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

Percentage Accurate: 95.1% → 97.9%

Time: 14.6s

Alternatives: 24

Speedup: 0.5×

• 37.0% 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: 95.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   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 t around inf 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. +-commutative 97.2%

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

   2. fma-def 98.4%

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

   3. associate--l+ 98.4%

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

   4. sub-neg 98.4%

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

   5. metadata-eval 98.4%

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

   6. sub-neg 98.4%

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

   7. associate--l+ 98.4%

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

   8. *-commutative 98.4%

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

   9. distribute-rgt-neg-in 98.4%

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

   10. fma-neg 98.4%

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

   11. neg-sub0 98.4%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

   12. sub-neg 98.4%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

   13. +-commutative 98.4%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

   14. associate--r+ 98.4%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

   15. metadata-eval 98.4%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

   16. metadata-eval 98.4%

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

   17. *-commutative 98.4%

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

   18. distribute-rgt-neg-in 98.4%

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

   19. neg-sub0 98.4%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

   20. sub-neg 98.4%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

   21. +-commutative 98.4%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

   22. associate--r+ 98.4%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 50.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := x - t \cdot a\\ t_3 := t \cdot \left(b - a\right)\\ t_4 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-29}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-168}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-70}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1300000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z)))
        (t_2 (- x (* t a)))
        (t_3 (* t (- b a)))
        (t_4 (* z (- 1.0 y))))
   (if (<= t -7.2e+52)
     t_3
     (if (<= t -2.3e+35)
       t_1
       (if (<= t -5.2e+25)
         t_2
         (if (<= t -4.5e-29)
           t_4
           (if (<= t -2.25e-46)
             t_1
             (if (<= t 4.3e-168)
               (+ x a)
               (if (<= t 1.7e-70)
                 t_4
                 (if (<= t 6e-33)
                   (* b (- y 2.0))
                   (if (<= t 1300000000000.0)
                     t_1
                     (if (<= t 2.75e+147) t_2 t_3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = x - (t * a);
	double t_3 = t * (b - a);
	double t_4 = z * (1.0 - y);
	double tmp;
	if (t <= -7.2e+52) {
		tmp = t_3;
	} else if (t <= -2.3e+35) {
		tmp = t_1;
	} else if (t <= -5.2e+25) {
		tmp = t_2;
	} else if (t <= -4.5e-29) {
		tmp = t_4;
	} else if (t <= -2.25e-46) {
		tmp = t_1;
	} else if (t <= 4.3e-168) {
		tmp = x + a;
	} else if (t <= 1.7e-70) {
		tmp = t_4;
	} else if (t <= 6e-33) {
		tmp = b * (y - 2.0);
	} else if (t <= 1300000000000.0) {
		tmp = t_1;
	} else if (t <= 2.75e+147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = x - (t * a)
    t_3 = t * (b - a)
    t_4 = z * (1.0d0 - y)
    if (t <= (-7.2d+52)) then
        tmp = t_3
    else if (t <= (-2.3d+35)) then
        tmp = t_1
    else if (t <= (-5.2d+25)) then
        tmp = t_2
    else if (t <= (-4.5d-29)) then
        tmp = t_4
    else if (t <= (-2.25d-46)) then
        tmp = t_1
    else if (t <= 4.3d-168) then
        tmp = x + a
    else if (t <= 1.7d-70) then
        tmp = t_4
    else if (t <= 6d-33) then
        tmp = b * (y - 2.0d0)
    else if (t <= 1300000000000.0d0) then
        tmp = t_1
    else if (t <= 2.75d+147) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = x - (t * a);
	double t_3 = t * (b - a);
	double t_4 = z * (1.0 - y);
	double tmp;
	if (t <= -7.2e+52) {
		tmp = t_3;
	} else if (t <= -2.3e+35) {
		tmp = t_1;
	} else if (t <= -5.2e+25) {
		tmp = t_2;
	} else if (t <= -4.5e-29) {
		tmp = t_4;
	} else if (t <= -2.25e-46) {
		tmp = t_1;
	} else if (t <= 4.3e-168) {
		tmp = x + a;
	} else if (t <= 1.7e-70) {
		tmp = t_4;
	} else if (t <= 6e-33) {
		tmp = b * (y - 2.0);
	} else if (t <= 1300000000000.0) {
		tmp = t_1;
	} else if (t <= 2.75e+147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = x - (t * a)
	t_3 = t * (b - a)
	t_4 = z * (1.0 - y)
	tmp = 0
	if t <= -7.2e+52:
		tmp = t_3
	elif t <= -2.3e+35:
		tmp = t_1
	elif t <= -5.2e+25:
		tmp = t_2
	elif t <= -4.5e-29:
		tmp = t_4
	elif t <= -2.25e-46:
		tmp = t_1
	elif t <= 4.3e-168:
		tmp = x + a
	elif t <= 1.7e-70:
		tmp = t_4
	elif t <= 6e-33:
		tmp = b * (y - 2.0)
	elif t <= 1300000000000.0:
		tmp = t_1
	elif t <= 2.75e+147:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(x - Float64(t * a))
	t_3 = Float64(t * Float64(b - a))
	t_4 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -7.2e+52)
		tmp = t_3;
	elseif (t <= -2.3e+35)
		tmp = t_1;
	elseif (t <= -5.2e+25)
		tmp = t_2;
	elseif (t <= -4.5e-29)
		tmp = t_4;
	elseif (t <= -2.25e-46)
		tmp = t_1;
	elseif (t <= 4.3e-168)
		tmp = Float64(x + a);
	elseif (t <= 1.7e-70)
		tmp = t_4;
	elseif (t <= 6e-33)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 1300000000000.0)
		tmp = t_1;
	elseif (t <= 2.75e+147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = x - (t * a);
	t_3 = t * (b - a);
	t_4 = z * (1.0 - y);
	tmp = 0.0;
	if (t <= -7.2e+52)
		tmp = t_3;
	elseif (t <= -2.3e+35)
		tmp = t_1;
	elseif (t <= -5.2e+25)
		tmp = t_2;
	elseif (t <= -4.5e-29)
		tmp = t_4;
	elseif (t <= -2.25e-46)
		tmp = t_1;
	elseif (t <= 4.3e-168)
		tmp = x + a;
	elseif (t <= 1.7e-70)
		tmp = t_4;
	elseif (t <= 6e-33)
		tmp = b * (y - 2.0);
	elseif (t <= 1300000000000.0)
		tmp = t_1;
	elseif (t <= 2.75e+147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+52], t$95$3, If[LessEqual[t, -2.3e+35], t$95$1, If[LessEqual[t, -5.2e+25], t$95$2, If[LessEqual[t, -4.5e-29], t$95$4, If[LessEqual[t, -2.25e-46], t$95$1, If[LessEqual[t, 4.3e-168], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.7e-70], t$95$4, If[LessEqual[t, 6e-33], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1300000000000.0], t$95$1, If[LessEqual[t, 2.75e+147], t$95$2, t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -7.2e52 or 2.7499999999999999e147 < 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 78.4%

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

   if -7.2e52 < t < -2.2999999999999998e35 or -4.4999999999999998e-29 < t < -2.25e-46 or 6.0000000000000003e-33 < t < 1.3e12

   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 y around inf 67.8%

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

   if -2.2999999999999998e35 < t < -5.1999999999999997e25 or 1.3e12 < t < 2.7499999999999999e147

   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 0 88.1%

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

   3. Taylor expanded in b around 0 66.3%

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

   4. Taylor expanded in t around inf 66.3%

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

      1. *-commutative 66.3%

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

   6. Simplified 66.3%

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

   if -5.1999999999999997e25 < t < -4.4999999999999998e-29 or 4.29999999999999995e-168 < t < 1.69999999999999998e-70

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 66.6%

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

   if -2.25e-46 < t < 4.29999999999999995e-168

   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 0 82.3%

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

   3. Taylor expanded in b around 0 51.7%

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

   4. Taylor expanded in t around 0 51.7%

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

      1. cancel-sign-sub-inv 51.7%

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

      2. metadata-eval 51.7%

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

      3. *-lft-identity 51.7%

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

   6. Simplified 51.7%

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

   if 1.69999999999999998e-70 < t < 6.0000000000000003e-33

   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 66.4%

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

   3. Taylor expanded in t around 0 66.4%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-168}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-70}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1300000000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+147}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 4: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-168}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))) (t_3 (* z (- 1.0 y))))
   (if (<= t -7.2e+52)
     t_2
     (if (<= t -2.55e+33)
       t_1
       (if (<= t -1.8e+26)
         t_2
         (if (<= t -2.35e-29)
           t_3
           (if (<= t -6.5e-47)
             t_1
             (if (<= t 4.3e-168)
               (+ x a)
               (if (<= t 9e-71)
                 t_3
                 (if (<= t 2.4e-33)
                   (* b (- y 2.0))
                   (if (<= t 2.4e+16) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (t <= -7.2e+52) {
		tmp = t_2;
	} else if (t <= -2.55e+33) {
		tmp = t_1;
	} else if (t <= -1.8e+26) {
		tmp = t_2;
	} else if (t <= -2.35e-29) {
		tmp = t_3;
	} else if (t <= -6.5e-47) {
		tmp = t_1;
	} else if (t <= 4.3e-168) {
		tmp = x + a;
	} else if (t <= 9e-71) {
		tmp = t_3;
	} else if (t <= 2.4e-33) {
		tmp = b * (y - 2.0);
	} else if (t <= 2.4e+16) {
		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 = y * (b - z)
    t_2 = t * (b - a)
    t_3 = z * (1.0d0 - y)
    if (t <= (-7.2d+52)) then
        tmp = t_2
    else if (t <= (-2.55d+33)) then
        tmp = t_1
    else if (t <= (-1.8d+26)) then
        tmp = t_2
    else if (t <= (-2.35d-29)) then
        tmp = t_3
    else if (t <= (-6.5d-47)) then
        tmp = t_1
    else if (t <= 4.3d-168) then
        tmp = x + a
    else if (t <= 9d-71) then
        tmp = t_3
    else if (t <= 2.4d-33) then
        tmp = b * (y - 2.0d0)
    else if (t <= 2.4d+16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (t <= -7.2e+52) {
		tmp = t_2;
	} else if (t <= -2.55e+33) {
		tmp = t_1;
	} else if (t <= -1.8e+26) {
		tmp = t_2;
	} else if (t <= -2.35e-29) {
		tmp = t_3;
	} else if (t <= -6.5e-47) {
		tmp = t_1;
	} else if (t <= 4.3e-168) {
		tmp = x + a;
	} else if (t <= 9e-71) {
		tmp = t_3;
	} else if (t <= 2.4e-33) {
		tmp = b * (y - 2.0);
	} else if (t <= 2.4e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	t_3 = z * (1.0 - y)
	tmp = 0
	if t <= -7.2e+52:
		tmp = t_2
	elif t <= -2.55e+33:
		tmp = t_1
	elif t <= -1.8e+26:
		tmp = t_2
	elif t <= -2.35e-29:
		tmp = t_3
	elif t <= -6.5e-47:
		tmp = t_1
	elif t <= 4.3e-168:
		tmp = x + a
	elif t <= 9e-71:
		tmp = t_3
	elif t <= 2.4e-33:
		tmp = b * (y - 2.0)
	elif t <= 2.4e+16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -7.2e+52)
		tmp = t_2;
	elseif (t <= -2.55e+33)
		tmp = t_1;
	elseif (t <= -1.8e+26)
		tmp = t_2;
	elseif (t <= -2.35e-29)
		tmp = t_3;
	elseif (t <= -6.5e-47)
		tmp = t_1;
	elseif (t <= 4.3e-168)
		tmp = Float64(x + a);
	elseif (t <= 9e-71)
		tmp = t_3;
	elseif (t <= 2.4e-33)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 2.4e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (t <= -7.2e+52)
		tmp = t_2;
	elseif (t <= -2.55e+33)
		tmp = t_1;
	elseif (t <= -1.8e+26)
		tmp = t_2;
	elseif (t <= -2.35e-29)
		tmp = t_3;
	elseif (t <= -6.5e-47)
		tmp = t_1;
	elseif (t <= 4.3e-168)
		tmp = x + a;
	elseif (t <= 9e-71)
		tmp = t_3;
	elseif (t <= 2.4e-33)
		tmp = b * (y - 2.0);
	elseif (t <= 2.4e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+52], t$95$2, If[LessEqual[t, -2.55e+33], t$95$1, If[LessEqual[t, -1.8e+26], t$95$2, If[LessEqual[t, -2.35e-29], t$95$3, If[LessEqual[t, -6.5e-47], t$95$1, If[LessEqual[t, 4.3e-168], N[(x + a), $MachinePrecision], If[LessEqual[t, 9e-71], t$95$3, If[LessEqual[t, 2.4e-33], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+16], t$95$1, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.2e52 or -2.5499999999999999e33 < t < -1.80000000000000012e26 or 2.4e16 < t

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 71.8%

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

   if -7.2e52 < t < -2.5499999999999999e33 or -2.3499999999999999e-29 < t < -6.5000000000000004e-47 or 2.4e-33 < t < 2.4e16

   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 63.8%

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

   if -1.80000000000000012e26 < t < -2.3499999999999999e-29 or 4.29999999999999995e-168 < t < 9.0000000000000004e-71

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 66.6%

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

   if -6.5000000000000004e-47 < t < 4.29999999999999995e-168

   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 0 82.3%

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

   3. Taylor expanded in b around 0 51.7%

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

   4. Taylor expanded in t around 0 51.7%

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

      1. cancel-sign-sub-inv 51.7%

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

      2. metadata-eval 51.7%

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

      3. *-lft-identity 51.7%

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

   6. Simplified 51.7%

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

   if 9.0000000000000004e-71 < t < 2.4e-33

   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 66.4%

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

   3. Taylor expanded in t around 0 66.4%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-168}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 5: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := t_2 + t_1\\ t_4 := x + \left(t_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{if}\;b \leq -4.9 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-55}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+79}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (+ t_2 t_1))
        (t_4 (+ x (+ t_1 (* z (- 1.0 y))))))
   (if (<= b -4.9e+29)
     t_3
     (if (<= b 9.6e-55)
       t_4
       (if (<= b 1.72e+56) t_3 (if (<= b 5.9e+79) t_4 (- t_2 (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = t_2 + t_1;
	double t_4 = x + (t_1 + (z * (1.0 - y)));
	double tmp;
	if (b <= -4.9e+29) {
		tmp = t_3;
	} else if (b <= 9.6e-55) {
		tmp = t_4;
	} else if (b <= 1.72e+56) {
		tmp = t_3;
	} else if (b <= 5.9e+79) {
		tmp = t_4;
	} else {
		tmp = t_2 - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = t_2 + t_1
    t_4 = x + (t_1 + (z * (1.0d0 - y)))
    if (b <= (-4.9d+29)) then
        tmp = t_3
    else if (b <= 9.6d-55) then
        tmp = t_4
    else if (b <= 1.72d+56) then
        tmp = t_3
    else if (b <= 5.9d+79) then
        tmp = t_4
    else
        tmp = t_2 - (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 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = t_2 + t_1;
	double t_4 = x + (t_1 + (z * (1.0 - y)));
	double tmp;
	if (b <= -4.9e+29) {
		tmp = t_3;
	} else if (b <= 9.6e-55) {
		tmp = t_4;
	} else if (b <= 1.72e+56) {
		tmp = t_3;
	} else if (b <= 5.9e+79) {
		tmp = t_4;
	} else {
		tmp = t_2 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = t_2 + t_1
	t_4 = x + (t_1 + (z * (1.0 - y)))
	tmp = 0
	if b <= -4.9e+29:
		tmp = t_3
	elif b <= 9.6e-55:
		tmp = t_4
	elif b <= 1.72e+56:
		tmp = t_3
	elif b <= 5.9e+79:
		tmp = t_4
	else:
		tmp = t_2 - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(t_2 + t_1)
	t_4 = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))))
	tmp = 0.0
	if (b <= -4.9e+29)
		tmp = t_3;
	elseif (b <= 9.6e-55)
		tmp = t_4;
	elseif (b <= 1.72e+56)
		tmp = t_3;
	elseif (b <= 5.9e+79)
		tmp = t_4;
	else
		tmp = Float64(t_2 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = t_2 + t_1;
	t_4 = x + (t_1 + (z * (1.0 - y)));
	tmp = 0.0;
	if (b <= -4.9e+29)
		tmp = t_3;
	elseif (b <= 9.6e-55)
		tmp = t_4;
	elseif (b <= 1.72e+56)
		tmp = t_3;
	elseif (b <= 5.9e+79)
		tmp = t_4;
	else
		tmp = t_2 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.9e+29], t$95$3, If[LessEqual[b, 9.6e-55], t$95$4, If[LessEqual[b, 1.72e+56], t$95$3, If[LessEqual[b, 5.9e+79], t$95$4, N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.9000000000000001e29 or 9.59999999999999966e-55 < b < 1.72e56

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0 90.3%

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

   if -4.9000000000000001e29 < b < 9.59999999999999966e-55 or 1.72e56 < b < 5.9e79

   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 95.3%

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

   if 5.9e79 < b

   1. Initial program 92.8%

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

   2. Taylor expanded in a around 0 94.7%

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

   3. Taylor expanded in y around inf 85.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.9 \cdot 10^{+29}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-55}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{+56}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+79}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) - y \cdot z\\ \end{array} \]

Alternative 6: 52.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-233}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-90}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-7}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -2.05e+52)
     t_2
     (if (<= b -8.5e-233)
       (+ x a)
       (if (<= b -3.1e-298)
         t_1
         (if (<= b 2.15e-90)
           (- x (* t a))
           (if (<= b 1.12e-57) t_1 (if (<= b 9.5e-7) (+ x a) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.05e+52) {
		tmp = t_2;
	} else if (b <= -8.5e-233) {
		tmp = x + a;
	} else if (b <= -3.1e-298) {
		tmp = t_1;
	} else if (b <= 2.15e-90) {
		tmp = x - (t * a);
	} else if (b <= 1.12e-57) {
		tmp = t_1;
	} else if (b <= 9.5e-7) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-2.05d+52)) then
        tmp = t_2
    else if (b <= (-8.5d-233)) then
        tmp = x + a
    else if (b <= (-3.1d-298)) then
        tmp = t_1
    else if (b <= 2.15d-90) then
        tmp = x - (t * a)
    else if (b <= 1.12d-57) then
        tmp = t_1
    else if (b <= 9.5d-7) then
        tmp = x + a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.05e+52) {
		tmp = t_2;
	} else if (b <= -8.5e-233) {
		tmp = x + a;
	} else if (b <= -3.1e-298) {
		tmp = t_1;
	} else if (b <= 2.15e-90) {
		tmp = x - (t * a);
	} else if (b <= 1.12e-57) {
		tmp = t_1;
	} else if (b <= 9.5e-7) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2.05e+52:
		tmp = t_2
	elif b <= -8.5e-233:
		tmp = x + a
	elif b <= -3.1e-298:
		tmp = t_1
	elif b <= 2.15e-90:
		tmp = x - (t * a)
	elif b <= 1.12e-57:
		tmp = t_1
	elif b <= 9.5e-7:
		tmp = x + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2.05e+52)
		tmp = t_2;
	elseif (b <= -8.5e-233)
		tmp = Float64(x + a);
	elseif (b <= -3.1e-298)
		tmp = t_1;
	elseif (b <= 2.15e-90)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 1.12e-57)
		tmp = t_1;
	elseif (b <= 9.5e-7)
		tmp = Float64(x + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.05e+52)
		tmp = t_2;
	elseif (b <= -8.5e-233)
		tmp = x + a;
	elseif (b <= -3.1e-298)
		tmp = t_1;
	elseif (b <= 2.15e-90)
		tmp = x - (t * a);
	elseif (b <= 1.12e-57)
		tmp = t_1;
	elseif (b <= 9.5e-7)
		tmp = x + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+52], t$95$2, If[LessEqual[b, -8.5e-233], N[(x + a), $MachinePrecision], If[LessEqual[b, -3.1e-298], t$95$1, If[LessEqual[b, 2.15e-90], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e-57], t$95$1, If[LessEqual[b, 9.5e-7], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.05e52 or 9.5000000000000001e-7 < b

   1. Initial program 94.0%

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

   2. Taylor expanded in b around inf 72.4%

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

   if -2.05e52 < b < -8.5000000000000005e-233 or 1.12e-57 < b < 9.5000000000000001e-7

   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 0 79.6%

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

   3. Taylor expanded in b around 0 68.6%

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

   4. Taylor expanded in t around 0 52.3%

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

      1. cancel-sign-sub-inv 52.3%

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

      2. metadata-eval 52.3%

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

      3. *-lft-identity 52.3%

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

   6. Simplified 52.3%

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

   if -8.5000000000000005e-233 < b < -3.1000000000000002e-298 or 2.1500000000000001e-90 < b < 1.12e-57

   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 68.1%

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

   if -3.1000000000000002e-298 < b < 2.1500000000000001e-90

   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 0 76.5%

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

   3. Taylor expanded in b around 0 74.7%

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

   4. Taylor expanded in t around inf 61.9%

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

      1. *-commutative 61.9%

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

   6. Simplified 61.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-233}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-298}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-90}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-7}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 7: 67.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-294}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x (* y b)) (* a (- 1.0 t))))
        (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -9e+34)
     t_2
     (if (<= b -4.6e-168)
       t_1
       (if (<= b -7.6e-294)
         (+ x (* z (- 1.0 y)))
         (if (<= b 2.1e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * b)) + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -9e+34) {
		tmp = t_2;
	} else if (b <= -4.6e-168) {
		tmp = t_1;
	} else if (b <= -7.6e-294) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 2.1e+37) {
		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 + (y * b)) + (a * (1.0d0 - t))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-9d+34)) then
        tmp = t_2
    else if (b <= (-4.6d-168)) then
        tmp = t_1
    else if (b <= (-7.6d-294)) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 2.1d+37) 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 + (y * b)) + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -9e+34) {
		tmp = t_2;
	} else if (b <= -4.6e-168) {
		tmp = t_1;
	} else if (b <= -7.6e-294) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 2.1e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * b)) + (a * (1.0 - t))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -9e+34:
		tmp = t_2
	elif b <= -4.6e-168:
		tmp = t_1
	elif b <= -7.6e-294:
		tmp = x + (z * (1.0 - y))
	elif b <= 2.1e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * b)) + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -9e+34)
		tmp = t_2;
	elseif (b <= -4.6e-168)
		tmp = t_1;
	elseif (b <= -7.6e-294)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 2.1e+37)
		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 + (y * b)) + (a * (1.0 - t));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -9e+34)
		tmp = t_2;
	elseif (b <= -4.6e-168)
		tmp = t_1;
	elseif (b <= -7.6e-294)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 2.1e+37)
		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 + N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e+34], t$95$2, If[LessEqual[b, -4.6e-168], t$95$1, If[LessEqual[b, -7.6e-294], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.0000000000000001e34 or 2.1000000000000001e37 < b

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 84.7%

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

   3. Taylor expanded in a around 0 82.2%

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

   if -9.0000000000000001e34 < b < -4.59999999999999971e-168 or -7.6e-294 < b < 2.1000000000000001e37

   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 0 75.1%

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

   3. Taylor expanded in y around inf 71.0%

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

   if -4.59999999999999971e-168 < b < -7.6e-294

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 89.2%

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

   3. Taylor expanded in b around 0 89.0%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-168}:\\ \;\;\;\;\left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-294}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+37}:\\ \;\;\;\;\left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 8: 85.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+34}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-64}:\\ \;\;\;\;x + \left(t_1 + t_3\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -5.2e+34)
     (+ t_2 t_1)
     (if (<= b 5.1e-64) (+ x (+ t_1 t_3)) (+ t_2 t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -5.2e+34) {
		tmp = t_2 + t_1;
	} else if (b <= 5.1e-64) {
		tmp = x + (t_1 + t_3);
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = z * (1.0d0 - y)
    if (b <= (-5.2d+34)) then
        tmp = t_2 + t_1
    else if (b <= 5.1d-64) then
        tmp = x + (t_1 + t_3)
    else
        tmp = t_2 + t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -5.2e+34) {
		tmp = t_2 + t_1;
	} else if (b <= 5.1e-64) {
		tmp = x + (t_1 + t_3);
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -5.2e+34:
		tmp = t_2 + t_1
	elif b <= 5.1e-64:
		tmp = x + (t_1 + t_3)
	else:
		tmp = t_2 + t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -5.2e+34)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 5.1e-64)
		tmp = Float64(x + Float64(t_1 + t_3));
	else
		tmp = Float64(t_2 + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -5.2e+34)
		tmp = t_2 + t_1;
	elseif (b <= 5.1e-64)
		tmp = x + (t_1 + t_3);
	else
		tmp = t_2 + t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+34], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 5.1e-64], N[(x + N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.19999999999999995e34

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 90.1%

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

   if -5.19999999999999995e34 < b < 5.09999999999999984e-64

   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 95.0%

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

   if 5.09999999999999984e-64 < b

   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 0 89.6%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+34}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-64}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 9: 64.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-294}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -1e+29)
     t_2
     (if (<= b -5.3e-168)
       t_1
       (if (<= b -5.6e-294)
         (+ x (* z (- 1.0 y)))
         (if (<= b 2.15e-63) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1e+29) {
		tmp = t_2;
	} else if (b <= -5.3e-168) {
		tmp = t_1;
	} else if (b <= -5.6e-294) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 2.15e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-1d+29)) then
        tmp = t_2
    else if (b <= (-5.3d-168)) then
        tmp = t_1
    else if (b <= (-5.6d-294)) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 2.15d-63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1e+29) {
		tmp = t_2;
	} else if (b <= -5.3e-168) {
		tmp = t_1;
	} else if (b <= -5.6e-294) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 2.15e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -1e+29:
		tmp = t_2
	elif b <= -5.3e-168:
		tmp = t_1
	elif b <= -5.6e-294:
		tmp = x + (z * (1.0 - y))
	elif b <= 2.15e-63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -1e+29)
		tmp = t_2;
	elseif (b <= -5.3e-168)
		tmp = t_1;
	elseif (b <= -5.6e-294)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 2.15e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -1e+29)
		tmp = t_2;
	elseif (b <= -5.3e-168)
		tmp = t_1;
	elseif (b <= -5.6e-294)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 2.15e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+29], t$95$2, If[LessEqual[b, -5.3e-168], t$95$1, If[LessEqual[b, -5.6e-294], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e-63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.99999999999999914e28 or 2.1499999999999999e-63 < b

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 84.0%

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

   3. Taylor expanded in a around 0 78.2%

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

   if -9.99999999999999914e28 < b < -5.29999999999999977e-168 or -5.59999999999999981e-294 < b < 2.1499999999999999e-63

   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 0 74.3%

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

   3. Taylor expanded in b around 0 68.6%

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

   if -5.29999999999999977e-168 < b < -5.59999999999999981e-294

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 89.2%

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

   3. Taylor expanded in b around 0 89.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+29}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-168}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-294}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-63}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 10: 83.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+92} \lor \neg \left(b \leq 7.2 \cdot 10^{+79}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.2e+92) (not (<= b 7.2e+79)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.2e+92) || !(b <= 7.2e+79)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.2d+92)) .or. (.not. (b <= 7.2d+79))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.2e+92) || !(b <= 7.2e+79)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.2e+92) or not (b <= 7.2e+79):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.2e+92) || !(b <= 7.2e+79))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.2e+92) || ~((b <= 7.2e+79)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.2e+92], N[Not[LessEqual[b, 7.2e+79]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.19999999999999972e92 or 7.1999999999999999e79 < 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 z around 0 86.5%

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

   3. Taylor expanded in a around 0 86.8%

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

   if -4.19999999999999972e92 < b < 7.1999999999999999e79

   1. Initial program 99.4%

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

   2. Taylor expanded in b around 0 89.3%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+92} \lor \neg \left(b \leq 7.2 \cdot 10^{+79}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 11: 83.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+94} \lor \neg \left(b \leq 1.01 \cdot 10^{+37}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.1e+94) (not (<= b 1.01e+37)))
   (- (+ x (* b (- (+ y t) 2.0))) (* y z))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.1e+94) || !(b <= 1.01e+37)) {
		tmp = (x + (b * ((y + t) - 2.0))) - (y * z);
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.1d+94)) .or. (.not. (b <= 1.01d+37))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) - (y * z)
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.1e+94) || !(b <= 1.01e+37)) {
		tmp = (x + (b * ((y + t) - 2.0))) - (y * z);
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.1e+94) or not (b <= 1.01e+37):
		tmp = (x + (b * ((y + t) - 2.0))) - (y * z)
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.1e+94) || !(b <= 1.01e+37))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) - Float64(y * z));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.1e+94) || ~((b <= 1.01e+37)))
		tmp = (x + (b * ((y + t) - 2.0))) - (y * z);
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.1e+94], N[Not[LessEqual[b, 1.01e+37]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.09999999999999989e94 or 1.00999999999999995e37 < b

   1. Initial program 94.1%

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

   2. Taylor expanded in a around 0 93.1%

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

   3. Taylor expanded in y around inf 86.2%

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

   if -2.09999999999999989e94 < b < 1.00999999999999995e37

   1. Initial program 99.3%

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

   2. Taylor expanded in b around 0 90.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+94} \lor \neg \left(b \leq 1.01 \cdot 10^{+37}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 12: 62.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{-295}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -2.3e+62)
     t_2
     (if (<= b -3.9e-168)
       t_1
       (if (<= b -5.7e-295)
         (+ x (* z (- 1.0 y)))
         (if (<= b 5e+38) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.3e+62) {
		tmp = t_2;
	} else if (b <= -3.9e-168) {
		tmp = t_1;
	} else if (b <= -5.7e-295) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 5e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-2.3d+62)) then
        tmp = t_2
    else if (b <= (-3.9d-168)) then
        tmp = t_1
    else if (b <= (-5.7d-295)) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 5d+38) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.3e+62) {
		tmp = t_2;
	} else if (b <= -3.9e-168) {
		tmp = t_1;
	} else if (b <= -5.7e-295) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 5e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2.3e+62:
		tmp = t_2
	elif b <= -3.9e-168:
		tmp = t_1
	elif b <= -5.7e-295:
		tmp = x + (z * (1.0 - y))
	elif b <= 5e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2.3e+62)
		tmp = t_2;
	elseif (b <= -3.9e-168)
		tmp = t_1;
	elseif (b <= -5.7e-295)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 5e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.3e+62)
		tmp = t_2;
	elseif (b <= -3.9e-168)
		tmp = t_1;
	elseif (b <= -5.7e-295)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 5e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+62], t$95$2, If[LessEqual[b, -3.9e-168], t$95$1, If[LessEqual[b, -5.7e-295], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.29999999999999984e62 or 4.9999999999999997e38 < 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 b around inf 75.1%

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

   if -2.29999999999999984e62 < b < -3.90000000000000012e-168 or -5.7e-295 < b < 4.9999999999999997e38

   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 0 75.7%

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

   3. Taylor expanded in b around 0 66.3%

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

   if -3.90000000000000012e-168 < b < -5.7e-295

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 89.2%

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

   3. Taylor expanded in b around 0 89.0%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-168}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{-295}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+38}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 13: 39.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-264}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1860000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))))
   (if (<= b -5.5e+67)
     t_1
     (if (<= b -1.32e-264)
       (+ x a)
       (if (<= b 2.6e-90)
         (* a (- 1.0 t))
         (if (<= b 1860000000000.0) (+ x a) 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 <= -5.5e+67) {
		tmp = t_1;
	} else if (b <= -1.32e-264) {
		tmp = x + a;
	} else if (b <= 2.6e-90) {
		tmp = a * (1.0 - t);
	} else if (b <= 1860000000000.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    if (b <= (-5.5d+67)) then
        tmp = t_1
    else if (b <= (-1.32d-264)) then
        tmp = x + a
    else if (b <= 2.6d-90) then
        tmp = a * (1.0d0 - t)
    else if (b <= 1860000000000.0d0) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -5.5e+67) {
		tmp = t_1;
	} else if (b <= -1.32e-264) {
		tmp = x + a;
	} else if (b <= 2.6e-90) {
		tmp = a * (1.0 - t);
	} else if (b <= 1860000000000.0) {
		tmp = x + a;
	} 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 <= -5.5e+67:
		tmp = t_1
	elif b <= -1.32e-264:
		tmp = x + a
	elif b <= 2.6e-90:
		tmp = a * (1.0 - t)
	elif b <= 1860000000000.0:
		tmp = x + a
	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 <= -5.5e+67)
		tmp = t_1;
	elseif (b <= -1.32e-264)
		tmp = Float64(x + a);
	elseif (b <= 2.6e-90)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 1860000000000.0)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -5.5e+67)
		tmp = t_1;
	elseif (b <= -1.32e-264)
		tmp = x + a;
	elseif (b <= 2.6e-90)
		tmp = a * (1.0 - t);
	elseif (b <= 1860000000000.0)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+67], t$95$1, If[LessEqual[b, -1.32e-264], N[(x + a), $MachinePrecision], If[LessEqual[b, 2.6e-90], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1860000000000.0], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.49999999999999968e67 or 1.86e12 < b

   1. Initial program 93.9%

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

   2. Taylor expanded in b around inf 73.4%

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

   3. Taylor expanded in y around 0 43.8%

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

   if -5.49999999999999968e67 < b < -1.32000000000000001e-264 or 2.6e-90 < b < 1.86e12

   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 0 76.5%

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

   3. Taylor expanded in b around 0 65.2%

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

   4. Taylor expanded in t around 0 50.4%

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

      1. cancel-sign-sub-inv 50.4%

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

      2. metadata-eval 50.4%

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

      3. *-lft-identity 50.4%

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

   6. Simplified 50.4%

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

   if -1.32000000000000001e-264 < b < 2.6e-90

   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 50.2%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-264}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1860000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 14: 40.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.82 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-251}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2100000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.82e+70)
   (* b (- y 2.0))
   (if (<= b -4.2e-251)
     (+ x a)
     (if (<= b 6e-90)
       (* a (- 1.0 t))
       (if (<= b 2100000000000.0) (+ x a) (* b (- t 2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.82e+70) {
		tmp = b * (y - 2.0);
	} else if (b <= -4.2e-251) {
		tmp = x + a;
	} else if (b <= 6e-90) {
		tmp = a * (1.0 - t);
	} else if (b <= 2100000000000.0) {
		tmp = x + a;
	} 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 <= (-1.82d+70)) then
        tmp = b * (y - 2.0d0)
    else if (b <= (-4.2d-251)) then
        tmp = x + a
    else if (b <= 6d-90) then
        tmp = a * (1.0d0 - t)
    else if (b <= 2100000000000.0d0) then
        tmp = x + a
    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 <= -1.82e+70) {
		tmp = b * (y - 2.0);
	} else if (b <= -4.2e-251) {
		tmp = x + a;
	} else if (b <= 6e-90) {
		tmp = a * (1.0 - t);
	} else if (b <= 2100000000000.0) {
		tmp = x + a;
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.82e+70:
		tmp = b * (y - 2.0)
	elif b <= -4.2e-251:
		tmp = x + a
	elif b <= 6e-90:
		tmp = a * (1.0 - t)
	elif b <= 2100000000000.0:
		tmp = x + a
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.82e+70)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= -4.2e-251)
		tmp = Float64(x + a);
	elseif (b <= 6e-90)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 2100000000000.0)
		tmp = Float64(x + a);
	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 <= -1.82e+70)
		tmp = b * (y - 2.0);
	elseif (b <= -4.2e-251)
		tmp = x + a;
	elseif (b <= 6e-90)
		tmp = a * (1.0 - t);
	elseif (b <= 2100000000000.0)
		tmp = x + a;
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.82e+70], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.2e-251], N[(x + a), $MachinePrecision], If[LessEqual[b, 6e-90], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2100000000000.0], N[(x + a), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.8199999999999999e70

   1. Initial program 93.1%

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

   2. Taylor expanded in b around inf 81.3%

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

   3. Taylor expanded in t around 0 56.3%

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

   if -1.8199999999999999e70 < b < -4.19999999999999964e-251 or 6.00000000000000041e-90 < b < 2.1e12

   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 0 77.0%

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

   3. Taylor expanded in b around 0 64.6%

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

   4. Taylor expanded in t around 0 49.4%

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

      1. cancel-sign-sub-inv 49.4%

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

      2. metadata-eval 49.4%

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

      3. *-lft-identity 49.4%

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

   6. Simplified 49.4%

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

   if -4.19999999999999964e-251 < b < 6.00000000000000041e-90

   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 50.2%

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

   if 2.1e12 < b

   1. Initial program 94.2%

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

   2. Taylor expanded in b around inf 69.0%

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

   3. Taylor expanded in y around 0 44.6%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.82 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-251}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2100000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 15: 50.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -0.018:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-161}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 55000000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -0.018)
     t_1
     (if (<= t 7.5e-161)
       (+ x a)
       (if (<= t 6.2e-31)
         (* b (- y 2.0))
         (if (<= t 55000000000000.0) (+ x a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -0.018) {
		tmp = t_1;
	} else if (t <= 7.5e-161) {
		tmp = x + a;
	} else if (t <= 6.2e-31) {
		tmp = b * (y - 2.0);
	} else if (t <= 55000000000000.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-0.018d0)) then
        tmp = t_1
    else if (t <= 7.5d-161) then
        tmp = x + a
    else if (t <= 6.2d-31) then
        tmp = b * (y - 2.0d0)
    else if (t <= 55000000000000.0d0) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -0.018) {
		tmp = t_1;
	} else if (t <= 7.5e-161) {
		tmp = x + a;
	} else if (t <= 6.2e-31) {
		tmp = b * (y - 2.0);
	} else if (t <= 55000000000000.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -0.018:
		tmp = t_1
	elif t <= 7.5e-161:
		tmp = x + a
	elif t <= 6.2e-31:
		tmp = b * (y - 2.0)
	elif t <= 55000000000000.0:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -0.018)
		tmp = t_1;
	elseif (t <= 7.5e-161)
		tmp = Float64(x + a);
	elseif (t <= 6.2e-31)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 55000000000000.0)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -0.018)
		tmp = t_1;
	elseif (t <= 7.5e-161)
		tmp = x + a;
	elseif (t <= 6.2e-31)
		tmp = b * (y - 2.0);
	elseif (t <= 55000000000000.0)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.018], t$95$1, If[LessEqual[t, 7.5e-161], N[(x + a), $MachinePrecision], If[LessEqual[t, 6.2e-31], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 55000000000000.0], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.0179999999999999986 or 5.5e13 < t

   1. Initial program 94.4%

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

   2. Taylor expanded in t around inf 65.7%

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

   if -0.0179999999999999986 < t < 7.49999999999999991e-161 or 6.19999999999999999e-31 < t < 5.5e13

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 77.2%

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

   3. Taylor expanded in b around 0 47.9%

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

   4. Taylor expanded in t around 0 47.2%

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

      1. cancel-sign-sub-inv 47.2%

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

      2. metadata-eval 47.2%

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

      3. *-lft-identity 47.2%

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

   6. Simplified 47.2%

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

   if 7.49999999999999991e-161 < t < 6.19999999999999999e-31

   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 41.5%

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

   3. Taylor expanded in t around 0 41.5%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.018:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-161}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 55000000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 16: 51.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-154}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -8e+52)
     t_2
     (if (<= t -1.02e-46)
       t_1
       (if (<= t 1.5e-154) (+ x a) (if (<= t 4.3e+15) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8e+52) {
		tmp = t_2;
	} else if (t <= -1.02e-46) {
		tmp = t_1;
	} else if (t <= 1.5e-154) {
		tmp = x + a;
	} else if (t <= 4.3e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-8d+52)) then
        tmp = t_2
    else if (t <= (-1.02d-46)) then
        tmp = t_1
    else if (t <= 1.5d-154) then
        tmp = x + a
    else if (t <= 4.3d+15) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8e+52) {
		tmp = t_2;
	} else if (t <= -1.02e-46) {
		tmp = t_1;
	} else if (t <= 1.5e-154) {
		tmp = x + a;
	} else if (t <= 4.3e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -8e+52:
		tmp = t_2
	elif t <= -1.02e-46:
		tmp = t_1
	elif t <= 1.5e-154:
		tmp = x + a
	elif t <= 4.3e+15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8e+52)
		tmp = t_2;
	elseif (t <= -1.02e-46)
		tmp = t_1;
	elseif (t <= 1.5e-154)
		tmp = Float64(x + a);
	elseif (t <= 4.3e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -8e+52)
		tmp = t_2;
	elseif (t <= -1.02e-46)
		tmp = t_1;
	elseif (t <= 1.5e-154)
		tmp = x + a;
	elseif (t <= 4.3e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+52], t$95$2, If[LessEqual[t, -1.02e-46], t$95$1, If[LessEqual[t, 1.5e-154], N[(x + a), $MachinePrecision], If[LessEqual[t, 4.3e+15], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.9999999999999999e52 or 4.3e15 < t

   1. Initial program 93.5%

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

   2. Taylor expanded in t around inf 71.7%

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

   if -7.9999999999999999e52 < t < -1.02e-46 or 1.5000000000000001e-154 < t < 4.3e15

   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 50.8%

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

   if -1.02e-46 < t < 1.5000000000000001e-154

   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 0 81.4%

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

   3. Taylor expanded in b around 0 51.1%

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

   4. Taylor expanded in t around 0 51.1%

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

      1. cancel-sign-sub-inv 51.1%

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

      2. metadata-eval 51.1%

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

      3. *-lft-identity 51.1%

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

   6. Simplified 51.1%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-154}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 17: 26.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-28}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-63}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3e-28)
   (* t b)
   (if (<= t -1.5e-216) x (if (<= t 5e-63) a (if (<= t 1.5e+146) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3e-28) {
		tmp = t * b;
	} else if (t <= -1.5e-216) {
		tmp = x;
	} else if (t <= 5e-63) {
		tmp = a;
	} else if (t <= 1.5e+146) {
		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 <= (-3d-28)) then
        tmp = t * b
    else if (t <= (-1.5d-216)) then
        tmp = x
    else if (t <= 5d-63) then
        tmp = a
    else if (t <= 1.5d+146) 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 <= -3e-28) {
		tmp = t * b;
	} else if (t <= -1.5e-216) {
		tmp = x;
	} else if (t <= 5e-63) {
		tmp = a;
	} else if (t <= 1.5e+146) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3e-28:
		tmp = t * b
	elif t <= -1.5e-216:
		tmp = x
	elif t <= 5e-63:
		tmp = a
	elif t <= 1.5e+146:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3e-28)
		tmp = Float64(t * b);
	elseif (t <= -1.5e-216)
		tmp = x;
	elseif (t <= 5e-63)
		tmp = a;
	elseif (t <= 1.5e+146)
		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 <= -3e-28)
		tmp = t * b;
	elseif (t <= -1.5e-216)
		tmp = x;
	elseif (t <= 5e-63)
		tmp = a;
	elseif (t <= 1.5e+146)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3e-28], N[(t * b), $MachinePrecision], If[LessEqual[t, -1.5e-216], x, If[LessEqual[t, 5e-63], a, If[LessEqual[t, 1.5e+146], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.00000000000000003e-28 or 1.50000000000000001e146 < t

   1. Initial program 93.3%

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

   2. Taylor expanded in b around inf 47.5%

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

   3. Taylor expanded in t around inf 37.6%

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

   if -3.00000000000000003e-28 < t < -1.50000000000000006e-216 or 5.0000000000000002e-63 < t < 1.50000000000000001e146

   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 34.7%

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

   if -1.50000000000000006e-216 < t < 5.0000000000000002e-63

   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 27.8%

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

   3. Taylor expanded in t around 0 27.8%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-28}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-63}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 18: 33.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+73}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-198}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-105}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 2100000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.65e+73)
   (* y b)
   (if (<= b 8e-198)
     (+ x a)
     (if (<= b 1.2e-105)
       (* t (- a))
       (if (<= b 2100000000000.0) (+ x a) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.65e+73) {
		tmp = y * b;
	} else if (b <= 8e-198) {
		tmp = x + a;
	} else if (b <= 1.2e-105) {
		tmp = t * -a;
	} else if (b <= 2100000000000.0) {
		tmp = x + 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 <= (-1.65d+73)) then
        tmp = y * b
    else if (b <= 8d-198) then
        tmp = x + a
    else if (b <= 1.2d-105) then
        tmp = t * -a
    else if (b <= 2100000000000.0d0) then
        tmp = x + 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 <= -1.65e+73) {
		tmp = y * b;
	} else if (b <= 8e-198) {
		tmp = x + a;
	} else if (b <= 1.2e-105) {
		tmp = t * -a;
	} else if (b <= 2100000000000.0) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.65e+73:
		tmp = y * b
	elif b <= 8e-198:
		tmp = x + a
	elif b <= 1.2e-105:
		tmp = t * -a
	elif b <= 2100000000000.0:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.65e+73)
		tmp = Float64(y * b);
	elseif (b <= 8e-198)
		tmp = Float64(x + a);
	elseif (b <= 1.2e-105)
		tmp = Float64(t * Float64(-a));
	elseif (b <= 2100000000000.0)
		tmp = Float64(x + 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 <= -1.65e+73)
		tmp = y * b;
	elseif (b <= 8e-198)
		tmp = x + a;
	elseif (b <= 1.2e-105)
		tmp = t * -a;
	elseif (b <= 2100000000000.0)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.65e+73], N[(y * b), $MachinePrecision], If[LessEqual[b, 8e-198], N[(x + a), $MachinePrecision], If[LessEqual[b, 1.2e-105], N[(t * (-a)), $MachinePrecision], If[LessEqual[b, 2100000000000.0], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.65000000000000015e73

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 45.6%

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

   3. Taylor expanded in b around inf 43.7%

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

   if -1.65000000000000015e73 < b < 7.9999999999999993e-198 or 1.20000000000000007e-105 < b < 2.1e12

   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 0 74.7%

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

   3. Taylor expanded in b around 0 65.0%

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

   4. Taylor expanded in t around 0 47.2%

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

      1. cancel-sign-sub-inv 47.2%

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

      2. metadata-eval 47.2%

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

      3. *-lft-identity 47.2%

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

   6. Simplified 47.2%

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

   if 7.9999999999999993e-198 < b < 1.20000000000000007e-105

   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 51.2%

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

   3. Taylor expanded in t around inf 47.3%

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

      1. associate-*r* 47.3%

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

      2. mul-1-neg 47.3%

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

   5. Simplified 47.3%

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

   if 2.1e12 < b

   1. Initial program 94.2%

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

   2. Taylor expanded in b around inf 69.0%

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

   3. Taylor expanded in t around inf 35.9%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+73}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-198}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-105}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 2100000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 19: 34.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+73}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -6.7 \cdot 10^{-259}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{-89}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 330000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.75e+73)
   (* y b)
   (if (<= b -6.7e-259)
     (+ x a)
     (if (<= b 1.46e-89)
       (* a (- 1.0 t))
       (if (<= b 330000000000.0) (+ x a) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+73) {
		tmp = y * b;
	} else if (b <= -6.7e-259) {
		tmp = x + a;
	} else if (b <= 1.46e-89) {
		tmp = a * (1.0 - t);
	} else if (b <= 330000000000.0) {
		tmp = x + 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 <= (-1.75d+73)) then
        tmp = y * b
    else if (b <= (-6.7d-259)) then
        tmp = x + a
    else if (b <= 1.46d-89) then
        tmp = a * (1.0d0 - t)
    else if (b <= 330000000000.0d0) then
        tmp = x + 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 <= -1.75e+73) {
		tmp = y * b;
	} else if (b <= -6.7e-259) {
		tmp = x + a;
	} else if (b <= 1.46e-89) {
		tmp = a * (1.0 - t);
	} else if (b <= 330000000000.0) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.75e+73:
		tmp = y * b
	elif b <= -6.7e-259:
		tmp = x + a
	elif b <= 1.46e-89:
		tmp = a * (1.0 - t)
	elif b <= 330000000000.0:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.75e+73)
		tmp = Float64(y * b);
	elseif (b <= -6.7e-259)
		tmp = Float64(x + a);
	elseif (b <= 1.46e-89)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 330000000000.0)
		tmp = Float64(x + 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 <= -1.75e+73)
		tmp = y * b;
	elseif (b <= -6.7e-259)
		tmp = x + a;
	elseif (b <= 1.46e-89)
		tmp = a * (1.0 - t);
	elseif (b <= 330000000000.0)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.75e+73], N[(y * b), $MachinePrecision], If[LessEqual[b, -6.7e-259], N[(x + a), $MachinePrecision], If[LessEqual[b, 1.46e-89], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 330000000000.0], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.75000000000000001e73

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 45.6%

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

   3. Taylor expanded in b around inf 43.7%

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

   if -1.75000000000000001e73 < b < -6.69999999999999954e-259 or 1.46e-89 < b < 3.3e11

   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 0 77.0%

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

   3. Taylor expanded in b around 0 64.6%

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

   4. Taylor expanded in t around 0 49.4%

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

      1. cancel-sign-sub-inv 49.4%

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

      2. metadata-eval 49.4%

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

      3. *-lft-identity 49.4%

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

   6. Simplified 49.4%

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

   if -6.69999999999999954e-259 < b < 1.46e-89

   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 50.2%

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

   if 3.3e11 < b

   1. Initial program 94.2%

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

   2. Taylor expanded in b around inf 69.0%

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

   3. Taylor expanded in t around inf 35.9%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+73}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -6.7 \cdot 10^{-259}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{-89}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 330000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 20: 62.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+62} \lor \neg \left(b \leq 1.3 \cdot 10^{+38}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.9e+62) (not (<= b 1.3e+38)))
   (* b (- (+ y t) 2.0))
   (+ x (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.9e+62) || !(b <= 1.3e+38)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.9d+62)) .or. (.not. (b <= 1.3d+38))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = x + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.9e+62) || !(b <= 1.3e+38)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.9e+62) or not (b <= 1.3e+38):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = x + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.9e+62) || !(b <= 1.3e+38))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.9e+62) || ~((b <= 1.3e+38)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = x + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.9e+62], N[Not[LessEqual[b, 1.3e+38]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.89999999999999984e62 or 1.3e38 < 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 b around inf 75.1%

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

   if -2.89999999999999984e62 < b < 1.3e38

   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 0 73.4%

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

   3. Taylor expanded in b around 0 65.1%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+62} \lor \neg \left(b \leq 1.3 \cdot 10^{+38}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 21: 26.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+70}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 2700000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.4e+70) (* y b) (if (<= b 2700000000.0) x (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.4e+70) {
		tmp = y * b;
	} else if (b <= 2700000000.0) {
		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 (b <= (-3.4d+70)) then
        tmp = y * b
    else if (b <= 2700000000.0d0) 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 (b <= -3.4e+70) {
		tmp = y * b;
	} else if (b <= 2700000000.0) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.4e+70:
		tmp = y * b
	elif b <= 2700000000.0:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.4e+70)
		tmp = Float64(y * b);
	elseif (b <= 2700000000.0)
		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 (b <= -3.4e+70)
		tmp = y * b;
	elseif (b <= 2700000000.0)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.4e+70], N[(y * b), $MachinePrecision], If[LessEqual[b, 2700000000.0], x, N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4000000000000001e70

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 45.6%

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

   3. Taylor expanded in b around inf 43.7%

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

   if -3.4000000000000001e70 < b < 2.7e9

   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 27.8%

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

   if 2.7e9 < b

   1. Initial program 94.2%

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

   2. Taylor expanded in b around inf 69.0%

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

   3. Taylor expanded in t around inf 35.9%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+70}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 2700000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 22: 34.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{+72}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 420000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.72e+72) (* y b) (if (<= b 420000000000.0) (+ x a) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.72e+72) {
		tmp = y * b;
	} else if (b <= 420000000000.0) {
		tmp = x + 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 <= (-1.72d+72)) then
        tmp = y * b
    else if (b <= 420000000000.0d0) then
        tmp = x + 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 <= -1.72e+72) {
		tmp = y * b;
	} else if (b <= 420000000000.0) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.72e+72:
		tmp = y * b
	elif b <= 420000000000.0:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.72e+72)
		tmp = Float64(y * b);
	elseif (b <= 420000000000.0)
		tmp = Float64(x + 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 <= -1.72e+72)
		tmp = y * b;
	elseif (b <= 420000000000.0)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.72e+72], N[(y * b), $MachinePrecision], If[LessEqual[b, 420000000000.0], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.71999999999999993e72

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 45.6%

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

   3. Taylor expanded in b around inf 43.7%

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

   if -1.71999999999999993e72 < b < 4.2e11

   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 0 74.3%

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

   3. Taylor expanded in b around 0 65.8%

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

   4. Taylor expanded in t around 0 43.2%

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

      1. cancel-sign-sub-inv 43.2%

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

      2. metadata-eval 43.2%

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

      3. *-lft-identity 43.2%

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

   6. Simplified 43.2%

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

   if 4.2e11 < b

   1. Initial program 94.2%

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

   2. Taylor expanded in b around inf 69.0%

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

   3. Taylor expanded in t around inf 35.9%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{+72}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 420000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 23: 20.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+39}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.8e+153) x (if (<= x 3.7e+39) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.8e+153) {
		tmp = x;
	} else if (x <= 3.7e+39) {
		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 <= (-3.8d+153)) then
        tmp = x
    else if (x <= 3.7d+39) 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 <= -3.8e+153) {
		tmp = x;
	} else if (x <= 3.7e+39) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.8e+153:
		tmp = x
	elif x <= 3.7e+39:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.8e+153)
		tmp = x;
	elseif (x <= 3.7e+39)
		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 <= -3.8e+153)
		tmp = x;
	elseif (x <= 3.7e+39)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.8e+153], x, If[LessEqual[x, 3.7e+39], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.79999999999999966e153 or 3.70000000000000012e39 < x

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf 47.9%

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

   if -3.79999999999999966e153 < x < 3.70000000000000012e39

   1. Initial program 96.8%

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

   2. Taylor expanded in a around inf 35.7%

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

   3. Taylor expanded in t around 0 15.8%

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

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+39}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 11.5% 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 97.2%

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

2. Taylor expanded in a around inf 27.3%

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

3. Taylor expanded in t around 0 11.6%

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

4. Final simplification 11.6%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023320 
(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)))