tmp = t_1;
	elseif (b <= 1.3e+31)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(t_1 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -5.5e+126)
		tmp = t_1;
	elseif (b <= 1.3e+31)
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	else
		tmp = t_1 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+126], t$95$1, If[LessEqual[b, 1.3e+31], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.5000000000000004e126

   1. Initial program 89.0%

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

   2. Taylor expanded in b around inf 83.0%

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

   if -5.5000000000000004e126 < b < 1.3e31

   1. Initial program 97.5%

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

   2. Taylor expanded in b around 0 88.7%

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

   if 1.3e31 < b

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. distribute-rgt-neg-in 77.0%

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

   4. Simplified 77.0%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+126}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \end{array} \]

Alternative 14: 36.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9 \cdot 10^{+190}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-98}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))))
   (if (<= b -8.2e+231)
     t_1
     (if (<= b -9e+190)
       (* y b)
       (if (<= b -2.6e+104)
         t_1
         (if (<= b -8.2e-98)
           (- (* y z))
           (if (<= b 2.1e+31) (* a (- 1.0 t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -8.2e+231) {
		tmp = t_1;
	} else if (b <= -9e+190) {
		tmp = y * b;
	} else if (b <= -2.6e+104) {
		tmp = t_1;
	} else if (b <= -8.2e-98) {
		tmp = -(y * z);
	} else if (b <= 2.1e+31) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    if (b <= (-8.2d+231)) then
        tmp = t_1
    else if (b <= (-9d+190)) then
        tmp = y * b
    else if (b <= (-2.6d+104)) then
        tmp = t_1
    else if (b <= (-8.2d-98)) then
        tmp = -(y * z)
    else if (b <= 2.1d+31) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -8.2e+231) {
		tmp = t_1;
	} else if (b <= -9e+190) {
		tmp = y * b;
	} else if (b <= -2.6e+104) {
		tmp = t_1;
	} else if (b <= -8.2e-98) {
		tmp = -(y * z);
	} else if (b <= 2.1e+31) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	tmp = 0
	if b <= -8.2e+231:
		tmp = t_1
	elif b <= -9e+190:
		tmp = y * b
	elif b <= -2.6e+104:
		tmp = t_1
	elif b <= -8.2e-98:
		tmp = -(y * z)
	elif b <= 2.1e+31:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -8.2e+231)
		tmp = t_1;
	elseif (b <= -9e+190)
		tmp = Float64(y * b);
	elseif (b <= -2.6e+104)
		tmp = t_1;
	elseif (b <= -8.2e-98)
		tmp = Float64(-Float64(y * z));
	elseif (b <= 2.1e+31)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -8.2e+231)
		tmp = t_1;
	elseif (b <= -9e+190)
		tmp = y * b;
	elseif (b <= -2.6e+104)
		tmp = t_1;
	elseif (b <= -8.2e-98)
		tmp = -(y * z);
	elseif (b <= 2.1e+31)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e+231], t$95$1, If[LessEqual[b, -9e+190], N[(y * b), $MachinePrecision], If[LessEqual[b, -2.6e+104], t$95$1, If[LessEqual[b, -8.2e-98], (-N[(y * z), $MachinePrecision]), If[LessEqual[b, 2.1e+31], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.2000000000000006e231 or -8.9999999999999999e190 < b < -2.6e104 or 2.09999999999999979e31 < b

   1. Initial program 89.7%

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

   2. Taylor expanded in b around inf 75.5%

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

   3. Taylor expanded in y around 0 56.0%

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

   if -8.2000000000000006e231 < b < -8.9999999999999999e190

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 87.5%

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

   3. Taylor expanded in b around inf 87.5%

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

   if -2.6e104 < b < -8.1999999999999996e-98

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 96.0%

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

   3. Taylor expanded in z around inf 48.8%

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

      1. distribute-rgt-in 48.8%

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

      2. metadata-eval 48.8%

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

      3. associate-*r* 48.8%

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

      4. mul-1-neg 48.8%

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

      5. unsub-neg 48.8%

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

      6. metadata-eval 48.8%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in y around inf 37.1%

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

      1. mul-1-neg 37.1%

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

      2. distribute-rgt-neg-out 37.1%

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

   8. Simplified 37.1%

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

   if -8.1999999999999996e-98 < b < 2.09999999999999979e31

   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. Taylor expanded in a around inf 44.3%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+231}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{+190}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-98}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 15: 41.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+130}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-164}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-133}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.2e+130)
   (* b (- y 2.0))
   (if (<= b -3.7e-14)
     (- x (* y z))
     (if (<= b -1.22e-164)
       (* z (- 1.0 y))
       (if (<= b 9.8e-133)
         (- x (* t a))
         (if (<= b 5.6e+31) (* a (- 1.0 t)) (* b (- t 2.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e+130) {
		tmp = b * (y - 2.0);
	} else if (b <= -3.7e-14) {
		tmp = x - (y * z);
	} else if (b <= -1.22e-164) {
		tmp = z * (1.0 - y);
	} else if (b <= 9.8e-133) {
		tmp = x - (t * a);
	} else if (b <= 5.6e+31) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8.2d+130)) then
        tmp = b * (y - 2.0d0)
    else if (b <= (-3.7d-14)) then
        tmp = x - (y * z)
    else if (b <= (-1.22d-164)) then
        tmp = z * (1.0d0 - y)
    else if (b <= 9.8d-133) then
        tmp = x - (t * a)
    else if (b <= 5.6d+31) then
        tmp = a * (1.0d0 - t)
    else
        tmp = b * (t - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e+130) {
		tmp = b * (y - 2.0);
	} else if (b <= -3.7e-14) {
		tmp = x - (y * z);
	} else if (b <= -1.22e-164) {
		tmp = z * (1.0 - y);
	} else if (b <= 9.8e-133) {
		tmp = x - (t * a);
	} else if (b <= 5.6e+31) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.2e+130:
		tmp = b * (y - 2.0)
	elif b <= -3.7e-14:
		tmp = x - (y * z)
	elif b <= -1.22e-164:
		tmp = z * (1.0 - y)
	elif b <= 9.8e-133:
		tmp = x - (t * a)
	elif b <= 5.6e+31:
		tmp = a * (1.0 - t)
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.2e+130)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= -3.7e-14)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= -1.22e-164)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 9.8e-133)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 5.6e+31)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.2e+130)
		tmp = b * (y - 2.0);
	elseif (b <= -3.7e-14)
		tmp = x - (y * z);
	elseif (b <= -1.22e-164)
		tmp = z * (1.0 - y);
	elseif (b <= 9.8e-133)
		tmp = x - (t * a);
	elseif (b <= 5.6e+31)
		tmp = a * (1.0 - t);
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.2e+130], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.7e-14], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.22e-164], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e-133], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+31], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -8.19999999999999955e130

   1. Initial program 88.8%

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

   2. Taylor expanded in b around inf 82.9%

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

   3. Taylor expanded in t around 0 61.4%

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

   if -8.19999999999999955e130 < b < -3.70000000000000001e-14

   1. Initial program 90.6%

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

   2. Taylor expanded in b around 0 70.9%

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

   3. Taylor expanded in y around inf 50.1%

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

   if -3.70000000000000001e-14 < b < -1.2199999999999999e-164

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 58.9%

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

   if -1.2199999999999999e-164 < b < 9.79999999999999992e-133

   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. Taylor expanded in b around 0 96.7%

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

   3. Taylor expanded in y around 0 76.3%

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

   4. Taylor expanded in t around inf 59.8%

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

      1. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if 9.79999999999999992e-133 < b < 5.60000000000000034e31

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 55.9%

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

   if 5.60000000000000034e31 < b

   1. Initial program 93.4%

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

   2. Taylor expanded in b around inf 76.5%

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

   3. Taylor expanded in y around 0 57.8%

      \[\leadsto b \cdot \color{blue}{\left(t - 2\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+130}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-164}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-133}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 16: 41.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+136}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-164}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-132}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.9e+136)
   (* b (- y 2.0))
   (if (<= b -3.4e-13)
     (- x (* y z))
     (if (<= b -1e-164)
       (- z (* y z))
       (if (<= b 1.2e-132)
         (- x (* t a))
         (if (<= b 3.8e+31) (* a (- 1.0 t)) (* b (- t 2.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.9e+136) {
		tmp = b * (y - 2.0);
	} else if (b <= -3.4e-13) {
		tmp = x - (y * z);
	} else if (b <= -1e-164) {
		tmp = z - (y * z);
	} else if (b <= 1.2e-132) {
		tmp = x - (t * a);
	} else if (b <= 3.8e+31) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.9d+136)) then
        tmp = b * (y - 2.0d0)
    else if (b <= (-3.4d-13)) then
        tmp = x - (y * z)
    else if (b <= (-1d-164)) then
        tmp = z - (y * z)
    else if (b <= 1.2d-132) then
        tmp = x - (t * a)
    else if (b <= 3.8d+31) then
        tmp = a * (1.0d0 - t)
    else
        tmp = b * (t - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.9e+136) {
		tmp = b * (y - 2.0);
	} else if (b <= -3.4e-13) {
		tmp = x - (y * z);
	} else if (b <= -1e-164) {
		tmp = z - (y * z);
	} else if (b <= 1.2e-132) {
		tmp = x - (t * a);
	} else if (b <= 3.8e+31) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.9e+136:
		tmp = b * (y - 2.0)
	elif b <= -3.4e-13:
		tmp = x - (y * z)
	elif b <= -1e-164:
		tmp = z - (y * z)
	elif b <= 1.2e-132:
		tmp = x - (t * a)
	elif b <= 3.8e+31:
		tmp = a * (1.0 - t)
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.9e+136)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= -3.4e-13)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= -1e-164)
		tmp = Float64(z - Float64(y * z));
	elseif (b <= 1.2e-132)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 3.8e+31)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.9e+136)
		tmp = b * (y - 2.0);
	elseif (b <= -3.4e-13)
		tmp = x - (y * z);
	elseif (b <= -1e-164)
		tmp = z - (y * z);
	elseif (b <= 1.2e-132)
		tmp = x - (t * a);
	elseif (b <= 3.8e+31)
		tmp = a * (1.0 - t);
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.9e+136], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.4e-13], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e-164], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-132], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+31], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.90000000000000019e136

   1. Initial program 88.8%

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

   2. Taylor expanded in b around inf 82.9%

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

   3. Taylor expanded in t around 0 61.4%

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

   if -3.90000000000000019e136 < b < -3.40000000000000015e-13

   1. Initial program 90.6%

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

   2. Taylor expanded in b around 0 70.9%

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

   3. Taylor expanded in y around inf 50.1%

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

   if -3.40000000000000015e-13 < b < -9.99999999999999962e-165

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

   3. Taylor expanded in z around inf 58.9%

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

      1. distribute-rgt-in 58.9%

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

      2. metadata-eval 58.9%

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

      3. associate-*r* 58.9%

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

      4. mul-1-neg 58.9%

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

      5. unsub-neg 58.9%

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

      6. metadata-eval 58.9%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 58.9%

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

   5. Simplified 58.9%

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

   if -9.99999999999999962e-165 < b < 1.20000000000000008e-132

   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. Taylor expanded in b around 0 96.7%

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

   3. Taylor expanded in y around 0 76.3%

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

   4. Taylor expanded in t around inf 59.8%

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

      1. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if 1.20000000000000008e-132 < b < 3.8000000000000001e31

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 55.9%

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

   if 3.8000000000000001e31 < b

   1. Initial program 93.4%

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

   2. Taylor expanded in b around inf 76.5%

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

   3. Taylor expanded in y around 0 57.8%

      \[\leadsto b \cdot \color{blue}{\left(t - 2\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+136}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-164}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-132}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 17: 58.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + a\right) - t \cdot a\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.58 \cdot 10^{-164}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ x a) (* t a))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.06e+71)
     t_2
     (if (<= b -6.8e-19)
       t_1
       (if (<= b -1.58e-164) (- z (* y z)) (if (<= b 2.9e+142) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + a) - (t * a);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.06e+71) {
		tmp = t_2;
	} else if (b <= -6.8e-19) {
		tmp = t_1;
	} else if (b <= -1.58e-164) {
		tmp = z - (y * z);
	} else if (b <= 2.9e+142) {
		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) - (t * a)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.06d+71)) then
        tmp = t_2
    else if (b <= (-6.8d-19)) then
        tmp = t_1
    else if (b <= (-1.58d-164)) then
        tmp = z - (y * z)
    else if (b <= 2.9d+142) 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) - (t * a);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.06e+71) {
		tmp = t_2;
	} else if (b <= -6.8e-19) {
		tmp = t_1;
	} else if (b <= -1.58e-164) {
		tmp = z - (y * z);
	} else if (b <= 2.9e+142) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + a) - (t * a)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.06e+71:
		tmp = t_2
	elif b <= -6.8e-19:
		tmp = t_1
	elif b <= -1.58e-164:
		tmp = z - (y * z)
	elif b <= 2.9e+142:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + a) - Float64(t * a))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.06e+71)
		tmp = t_2;
	elseif (b <= -6.8e-19)
		tmp = t_1;
	elseif (b <= -1.58e-164)
		tmp = Float64(z - Float64(y * z));
	elseif (b <= 2.9e+142)
		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) - (t * a);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.06e+71)
		tmp = t_2;
	elseif (b <= -6.8e-19)
		tmp = t_1;
	elseif (b <= -1.58e-164)
		tmp = z - (y * z);
	elseif (b <= 2.9e+142)
		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[(N[(x + a), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.06e+71], t$95$2, If[LessEqual[b, -6.8e-19], t$95$1, If[LessEqual[b, -1.58e-164], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e+142], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.06e71 or 2.90000000000000013e142 < b

   1. Initial program 87.3%

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

   2. Taylor expanded in b around inf 83.9%

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

   if -1.06e71 < b < -6.8000000000000004e-19 or -1.57999999999999998e-164 < b < 2.90000000000000013e142

   1. Initial program 98.5%

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

   2. Taylor expanded in y around 0 98.5%

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

   3. Taylor expanded in z around 0 73.0%

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

      1. associate--l+ 73.0%

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

      2. sub-neg 73.0%

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

      3. metadata-eval 73.0%

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

      4. distribute-lft-out 73.0%

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

      5. sub-neg 73.0%

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

      6. metadata-eval 73.0%

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

      7. fma-neg 73.7%

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

      8. associate-+r+ 73.7%

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

      9. +-commutative 73.7%

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

      10. associate-+l+ 73.7%

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

      11. distribute-rgt-in 73.7%

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

      12. *-commutative 73.7%

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

      13. +-commutative 73.7%

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

      14. distribute-neg-in 73.7%

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

      15. mul-1-neg 73.7%

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

      16. remove-double-neg 73.7%

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

      17. unsub-neg 73.7%

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

      18. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in b around 0 59.7%

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

   if -6.8000000000000004e-19 < b < -1.57999999999999998e-164

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

   3. Taylor expanded in z around inf 60.6%

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

      1. distribute-rgt-in 60.7%

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

      2. metadata-eval 60.7%

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

      3. associate-*r* 60.7%

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

      4. mul-1-neg 60.7%

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

      5. unsub-neg 60.7%

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

      6. metadata-eval 60.7%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 60.7%

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

   5. Simplified 60.7%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-19}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{elif}\;b \leq -1.58 \cdot 10^{-164}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+142}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 18: 68.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-164}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+142}:\\ \;\;\;\;x + \left(z - a \cdot \left(t + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -8.5e+126)
     t_1
     (if (<= b -1.45e-164)
       (+ x (+ a (- z (* y z))))
       (if (<= b 3e+142) (+ x (- z (* a (+ t -1.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -8.5e+126) {
		tmp = t_1;
	} else if (b <= -1.45e-164) {
		tmp = x + (a + (z - (y * z)));
	} else if (b <= 3e+142) {
		tmp = x + (z - (a * (t + -1.0)));
	} 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 = b * ((y + t) - 2.0d0)
    if (b <= (-8.5d+126)) then
        tmp = t_1
    else if (b <= (-1.45d-164)) then
        tmp = x + (a + (z - (y * z)))
    else if (b <= 3d+142) then
        tmp = x + (z - (a * (t + (-1.0d0))))
    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 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -8.5e+126) {
		tmp = t_1;
	} else if (b <= -1.45e-164) {
		tmp = x + (a + (z - (y * z)));
	} else if (b <= 3e+142) {
		tmp = x + (z - (a * (t + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -8.5e+126:
		tmp = t_1
	elif b <= -1.45e-164:
		tmp = x + (a + (z - (y * z)))
	elif b <= 3e+142:
		tmp = x + (z - (a * (t + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -8.5e+126)
		tmp = t_1;
	elseif (b <= -1.45e-164)
		tmp = Float64(x + Float64(a + Float64(z - Float64(y * z))));
	elseif (b <= 3e+142)
		tmp = Float64(x + Float64(z - Float64(a * Float64(t + -1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -8.5e+126)
		tmp = t_1;
	elseif (b <= -1.45e-164)
		tmp = x + (a + (z - (y * z)));
	elseif (b <= 3e+142)
		tmp = x + (z - (a * (t + -1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.5e+126], t$95$1, If[LessEqual[b, -1.45e-164], N[(x + N[(a + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+142], N[(x + N[(z - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.49999999999999944e126 or 2.99999999999999975e142 < b

   1. Initial program 89.0%

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

   2. Taylor expanded in b around inf 86.5%

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

   if -8.49999999999999944e126 < b < -1.45e-164

   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. Taylor expanded in b around 0 80.7%

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

   3. Taylor expanded in t around 0 68.3%

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

      1. +-commutative 68.3%

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

      2. sub-neg 68.3%

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

      3. metadata-eval 68.3%

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

      4. mul-1-neg 68.3%

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

      5. unsub-neg 68.3%

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

      6. distribute-rgt-in 68.3%

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

      7. neg-mul-1 68.3%

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

      8. unsub-neg 68.3%

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

   5. Simplified 68.3%

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

   if -1.45e-164 < b < 2.99999999999999975e142

   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. Taylor expanded in b around 0 88.1%

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

   3. Taylor expanded in y around 0 69.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+126}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-164}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+142}:\\ \;\;\;\;x + \left(z - a \cdot \left(t + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 19: 26.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+131}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-164}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= b -4.5e+131)
     (* y b)
     (if (<= b -1e-164)
       (- (* y z))
       (if (<= b 2.2e-267)
         t_1
         (if (<= b 6e-159) x (if (<= b 1.45e+32) t_1 (* t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (b <= -4.5e+131) {
		tmp = y * b;
	} else if (b <= -1e-164) {
		tmp = -(y * z);
	} else if (b <= 2.2e-267) {
		tmp = t_1;
	} else if (b <= 6e-159) {
		tmp = x;
	} else if (b <= 1.45e+32) {
		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 = t * -a
    if (b <= (-4.5d+131)) then
        tmp = y * b
    else if (b <= (-1d-164)) then
        tmp = -(y * z)
    else if (b <= 2.2d-267) then
        tmp = t_1
    else if (b <= 6d-159) then
        tmp = x
    else if (b <= 1.45d+32) 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 = t * -a;
	double tmp;
	if (b <= -4.5e+131) {
		tmp = y * b;
	} else if (b <= -1e-164) {
		tmp = -(y * z);
	} else if (b <= 2.2e-267) {
		tmp = t_1;
	} else if (b <= 6e-159) {
		tmp = x;
	} else if (b <= 1.45e+32) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if b <= -4.5e+131:
		tmp = y * b
	elif b <= -1e-164:
		tmp = -(y * z)
	elif b <= 2.2e-267:
		tmp = t_1
	elif b <= 6e-159:
		tmp = x
	elif b <= 1.45e+32:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (b <= -4.5e+131)
		tmp = Float64(y * b);
	elseif (b <= -1e-164)
		tmp = Float64(-Float64(y * z));
	elseif (b <= 2.2e-267)
		tmp = t_1;
	elseif (b <= 6e-159)
		tmp = x;
	elseif (b <= 1.45e+32)
		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 = t * -a;
	tmp = 0.0;
	if (b <= -4.5e+131)
		tmp = y * b;
	elseif (b <= -1e-164)
		tmp = -(y * z);
	elseif (b <= 2.2e-267)
		tmp = t_1;
	elseif (b <= 6e-159)
		tmp = x;
	elseif (b <= 1.45e+32)
		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[(t * (-a)), $MachinePrecision]}, If[LessEqual[b, -4.5e+131], N[(y * b), $MachinePrecision], If[LessEqual[b, -1e-164], (-N[(y * z), $MachinePrecision]), If[LessEqual[b, 2.2e-267], t$95$1, If[LessEqual[b, 6e-159], x, If[LessEqual[b, 1.45e+32], t$95$1, N[(t * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.5000000000000002e131

   1. Initial program 88.8%

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

   2. Taylor expanded in y around inf 46.2%

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

   3. Taylor expanded in b around inf 41.8%

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

   if -4.5000000000000002e131 < b < -9.99999999999999962e-165

   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. Taylor expanded in y around 0 96.0%

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

   3. Taylor expanded in z around inf 46.9%

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

      1. distribute-rgt-in 46.9%

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

      2. metadata-eval 46.9%

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

      3. associate-*r* 46.9%

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

      4. mul-1-neg 46.9%

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

      5. unsub-neg 46.9%

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

      6. metadata-eval 46.9%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in y around inf 32.6%

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

      1. mul-1-neg 32.6%

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

      2. distribute-rgt-neg-out 32.6%

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

   8. Simplified 32.6%

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

   if -9.99999999999999962e-165 < b < 2.19999999999999988e-267 or 6.00000000000000018e-159 < b < 1.45000000000000001e32

   1. Initial program 98.5%

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

   2. Taylor expanded in a around inf 53.5%

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

   3. Taylor expanded in t around inf 41.3%

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

      1. associate-*r* 41.3%

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

      2. mul-1-neg 41.3%

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

   5. Simplified 41.3%

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

   if 2.19999999999999988e-267 < b < 6.00000000000000018e-159

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 39.1%

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

   if 1.45000000000000001e32 < b

   1. Initial program 93.4%

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

   2. Taylor expanded in b around inf 76.5%

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

   3. Taylor expanded in t around inf 44.3%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+131}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-164}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 20: 45.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5400:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-266}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 760:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -5400.0)
     t_2
     (if (<= t -6e-169)
       t_1
       (if (<= t -1.8e-266) a (if (<= t 760.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -5400.0) {
		tmp = t_2;
	} else if (t <= -6e-169) {
		tmp = t_1;
	} else if (t <= -1.8e-266) {
		tmp = a;
	} else if (t <= 760.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-5400.0d0)) then
        tmp = t_2
    else if (t <= (-6d-169)) then
        tmp = t_1
    else if (t <= (-1.8d-266)) then
        tmp = a
    else if (t <= 760.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -5400.0) {
		tmp = t_2;
	} else if (t <= -6e-169) {
		tmp = t_1;
	} else if (t <= -1.8e-266) {
		tmp = a;
	} else if (t <= 760.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -5400.0:
		tmp = t_2
	elif t <= -6e-169:
		tmp = t_1
	elif t <= -1.8e-266:
		tmp = a
	elif t <= 760.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -5400.0)
		tmp = t_2;
	elseif (t <= -6e-169)
		tmp = t_1;
	elseif (t <= -1.8e-266)
		tmp = a;
	elseif (t <= 760.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -5400.0)
		tmp = t_2;
	elseif (t <= -6e-169)
		tmp = t_1;
	elseif (t <= -1.8e-266)
		tmp = a;
	elseif (t <= 760.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5400.0], t$95$2, If[LessEqual[t, -6e-169], t$95$1, If[LessEqual[t, -1.8e-266], a, If[LessEqual[t, 760.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5400 or 760 < t

   1. Initial program 92.6%

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

   2. Taylor expanded in t around inf 63.6%

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

   if -5400 < t < -5.9999999999999998e-169 or -1.8e-266 < t < 760

   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. Taylor expanded in b around inf 39.7%

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

   3. Taylor expanded in t around 0 39.4%

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

   if -5.9999999999999998e-169 < t < -1.8e-266

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 38.3%

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

   3. Taylor expanded in t around 0 38.3%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5400:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-266}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 760:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 21: 42.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-164}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-132}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+73)
   (* b (- y 2.0))
   (if (<= b -1.55e-164)
     (* z (- 1.0 y))
     (if (<= b 1.2e-132)
       (- x (* t a))
       (if (<= b 6.4e+32) (* a (- 1.0 t)) (* b (- t 2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+73) {
		tmp = b * (y - 2.0);
	} else if (b <= -1.55e-164) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.2e-132) {
		tmp = x - (t * a);
	} else if (b <= 6.4e+32) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.15d+73)) then
        tmp = b * (y - 2.0d0)
    else if (b <= (-1.55d-164)) then
        tmp = z * (1.0d0 - y)
    else if (b <= 1.2d-132) then
        tmp = x - (t * a)
    else if (b <= 6.4d+32) then
        tmp = a * (1.0d0 - t)
    else
        tmp = b * (t - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+73) {
		tmp = b * (y - 2.0);
	} else if (b <= -1.55e-164) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.2e-132) {
		tmp = x - (t * a);
	} else if (b <= 6.4e+32) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+73:
		tmp = b * (y - 2.0)
	elif b <= -1.55e-164:
		tmp = z * (1.0 - y)
	elif b <= 1.2e-132:
		tmp = x - (t * a)
	elif b <= 6.4e+32:
		tmp = a * (1.0 - t)
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+73)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= -1.55e-164)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 1.2e-132)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 6.4e+32)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.15e+73)
		tmp = b * (y - 2.0);
	elseif (b <= -1.55e-164)
		tmp = z * (1.0 - y);
	elseif (b <= 1.2e-132)
		tmp = x - (t * a);
	elseif (b <= 6.4e+32)
		tmp = a * (1.0 - t);
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+73], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.55e-164], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-132], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e+32], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.15e73

   1. Initial program 86.4%

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

   2. Taylor expanded in b around inf 79.4%

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

   3. Taylor expanded in t around 0 57.3%

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

   if -1.15e73 < b < -1.55e-164

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 48.6%

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

   if -1.55e-164 < b < 1.20000000000000008e-132

   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. Taylor expanded in b around 0 96.7%

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

   3. Taylor expanded in y around 0 76.3%

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

   4. Taylor expanded in t around inf 59.8%

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

      1. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if 1.20000000000000008e-132 < b < 6.3999999999999998e32

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 55.9%

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

   if 6.3999999999999998e32 < b

   1. Initial program 93.4%

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

   2. Taylor expanded in b around inf 76.5%

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

   3. Taylor expanded in y around 0 57.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-164}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-132}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 22: 27.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -y \cdot z\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{-219}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 2.52 \cdot 10^{-107}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* y z))))
   (if (<= y -1.8e+95)
     t_1
     (if (<= y 1.14e-219)
       (* t b)
       (if (<= y 2.52e-107) z (if (<= y 5.8e-6) (* t b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(y * z);
	double tmp;
	if (y <= -1.8e+95) {
		tmp = t_1;
	} else if (y <= 1.14e-219) {
		tmp = t * b;
	} else if (y <= 2.52e-107) {
		tmp = z;
	} else if (y <= 5.8e-6) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(y * z)
    if (y <= (-1.8d+95)) then
        tmp = t_1
    else if (y <= 1.14d-219) then
        tmp = t * b
    else if (y <= 2.52d-107) then
        tmp = z
    else if (y <= 5.8d-6) then
        tmp = t * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(y * z);
	double tmp;
	if (y <= -1.8e+95) {
		tmp = t_1;
	} else if (y <= 1.14e-219) {
		tmp = t * b;
	} else if (y <= 2.52e-107) {
		tmp = z;
	} else if (y <= 5.8e-6) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -(y * z)
	tmp = 0
	if y <= -1.8e+95:
		tmp = t_1
	elif y <= 1.14e-219:
		tmp = t * b
	elif y <= 2.52e-107:
		tmp = z
	elif y <= 5.8e-6:
		tmp = t * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-Float64(y * z))
	tmp = 0.0
	if (y <= -1.8e+95)
		tmp = t_1;
	elseif (y <= 1.14e-219)
		tmp = Float64(t * b);
	elseif (y <= 2.52e-107)
		tmp = z;
	elseif (y <= 5.8e-6)
		tmp = Float64(t * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -(y * z);
	tmp = 0.0;
	if (y <= -1.8e+95)
		tmp = t_1;
	elseif (y <= 1.14e-219)
		tmp = t * b;
	elseif (y <= 2.52e-107)
		tmp = z;
	elseif (y <= 5.8e-6)
		tmp = t * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = (-N[(y * z), $MachinePrecision])}, If[LessEqual[y, -1.8e+95], t$95$1, If[LessEqual[y, 1.14e-219], N[(t * b), $MachinePrecision], If[LessEqual[y, 2.52e-107], z, If[LessEqual[y, 5.8e-6], N[(t * b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999989e95 or 5.8000000000000004e-6 < 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. Taylor expanded in y around 0 91.7%

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

   3. Taylor expanded in z around inf 45.9%

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

      1. distribute-rgt-in 45.9%

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

      2. metadata-eval 45.9%

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

      3. associate-*r* 45.9%

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

      4. mul-1-neg 45.9%

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

      5. unsub-neg 45.9%

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

      6. metadata-eval 45.9%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in y around inf 45.6%

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

      1. mul-1-neg 45.6%

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

      2. distribute-rgt-neg-out 45.6%

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

   8. Simplified 45.6%

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

   if -1.79999999999999989e95 < y < 1.1399999999999999e-219 or 2.5199999999999999e-107 < y < 5.8000000000000004e-6

   1. Initial program 98.2%

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

   2. Taylor expanded in b around inf 42.9%

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

   3. Taylor expanded in t around inf 28.0%

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

   if 1.1399999999999999e-219 < y < 2.5199999999999999e-107

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in z around inf 36.7%

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

      1. distribute-rgt-in 36.7%

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

      2. metadata-eval 36.7%

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

      3. associate-*r* 36.7%

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

      4. mul-1-neg 36.7%

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

      5. unsub-neg 36.7%

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

      6. metadata-eval 36.7%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in y around 0 36.7%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+95}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{-219}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 2.52 \cdot 10^{-107}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;-y \cdot z\\ \end{array} \]

Alternative 23: 26.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+72}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-128}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.8e+72)
   (* t b)
   (if (<= t 3.5e-208)
     x
     (if (<= t 8.2e-128) (* -2.0 b) (if (<= t 3.9e+28) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.8e+72) {
		tmp = t * b;
	} else if (t <= 3.5e-208) {
		tmp = x;
	} else if (t <= 8.2e-128) {
		tmp = -2.0 * b;
	} else if (t <= 3.9e+28) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.8d+72)) then
        tmp = t * b
    else if (t <= 3.5d-208) then
        tmp = x
    else if (t <= 8.2d-128) then
        tmp = (-2.0d0) * b
    else if (t <= 3.9d+28) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.8e+72) {
		tmp = t * b;
	} else if (t <= 3.5e-208) {
		tmp = x;
	} else if (t <= 8.2e-128) {
		tmp = -2.0 * b;
	} else if (t <= 3.9e+28) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.8e+72:
		tmp = t * b
	elif t <= 3.5e-208:
		tmp = x
	elif t <= 8.2e-128:
		tmp = -2.0 * b
	elif t <= 3.9e+28:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.8e+72)
		tmp = Float64(t * b);
	elseif (t <= 3.5e-208)
		tmp = x;
	elseif (t <= 8.2e-128)
		tmp = Float64(-2.0 * b);
	elseif (t <= 3.9e+28)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.8e+72)
		tmp = t * b;
	elseif (t <= 3.5e-208)
		tmp = x;
	elseif (t <= 8.2e-128)
		tmp = -2.0 * b;
	elseif (t <= 3.9e+28)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.8e+72], N[(t * b), $MachinePrecision], If[LessEqual[t, 3.5e-208], x, If[LessEqual[t, 8.2e-128], N[(-2.0 * b), $MachinePrecision], If[LessEqual[t, 3.9e+28], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7999999999999999e72 or 3.8999999999999999e28 < t

   1. Initial program 91.9%

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

   2. Taylor expanded in b around inf 43.1%

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

   3. Taylor expanded in t around inf 38.6%

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

   if -2.7999999999999999e72 < t < 3.49999999999999991e-208 or 8.1999999999999999e-128 < t < 3.8999999999999999e28

   1. Initial program 97.5%

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

   2. Taylor expanded in x around inf 21.7%

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

   if 3.49999999999999991e-208 < t < 8.1999999999999999e-128

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 54.7%

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

   3. Taylor expanded in t around 0 54.7%

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

   4. Taylor expanded in y around 0 29.8%

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

      1. *-commutative 29.8%

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

   6. Simplified 29.8%

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

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+72}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-128}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 24: 24.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{-21}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-195}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.95e-21)
   (* y b)
   (if (<= b -2.4e-195)
     z
     (if (<= b 5.5e-135) x (if (<= b 2.5e+25) a (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.95e-21) {
		tmp = y * b;
	} else if (b <= -2.4e-195) {
		tmp = z;
	} else if (b <= 5.5e-135) {
		tmp = x;
	} else if (b <= 2.5e+25) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.95d-21)) then
        tmp = y * b
    else if (b <= (-2.4d-195)) then
        tmp = z
    else if (b <= 5.5d-135) then
        tmp = x
    else if (b <= 2.5d+25) then
        tmp = a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.95e-21) {
		tmp = y * b;
	} else if (b <= -2.4e-195) {
		tmp = z;
	} else if (b <= 5.5e-135) {
		tmp = x;
	} else if (b <= 2.5e+25) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.95e-21:
		tmp = y * b
	elif b <= -2.4e-195:
		tmp = z
	elif b <= 5.5e-135:
		tmp = x
	elif b <= 2.5e+25:
		tmp = a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.95e-21)
		tmp = Float64(y * b);
	elseif (b <= -2.4e-195)
		tmp = z;
	elseif (b <= 5.5e-135)
		tmp = x;
	elseif (b <= 2.5e+25)
		tmp = a;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.95e-21)
		tmp = y * b;
	elseif (b <= -2.4e-195)
		tmp = z;
	elseif (b <= 5.5e-135)
		tmp = x;
	elseif (b <= 2.5e+25)
		tmp = a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.95e-21], N[(y * b), $MachinePrecision], If[LessEqual[b, -2.4e-195], z, If[LessEqual[b, 5.5e-135], x, If[LessEqual[b, 2.5e+25], a, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.9500000000000001e-21

   1. Initial program 90.2%

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

   2. Taylor expanded in y around inf 43.0%

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

   3. Taylor expanded in b around inf 28.8%

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

   if -2.9500000000000001e-21 < b < -2.4e-195

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

   3. Taylor expanded in z around inf 54.4%

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

      1. distribute-rgt-in 54.5%

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

      2. metadata-eval 54.5%

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

      3. associate-*r* 54.5%

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

      4. mul-1-neg 54.5%

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

      5. unsub-neg 54.5%

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

      6. metadata-eval 54.5%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in y around 0 25.2%

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

   if -2.4e-195 < b < 5.4999999999999999e-135

   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. Taylor expanded in x around inf 26.5%

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

   if 5.4999999999999999e-135 < b < 2.50000000000000012e25

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 56.3%

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

   3. Taylor expanded in t around 0 29.4%

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

   if 2.50000000000000012e25 < b

   1. Initial program 93.7%

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

   2. Taylor expanded in b around inf 73.4%

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

   3. Taylor expanded in t around inf 42.6%

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

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{-21}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-195}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 25: 37.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -1.56 \cdot 10^{-103}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.2e+79)
   (* b (- y 2.0))
   (if (<= b -1.56e-103)
     (- (* y z))
     (if (<= b 2.4e+32) (* a (- 1.0 t)) (* b (- t 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e+79) {
		tmp = b * (y - 2.0);
	} else if (b <= -1.56e-103) {
		tmp = -(y * z);
	} else if (b <= 2.4e+32) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.2d+79)) then
        tmp = b * (y - 2.0d0)
    else if (b <= (-1.56d-103)) then
        tmp = -(y * z)
    else if (b <= 2.4d+32) then
        tmp = a * (1.0d0 - t)
    else
        tmp = b * (t - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e+79) {
		tmp = b * (y - 2.0);
	} else if (b <= -1.56e-103) {
		tmp = -(y * z);
	} else if (b <= 2.4e+32) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.2e+79:
		tmp = b * (y - 2.0)
	elif b <= -1.56e-103:
		tmp = -(y * z)
	elif b <= 2.4e+32:
		tmp = a * (1.0 - t)
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.2e+79)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= -1.56e-103)
		tmp = Float64(-Float64(y * z));
	elseif (b <= 2.4e+32)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.2e+79)
		tmp = b * (y - 2.0);
	elseif (b <= -1.56e-103)
		tmp = -(y * z);
	elseif (b <= 2.4e+32)
		tmp = a * (1.0 - t);
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.2e+79], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.56e-103], (-N[(y * z), $MachinePrecision]), If[LessEqual[b, 2.4e+32], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.19999999999999993e79

   1. Initial program 86.4%

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

   2. Taylor expanded in b around inf 79.4%

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

   3. Taylor expanded in t around 0 57.3%

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

   if -1.19999999999999993e79 < b < -1.5600000000000001e-103

   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. Taylor expanded in y around 0 97.9%

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

   3. Taylor expanded in z around inf 48.7%

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

      1. distribute-rgt-in 48.7%

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

      2. metadata-eval 48.7%

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

      3. associate-*r* 48.7%

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

      4. mul-1-neg 48.7%

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

      5. unsub-neg 48.7%

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

      6. metadata-eval 48.7%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in y around inf 36.5%

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

      1. mul-1-neg 36.5%

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

      2. distribute-rgt-neg-out 36.5%

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

   8. Simplified 36.5%

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

   if -1.5600000000000001e-103 < b < 2.39999999999999991e32

   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. Taylor expanded in a around inf 44.3%

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

   if 2.39999999999999991e32 < b

   1. Initial program 93.4%

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

   2. Taylor expanded in b around inf 76.5%

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

   3. Taylor expanded in y around 0 57.8%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -1.56 \cdot 10^{-103}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 26: 34.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+73} \lor \neg \left(z \leq 340000000000\right):\\ \;\;\;\;-y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.22e+73) (not (<= z 340000000000.0)))
   (- (* y z))
   (* a (- 1.0 t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.22e+73) || !(z <= 340000000000.0)) {
		tmp = -(y * z);
	} else {
		tmp = 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 ((z <= (-1.22d+73)) .or. (.not. (z <= 340000000000.0d0))) then
        tmp = -(y * z)
    else
        tmp = 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 ((z <= -1.22e+73) || !(z <= 340000000000.0)) {
		tmp = -(y * z);
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.22e+73) or not (z <= 340000000000.0):
		tmp = -(y * z)
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.22e+73) || !(z <= 340000000000.0))
		tmp = Float64(-Float64(y * z));
	else
		tmp = 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 ((z <= -1.22e+73) || ~((z <= 340000000000.0)))
		tmp = -(y * z);
	else
		tmp = a * (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.22e+73], N[Not[LessEqual[z, 340000000000.0]], $MachinePrecision]], (-N[(y * z), $MachinePrecision]), N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.21999999999999998e73 or 3.4e11 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0 98.2%

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

   3. Taylor expanded in z around inf 60.4%

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

      1. distribute-rgt-in 60.4%

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

      2. metadata-eval 60.4%

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

      3. associate-*r* 60.4%

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

      4. mul-1-neg 60.4%

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

      5. unsub-neg 60.4%

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

      6. metadata-eval 60.4%

         \[\leadsto \color{blue}{1} \cdot z - y \cdot z \]

      7. *-lft-identity 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in y around inf 41.8%

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

      1. mul-1-neg 41.8%

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

      2. distribute-rgt-neg-out 41.8%

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

   8. Simplified 41.8%

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

   if -1.21999999999999998e73 < z < 3.4e11

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf 40.4%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+73} \lor \neg \left(z \leq 340000000000\right):\\ \;\;\;\;-y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 27: 20.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-53}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.22e+113) x (if (<= x 5.6e-53) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.22e+113) {
		tmp = x;
	} else if (x <= 5.6e-53) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.22d+113)) then
        tmp = x
    else if (x <= 5.6d-53) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.22e+113) {
		tmp = x;
	} else if (x <= 5.6e-53) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.22e+113:
		tmp = x
	elif x <= 5.6e-53:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.22e+113)
		tmp = x;
	elseif (x <= 5.6e-53)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.22e+113)
		tmp = x;
	elseif (x <= 5.6e-53)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.22e+113], x, If[LessEqual[x, 5.6e-53], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2199999999999999e113 or 5.59999999999999971e-53 < x

   1. Initial program 92.5%

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

   2. Taylor expanded in x around inf 29.2%

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

   if -1.2199999999999999e113 < x < 5.59999999999999971e-53

   1. Initial program 97.3%

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

   2. Taylor expanded in a around inf 32.9%

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

   3. Taylor expanded in t around 0 14.6%

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

4. Final simplification 20.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-53}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 28: 11.3% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

2. Taylor expanded in a around inf 28.4%

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

3. Taylor expanded in t around 0 10.5%

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

4. Final simplification 10.5%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023293 
(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)))