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

Percentage Accurate: 94.9% → 97.9%

Time: 21.4s

Alternatives: 25

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.9% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 71.6%

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

4. Final simplification 99.2%

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

Alternative 2: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 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 98.8%

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

   3. associate--l+ 98.8%

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

   4. sub-neg 98.8%

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

   5. metadata-eval 98.8%

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

   6. sub-neg 98.8%

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

   7. associate-+l- 98.8%

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

   8. fma-neg 98.8%

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

   9. sub-neg 98.8%

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

   10. metadata-eval 98.8%

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

   11. remove-double-neg 98.8%

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

   12. sub-neg 98.8%

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

   13. metadata-eval 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 3: 49.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-33}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-210}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-270}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-224}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+70}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -7.2e+86)
     t_2
     (if (<= y -4.6e+17)
       t_1
       (if (<= y -7.6e-33)
         (+ x a)
         (if (<= y -4.4e-70)
           t_1
           (if (<= y -5.4e-210)
             (+ x z)
             (if (<= y 5e-270)
               (- x (* t a))
               (if (<= y 7.8e-224)
                 (+ x z)
                 (if (<= y 2.55e+70) (* a (- 1.0 t)) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -7.2e+86) {
		tmp = t_2;
	} else if (y <= -4.6e+17) {
		tmp = t_1;
	} else if (y <= -7.6e-33) {
		tmp = x + a;
	} else if (y <= -4.4e-70) {
		tmp = t_1;
	} else if (y <= -5.4e-210) {
		tmp = x + z;
	} else if (y <= 5e-270) {
		tmp = x - (t * a);
	} else if (y <= 7.8e-224) {
		tmp = x + z;
	} else if (y <= 2.55e+70) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-7.2d+86)) then
        tmp = t_2
    else if (y <= (-4.6d+17)) then
        tmp = t_1
    else if (y <= (-7.6d-33)) then
        tmp = x + a
    else if (y <= (-4.4d-70)) then
        tmp = t_1
    else if (y <= (-5.4d-210)) then
        tmp = x + z
    else if (y <= 5d-270) then
        tmp = x - (t * a)
    else if (y <= 7.8d-224) then
        tmp = x + z
    else if (y <= 2.55d+70) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -7.2e+86) {
		tmp = t_2;
	} else if (y <= -4.6e+17) {
		tmp = t_1;
	} else if (y <= -7.6e-33) {
		tmp = x + a;
	} else if (y <= -4.4e-70) {
		tmp = t_1;
	} else if (y <= -5.4e-210) {
		tmp = x + z;
	} else if (y <= 5e-270) {
		tmp = x - (t * a);
	} else if (y <= 7.8e-224) {
		tmp = x + z;
	} else if (y <= 2.55e+70) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -7.2e+86:
		tmp = t_2
	elif y <= -4.6e+17:
		tmp = t_1
	elif y <= -7.6e-33:
		tmp = x + a
	elif y <= -4.4e-70:
		tmp = t_1
	elif y <= -5.4e-210:
		tmp = x + z
	elif y <= 5e-270:
		tmp = x - (t * a)
	elif y <= 7.8e-224:
		tmp = x + z
	elif y <= 2.55e+70:
		tmp = a * (1.0 - t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -7.2e+86)
		tmp = t_2;
	elseif (y <= -4.6e+17)
		tmp = t_1;
	elseif (y <= -7.6e-33)
		tmp = Float64(x + a);
	elseif (y <= -4.4e-70)
		tmp = t_1;
	elseif (y <= -5.4e-210)
		tmp = Float64(x + z);
	elseif (y <= 5e-270)
		tmp = Float64(x - Float64(t * a));
	elseif (y <= 7.8e-224)
		tmp = Float64(x + z);
	elseif (y <= 2.55e+70)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -7.2e+86)
		tmp = t_2;
	elseif (y <= -4.6e+17)
		tmp = t_1;
	elseif (y <= -7.6e-33)
		tmp = x + a;
	elseif (y <= -4.4e-70)
		tmp = t_1;
	elseif (y <= -5.4e-210)
		tmp = x + z;
	elseif (y <= 5e-270)
		tmp = x - (t * a);
	elseif (y <= 7.8e-224)
		tmp = x + z;
	elseif (y <= 2.55e+70)
		tmp = a * (1.0 - t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+86], t$95$2, If[LessEqual[y, -4.6e+17], t$95$1, If[LessEqual[y, -7.6e-33], N[(x + a), $MachinePrecision], If[LessEqual[y, -4.4e-70], t$95$1, If[LessEqual[y, -5.4e-210], N[(x + z), $MachinePrecision], If[LessEqual[y, 5e-270], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-224], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.55e+70], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -7.20000000000000011e86 or 2.55000000000000007e70 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 73.5%

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

   if -7.20000000000000011e86 < y < -4.6e17 or -7.59999999999999988e-33 < y < -4.3999999999999998e-70

   1. Initial program 96.9%

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

   2. Taylor expanded in t around inf 67.4%

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

   if -4.6e17 < y < -7.59999999999999988e-33

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 71.2%

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

   3. Taylor expanded in b around 0 52.2%

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

   4. Taylor expanded in t around 0 52.2%

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

      1. cancel-sign-sub-inv 52.2%

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

      2. metadata-eval 52.2%

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

      3. *-lft-identity 52.2%

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

      4. +-commutative 52.2%

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

   6. Simplified 52.2%

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

   if -4.3999999999999998e-70 < y < -5.39999999999999983e-210 or 4.9999999999999998e-270 < y < 7.7999999999999996e-224

   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 y around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. mul-1-neg 100.0%

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

      10. remove-double-neg 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 55.3%

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

   if -5.39999999999999983e-210 < y < 4.9999999999999998e-270

   1. Initial program 97.0%

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

   2. Taylor expanded in z around 0 77.3%

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

   3. Taylor expanded in b around 0 64.2%

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

   4. Taylor expanded in t around inf 57.4%

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

      1. *-commutative 57.4%

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

   6. Simplified 57.4%

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

   if 7.7999999999999996e-224 < y < 2.55000000000000007e70

   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 52.6%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-33}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-210}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-270}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-224}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+70}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 4: 58.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + b \cdot \left(t - 2\right)\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-161}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* b (- t 2.0))))) (t_2 (+ x (* a (- 1.0 t)))))
   (if (<= a -1.95e+54)
     t_2
     (if (<= a -3.1e-78)
       t_1
       (if (<= a -3.1e-161)
         (+ x (* b (- (+ y t) 2.0)))
         (if (<= a 1.6e-247)
           t_1
           (if (<= a 4e-184) (* y (- b z)) (if (<= a 8e+148) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (b * (t - 2.0)));
	double t_2 = x + (a * (1.0 - t));
	double tmp;
	if (a <= -1.95e+54) {
		tmp = t_2;
	} else if (a <= -3.1e-78) {
		tmp = t_1;
	} else if (a <= -3.1e-161) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (a <= 1.6e-247) {
		tmp = t_1;
	} else if (a <= 4e-184) {
		tmp = y * (b - z);
	} else if (a <= 8e+148) {
		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 + (z + (b * (t - 2.0d0)))
    t_2 = x + (a * (1.0d0 - t))
    if (a <= (-1.95d+54)) then
        tmp = t_2
    else if (a <= (-3.1d-78)) then
        tmp = t_1
    else if (a <= (-3.1d-161)) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else if (a <= 1.6d-247) then
        tmp = t_1
    else if (a <= 4d-184) then
        tmp = y * (b - z)
    else if (a <= 8d+148) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (b * (t - 2.0)));
	double t_2 = x + (a * (1.0 - t));
	double tmp;
	if (a <= -1.95e+54) {
		tmp = t_2;
	} else if (a <= -3.1e-78) {
		tmp = t_1;
	} else if (a <= -3.1e-161) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (a <= 1.6e-247) {
		tmp = t_1;
	} else if (a <= 4e-184) {
		tmp = y * (b - z);
	} else if (a <= 8e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (b * (t - 2.0)))
	t_2 = x + (a * (1.0 - t))
	tmp = 0
	if a <= -1.95e+54:
		tmp = t_2
	elif a <= -3.1e-78:
		tmp = t_1
	elif a <= -3.1e-161:
		tmp = x + (b * ((y + t) - 2.0))
	elif a <= 1.6e-247:
		tmp = t_1
	elif a <= 4e-184:
		tmp = y * (b - z)
	elif a <= 8e+148:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(b * Float64(t - 2.0))))
	t_2 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (a <= -1.95e+54)
		tmp = t_2;
	elseif (a <= -3.1e-78)
		tmp = t_1;
	elseif (a <= -3.1e-161)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	elseif (a <= 1.6e-247)
		tmp = t_1;
	elseif (a <= 4e-184)
		tmp = Float64(y * Float64(b - z));
	elseif (a <= 8e+148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (b * (t - 2.0)));
	t_2 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (a <= -1.95e+54)
		tmp = t_2;
	elseif (a <= -3.1e-78)
		tmp = t_1;
	elseif (a <= -3.1e-161)
		tmp = x + (b * ((y + t) - 2.0));
	elseif (a <= 1.6e-247)
		tmp = t_1;
	elseif (a <= 4e-184)
		tmp = y * (b - z);
	elseif (a <= 8e+148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.95e+54], t$95$2, If[LessEqual[a, -3.1e-78], t$95$1, If[LessEqual[a, -3.1e-161], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-247], t$95$1, If[LessEqual[a, 4e-184], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+148], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9500000000000001e54 or 8.0000000000000004e148 < a

   1. Initial program 96.6%

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

   2. Taylor expanded in z around 0 88.0%

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

   3. Taylor expanded in b around 0 75.7%

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

   if -1.9500000000000001e54 < a < -3.10000000000000018e-78 or -3.0999999999999999e-161 < a < 1.59999999999999997e-247 or 4.0000000000000002e-184 < a < 8.0000000000000004e148

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 76.2%

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

      1. associate--l+ 76.2%

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

      2. fma-neg 76.2%

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

      3. sub-neg 76.2%

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

      4. metadata-eval 76.2%

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

      5. sub-neg 76.2%

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

      6. metadata-eval 76.2%

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

      7. *-commutative 76.2%

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

      8. distribute-neg-in 76.2%

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

      9. mul-1-neg 76.2%

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

      10. remove-double-neg 76.2%

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

      11. *-commutative 76.2%

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

      12. distribute-rgt-neg-in 76.2%

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

      13. +-commutative 76.2%

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

      14. distribute-neg-in 76.2%

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

      15. metadata-eval 76.2%

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

      16. sub-neg 76.2%

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

   4. Simplified 76.2%

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

   5. Taylor expanded in a around 0 66.0%

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

   if -3.10000000000000018e-78 < a < -3.0999999999999999e-161

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 84.9%

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

   3. Taylor expanded in a around 0 80.7%

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

   if 1.59999999999999997e-247 < a < 4.0000000000000002e-184

   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 85.9%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+54}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-78}:\\ \;\;\;\;x + \left(z + b \cdot \left(t - 2\right)\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-161}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-247}:\\ \;\;\;\;x + \left(z + b \cdot \left(t - 2\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+148}:\\ \;\;\;\;x + \left(z + b \cdot \left(t - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 5: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+175}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1600000:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+72}:\\ \;\;\;\;\left(\left(t + -2\right) \cdot b + \left(x + z\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))) (t_2 (* a (- 1.0 t))))
   (if (<= y -2.1e+175)
     (* y (- b z))
     (if (<= y -1600000.0)
       (+ t_1 t_2)
       (if (<= y 2.9e+72)
         (+ (+ (* (+ t -2.0) b) (+ x z)) t_2)
         (+ t_1 (* z (- 1.0 y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double t_2 = a * (1.0 - t);
	double tmp;
	if (y <= -2.1e+175) {
		tmp = y * (b - z);
	} else if (y <= -1600000.0) {
		tmp = t_1 + t_2;
	} else if (y <= 2.9e+72) {
		tmp = (((t + -2.0) * b) + (x + z)) + t_2;
	} else {
		tmp = t_1 + (z * (1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    t_2 = a * (1.0d0 - t)
    if (y <= (-2.1d+175)) then
        tmp = y * (b - z)
    else if (y <= (-1600000.0d0)) then
        tmp = t_1 + t_2
    else if (y <= 2.9d+72) then
        tmp = (((t + (-2.0d0)) * b) + (x + z)) + t_2
    else
        tmp = t_1 + (z * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double t_2 = a * (1.0 - t);
	double tmp;
	if (y <= -2.1e+175) {
		tmp = y * (b - z);
	} else if (y <= -1600000.0) {
		tmp = t_1 + t_2;
	} else if (y <= 2.9e+72) {
		tmp = (((t + -2.0) * b) + (x + z)) + t_2;
	} else {
		tmp = t_1 + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	t_2 = a * (1.0 - t)
	tmp = 0
	if y <= -2.1e+175:
		tmp = y * (b - z)
	elif y <= -1600000.0:
		tmp = t_1 + t_2
	elif y <= 2.9e+72:
		tmp = (((t + -2.0) * b) + (x + z)) + t_2
	else:
		tmp = t_1 + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (y <= -2.1e+175)
		tmp = Float64(y * Float64(b - z));
	elseif (y <= -1600000.0)
		tmp = Float64(t_1 + t_2);
	elseif (y <= 2.9e+72)
		tmp = Float64(Float64(Float64(Float64(t + -2.0) * b) + Float64(x + z)) + t_2);
	else
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (y <= -2.1e+175)
		tmp = y * (b - z);
	elseif (y <= -1600000.0)
		tmp = t_1 + t_2;
	elseif (y <= 2.9e+72)
		tmp = (((t + -2.0) * b) + (x + z)) + t_2;
	else
		tmp = t_1 + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+175], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1600000.0], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[y, 2.9e+72], N[(N[(N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.0999999999999999e175

   1. Initial program 81.3%

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

   2. Taylor expanded in y around inf 97.2%

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

   if -2.0999999999999999e175 < y < -1.6e6

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0 88.8%

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

   if -1.6e6 < y < 2.90000000000000017e72

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 99.2%

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

      1. +-commutative 99.2%

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

      2. mul-1-neg 99.2%

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

      3. unsub-neg 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around 0 97.2%

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

      1. associate-+r+ 97.2%

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

      2. +-commutative 97.2%

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

      3. sub-neg 97.2%

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

      4. metadata-eval 97.2%

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

      5. sub-neg 97.2%

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

      6. metadata-eval 97.2%

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

   7. Simplified 97.2%

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

   if 2.90000000000000017e72 < y

   1. Initial program 96.5%

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

   2. Taylor expanded in a around 0 80.6%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+175}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1600000:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+72}:\\ \;\;\;\;\left(\left(t + -2\right) \cdot b + \left(x + z\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 6: 86.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{-48} \lor \neg \left(b \leq 9.2 \cdot 10^{+22}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_1 + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -2.8e-48) (not (<= b 9.2e+22)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (+ t_1 (* z (- 1.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -2.8e-48) || !(b <= 9.2e+22)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-2.8d-48)) .or. (.not. (b <= 9.2d+22))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -2.8e-48) || !(b <= 9.2e+22)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -2.8e-48) or not (b <= 9.2e+22):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + (t_1 + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -2.8e-48) || !(b <= 9.2e+22))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((b <= -2.8e-48) || ~((b <= 9.2e+22)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + (t_1 + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2.8e-48], N[Not[LessEqual[b, 9.2e+22]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.80000000000000005e-48 or 9.2000000000000008e22 < b

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0 85.3%

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

   if -2.80000000000000005e-48 < b < 9.2000000000000008e22

   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 91.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{-48} \lor \neg \left(b \leq 9.2 \cdot 10^{+22}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 7: 84.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+51} \lor \neg \left(a \leq 1.95 \cdot 10^{+34}\right):\\ \;\;\;\;t_1 + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (or (<= a -7.8e+51) (not (<= a 1.95e+34)))
     (+ t_1 (* a (- 1.0 t)))
     (+ t_1 (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if ((a <= -7.8e+51) || !(a <= 1.95e+34)) {
		tmp = t_1 + (a * (1.0 - t));
	} else {
		tmp = t_1 + (z * (1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if ((a <= (-7.8d+51)) .or. (.not. (a <= 1.95d+34))) then
        tmp = t_1 + (a * (1.0d0 - t))
    else
        tmp = t_1 + (z * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if ((a <= -7.8e+51) || !(a <= 1.95e+34)) {
		tmp = t_1 + (a * (1.0 - t));
	} else {
		tmp = t_1 + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if (a <= -7.8e+51) or not (a <= 1.95e+34):
		tmp = t_1 + (a * (1.0 - t))
	else:
		tmp = t_1 + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if ((a <= -7.8e+51) || !(a <= 1.95e+34))
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if ((a <= -7.8e+51) || ~((a <= 1.95e+34)))
		tmp = t_1 + (a * (1.0 - t));
	else
		tmp = t_1 + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -7.8e+51], N[Not[LessEqual[a, 1.95e+34]], $MachinePrecision]], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.79999999999999968e51 or 1.9500000000000001e34 < a

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 87.4%

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

   if -7.79999999999999968e51 < a < 1.9500000000000001e34

   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 a around 0 89.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+51} \lor \neg \left(a \leq 1.95 \cdot 10^{+34}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 8: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-239}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-184}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+24}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+146}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.25e-34)
     t_1
     (if (<= a 1.6e-239)
       (+ x z)
       (if (<= a 4.6e-184)
         (* y b)
         (if (<= a 7.5e+24)
           (+ x z)
           (if (<= a 3.2e+146) (* t b) (if (<= a 4.6e+146) x t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.25e-34) {
		tmp = t_1;
	} else if (a <= 1.6e-239) {
		tmp = x + z;
	} else if (a <= 4.6e-184) {
		tmp = y * b;
	} else if (a <= 7.5e+24) {
		tmp = x + z;
	} else if (a <= 3.2e+146) {
		tmp = t * b;
	} else if (a <= 4.6e+146) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-1.25d-34)) then
        tmp = t_1
    else if (a <= 1.6d-239) then
        tmp = x + z
    else if (a <= 4.6d-184) then
        tmp = y * b
    else if (a <= 7.5d+24) then
        tmp = x + z
    else if (a <= 3.2d+146) then
        tmp = t * b
    else if (a <= 4.6d+146) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.25e-34) {
		tmp = t_1;
	} else if (a <= 1.6e-239) {
		tmp = x + z;
	} else if (a <= 4.6e-184) {
		tmp = y * b;
	} else if (a <= 7.5e+24) {
		tmp = x + z;
	} else if (a <= 3.2e+146) {
		tmp = t * b;
	} else if (a <= 4.6e+146) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -1.25e-34:
		tmp = t_1
	elif a <= 1.6e-239:
		tmp = x + z
	elif a <= 4.6e-184:
		tmp = y * b
	elif a <= 7.5e+24:
		tmp = x + z
	elif a <= 3.2e+146:
		tmp = t * b
	elif a <= 4.6e+146:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.25e-34)
		tmp = t_1;
	elseif (a <= 1.6e-239)
		tmp = Float64(x + z);
	elseif (a <= 4.6e-184)
		tmp = Float64(y * b);
	elseif (a <= 7.5e+24)
		tmp = Float64(x + z);
	elseif (a <= 3.2e+146)
		tmp = Float64(t * b);
	elseif (a <= 4.6e+146)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.25e-34)
		tmp = t_1;
	elseif (a <= 1.6e-239)
		tmp = x + z;
	elseif (a <= 4.6e-184)
		tmp = y * b;
	elseif (a <= 7.5e+24)
		tmp = x + z;
	elseif (a <= 3.2e+146)
		tmp = t * b;
	elseif (a <= 4.6e+146)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e-34], t$95$1, If[LessEqual[a, 1.6e-239], N[(x + z), $MachinePrecision], If[LessEqual[a, 4.6e-184], N[(y * b), $MachinePrecision], If[LessEqual[a, 7.5e+24], N[(x + z), $MachinePrecision], If[LessEqual[a, 3.2e+146], N[(t * b), $MachinePrecision], If[LessEqual[a, 4.6e+146], x, t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.2500000000000001e-34 or 4.60000000000000001e146 < a

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 62.1%

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

   if -1.2500000000000001e-34 < a < 1.6e-239 or 4.5999999999999999e-184 < a < 7.50000000000000014e24

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0 71.9%

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

      1. associate--l+ 71.9%

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

      2. fma-neg 71.9%

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

      3. sub-neg 71.9%

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

      4. metadata-eval 71.9%

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

      5. sub-neg 71.9%

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

      6. metadata-eval 71.9%

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

      7. *-commutative 71.9%

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

      8. distribute-neg-in 71.9%

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

      9. mul-1-neg 71.9%

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

      10. remove-double-neg 71.9%

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

      11. *-commutative 71.9%

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

      12. distribute-rgt-neg-in 71.9%

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

      13. +-commutative 71.9%

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

      14. distribute-neg-in 71.9%

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

      15. metadata-eval 71.9%

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

      16. sub-neg 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in z around inf 38.5%

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

   if 1.6e-239 < a < 4.5999999999999999e-184

   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 58.1%

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

   3. Taylor expanded in y around inf 55.1%

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

   if 7.50000000000000014e24 < a < 3.2e146

   1. Initial program 95.2%

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

   2. Taylor expanded in z around 0 81.6%

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

   3. Taylor expanded in a around 0 72.2%

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

   4. Taylor expanded in t around inf 58.1%

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

   5. Taylor expanded in x around 0 44.0%

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

      1. *-commutative 44.0%

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

   7. Simplified 44.0%

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

   if 3.2e146 < a < 4.60000000000000001e146

   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 100.0%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-239}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-184}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+24}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+146}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 9: 48.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-30}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-222}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -7.2e+86)
     t_2
     (if (<= y -1.85e+15)
       t_1
       (if (<= y -1.16e-30)
         (+ x a)
         (if (<= y -4.9e-70)
           t_1
           (if (<= y 1.2e-222)
             (+ x z)
             (if (<= y 4.9e+69) (* a (- 1.0 t)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -7.2e+86) {
		tmp = t_2;
	} else if (y <= -1.85e+15) {
		tmp = t_1;
	} else if (y <= -1.16e-30) {
		tmp = x + a;
	} else if (y <= -4.9e-70) {
		tmp = t_1;
	} else if (y <= 1.2e-222) {
		tmp = x + z;
	} else if (y <= 4.9e+69) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-7.2d+86)) then
        tmp = t_2
    else if (y <= (-1.85d+15)) then
        tmp = t_1
    else if (y <= (-1.16d-30)) then
        tmp = x + a
    else if (y <= (-4.9d-70)) then
        tmp = t_1
    else if (y <= 1.2d-222) then
        tmp = x + z
    else if (y <= 4.9d+69) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -7.2e+86) {
		tmp = t_2;
	} else if (y <= -1.85e+15) {
		tmp = t_1;
	} else if (y <= -1.16e-30) {
		tmp = x + a;
	} else if (y <= -4.9e-70) {
		tmp = t_1;
	} else if (y <= 1.2e-222) {
		tmp = x + z;
	} else if (y <= 4.9e+69) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -7.2e+86:
		tmp = t_2
	elif y <= -1.85e+15:
		tmp = t_1
	elif y <= -1.16e-30:
		tmp = x + a
	elif y <= -4.9e-70:
		tmp = t_1
	elif y <= 1.2e-222:
		tmp = x + z
	elif y <= 4.9e+69:
		tmp = a * (1.0 - t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -7.2e+86)
		tmp = t_2;
	elseif (y <= -1.85e+15)
		tmp = t_1;
	elseif (y <= -1.16e-30)
		tmp = Float64(x + a);
	elseif (y <= -4.9e-70)
		tmp = t_1;
	elseif (y <= 1.2e-222)
		tmp = Float64(x + z);
	elseif (y <= 4.9e+69)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -7.2e+86)
		tmp = t_2;
	elseif (y <= -1.85e+15)
		tmp = t_1;
	elseif (y <= -1.16e-30)
		tmp = x + a;
	elseif (y <= -4.9e-70)
		tmp = t_1;
	elseif (y <= 1.2e-222)
		tmp = x + z;
	elseif (y <= 4.9e+69)
		tmp = a * (1.0 - t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+86], t$95$2, If[LessEqual[y, -1.85e+15], t$95$1, If[LessEqual[y, -1.16e-30], N[(x + a), $MachinePrecision], If[LessEqual[y, -4.9e-70], t$95$1, If[LessEqual[y, 1.2e-222], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.9e+69], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.20000000000000011e86 or 4.9e69 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 73.5%

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

   if -7.20000000000000011e86 < y < -1.85e15 or -1.16e-30 < y < -4.9e-70

   1. Initial program 96.9%

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

   2. Taylor expanded in t around inf 67.4%

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

   if -1.85e15 < y < -1.16e-30

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 71.2%

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

   3. Taylor expanded in b around 0 52.2%

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

   4. Taylor expanded in t around 0 52.2%

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

      1. cancel-sign-sub-inv 52.2%

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

      2. metadata-eval 52.2%

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

      3. *-lft-identity 52.2%

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

      4. +-commutative 52.2%

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

   6. Simplified 52.2%

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

   if -4.9e-70 < y < 1.19999999999999997e-222

   1. Initial program 98.6%

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

   2. Taylor expanded in y around 0 98.6%

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

      1. associate--l+ 98.6%

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

      2. fma-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. mul-1-neg 100.0%

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

      10. remove-double-neg 100.0%

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

      11. *-commutative 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 50.4%

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

   if 1.19999999999999997e-222 < y < 4.9e69

   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 52.6%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-30}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-222}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 10: 71.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + \left(x + a\right)\right) - y \cdot z\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-129}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z (+ x a)) (* y z))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -5e+56)
     t_2
     (if (<= b -8.6e-80)
       t_1
       (if (<= b -1.9e-129)
         (+ x (* a (- 1.0 t)))
         (if (<= b 1.25e+26) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (x + a)) - (y * z);
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -5e+56) {
		tmp = t_2;
	} else if (b <= -8.6e-80) {
		tmp = t_1;
	} else if (b <= -1.9e-129) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 1.25e+26) {
		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 = (z + (x + a)) - (y * z)
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-5d+56)) then
        tmp = t_2
    else if (b <= (-8.6d-80)) then
        tmp = t_1
    else if (b <= (-1.9d-129)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 1.25d+26) 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 = (z + (x + a)) - (y * z);
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -5e+56) {
		tmp = t_2;
	} else if (b <= -8.6e-80) {
		tmp = t_1;
	} else if (b <= -1.9e-129) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 1.25e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (x + a)) - (y * z)
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -5e+56:
		tmp = t_2
	elif b <= -8.6e-80:
		tmp = t_1
	elif b <= -1.9e-129:
		tmp = x + (a * (1.0 - t))
	elif b <= 1.25e+26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(x + a)) - Float64(y * z))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -5e+56)
		tmp = t_2;
	elseif (b <= -8.6e-80)
		tmp = t_1;
	elseif (b <= -1.9e-129)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 1.25e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (x + a)) - (y * z);
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -5e+56)
		tmp = t_2;
	elseif (b <= -8.6e-80)
		tmp = t_1;
	elseif (b <= -1.9e-129)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 1.25e+26)
		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[(z + N[(x + a), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+56], t$95$2, If[LessEqual[b, -8.6e-80], t$95$1, If[LessEqual[b, -1.9e-129], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+26], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.00000000000000024e56 or 1.25e26 < 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 85.8%

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

   3. Taylor expanded in a around 0 75.0%

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

   if -5.00000000000000024e56 < b < -8.6000000000000002e-80 or -1.89999999999999992e-129 < b < 1.25e26

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in b around 0 89.3%

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

   6. Taylor expanded in t around 0 66.0%

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

      1. neg-mul-1 66.0%

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

      2. associate--r+ 66.0%

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

      3. +-commutative 66.0%

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

      4. associate--l+ 66.0%

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

      5. sub-neg 66.0%

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

      6. remove-double-neg 66.0%

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

      7. +-commutative 66.0%

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

      8. *-commutative 66.0%

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

   8. Simplified 66.0%

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

   if -8.6000000000000002e-80 < b < -1.89999999999999992e-129

   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 0 100.0%

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

   3. Taylor expanded in b around 0 88.1%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+56}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-80}:\\ \;\;\;\;\left(z + \left(x + a\right)\right) - y \cdot z\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-129}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;\left(z + \left(x + a\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 11: 67.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-219}:\\ \;\;\;\;\left(z + \left(x + a\right)\right) - y \cdot z\\ \mathbf{elif}\;t \leq 25000000:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* b (- (+ y t) 2.0)) (* t a))))
   (if (<= t -7.2e-20)
     t_1
     (if (<= t 1.1e-219)
       (- (+ z (+ x a)) (* y z))
       (if (<= t 25000000.0) (+ x (+ a (* b (+ y -2.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((y + t) - 2.0)) - (t * a);
	double tmp;
	if (t <= -7.2e-20) {
		tmp = t_1;
	} else if (t <= 1.1e-219) {
		tmp = (z + (x + a)) - (y * z);
	} else if (t <= 25000000.0) {
		tmp = x + (a + (b * (y + -2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * ((y + t) - 2.0d0)) - (t * a)
    if (t <= (-7.2d-20)) then
        tmp = t_1
    else if (t <= 1.1d-219) then
        tmp = (z + (x + a)) - (y * z)
    else if (t <= 25000000.0d0) then
        tmp = x + (a + (b * (y + (-2.0d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((y + t) - 2.0)) - (t * a);
	double tmp;
	if (t <= -7.2e-20) {
		tmp = t_1;
	} else if (t <= 1.1e-219) {
		tmp = (z + (x + a)) - (y * z);
	} else if (t <= 25000000.0) {
		tmp = x + (a + (b * (y + -2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * ((y + t) - 2.0)) - (t * a)
	tmp = 0
	if t <= -7.2e-20:
		tmp = t_1
	elif t <= 1.1e-219:
		tmp = (z + (x + a)) - (y * z)
	elif t <= 25000000.0:
		tmp = x + (a + (b * (y + -2.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(t * a))
	tmp = 0.0
	if (t <= -7.2e-20)
		tmp = t_1;
	elseif (t <= 1.1e-219)
		tmp = Float64(Float64(z + Float64(x + a)) - Float64(y * z));
	elseif (t <= 25000000.0)
		tmp = Float64(x + Float64(a + Float64(b * Float64(y + -2.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * ((y + t) - 2.0)) - (t * a);
	tmp = 0.0;
	if (t <= -7.2e-20)
		tmp = t_1;
	elseif (t <= 1.1e-219)
		tmp = (z + (x + a)) - (y * z);
	elseif (t <= 25000000.0)
		tmp = x + (a + (b * (y + -2.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e-20], t$95$1, If[LessEqual[t, 1.1e-219], N[(N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 25000000.0], N[(x + N[(a + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.19999999999999948e-20 or 2.5e7 < t

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0 81.5%

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

   3. Taylor expanded in t around inf 81.3%

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

      1. *-commutative 47.7%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in x around 0 70.3%

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

   if -7.19999999999999948e-20 < t < 1.1e-219

   1. Initial program 98.8%

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

   2. Taylor expanded in y around 0 98.7%

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

      1. +-commutative 98.7%

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

      2. mul-1-neg 98.7%

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

      3. unsub-neg 98.7%

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

   4. Simplified 98.7%

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

   5. Taylor expanded in b around 0 72.8%

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

   6. Taylor expanded in t around 0 72.8%

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

      1. neg-mul-1 72.8%

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

      2. associate--r+ 72.8%

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

      3. +-commutative 72.8%

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

      4. associate--l+ 72.8%

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

      5. sub-neg 72.8%

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

      6. remove-double-neg 72.8%

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

      7. +-commutative 72.8%

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

      8. *-commutative 72.8%

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

   8. Simplified 72.8%

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

   if 1.1e-219 < t < 2.5e7

   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 83.2%

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

   3. Taylor expanded in t around 0 80.4%

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

      1. associate--l+ 80.4%

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

      2. sub-neg 80.4%

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

      3. metadata-eval 80.4%

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

      4. neg-mul-1 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-219}:\\ \;\;\;\;\left(z + \left(x + a\right)\right) - y \cdot z\\ \mathbf{elif}\;t \leq 25000000:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \end{array} \]

Alternative 12: 82.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+131} \lor \neg \left(b \leq 1.1 \cdot 10^{+149}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.8e+131) (not (<= b 1.1e+149)))
   (+ 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 <= -3.8e+131) || !(b <= 1.1e+149)) {
		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 <= (-3.8d+131)) .or. (.not. (b <= 1.1d+149))) 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 <= -3.8e+131) || !(b <= 1.1e+149)) {
		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 <= -3.8e+131) or not (b <= 1.1e+149):
		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 <= -3.8e+131) || !(b <= 1.1e+149))
		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 <= -3.8e+131) || ~((b <= 1.1e+149)))
		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, -3.8e+131], N[Not[LessEqual[b, 1.1e+149]], $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 < -3.8000000000000004e131 or 1.1e149 < b

   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 z around 0 93.4%

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

   3. Taylor expanded in a around 0 89.3%

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

   if -3.8000000000000004e131 < b < 1.1e149

   1. Initial program 98.9%

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

   2. Taylor expanded in b around 0 82.4%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+131} \lor \neg \left(b \leq 1.1 \cdot 10^{+149}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 13: 84.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.6 \cdot 10^{+54} \lor \neg \left(b \leq 1.9 \cdot 10^{+23}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.6e+54) (not (<= b 1.9e+23)))
   (- (+ x (* b (- (+ y t) 2.0))) (* t a))
   (+ 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 <= -9.6e+54) || !(b <= 1.9e+23)) {
		tmp = (x + (b * ((y + t) - 2.0))) - (t * a);
	} 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 <= (-9.6d+54)) .or. (.not. (b <= 1.9d+23))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) - (t * a)
    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 <= -9.6e+54) || !(b <= 1.9e+23)) {
		tmp = (x + (b * ((y + t) - 2.0))) - (t * a);
	} 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 <= -9.6e+54) or not (b <= 1.9e+23):
		tmp = (x + (b * ((y + t) - 2.0))) - (t * a)
	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 <= -9.6e+54) || !(b <= 1.9e+23))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) - Float64(t * a));
	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 <= -9.6e+54) || ~((b <= 1.9e+23)))
		tmp = (x + (b * ((y + t) - 2.0))) - (t * a);
	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, -9.6e+54], N[Not[LessEqual[b, 1.9e+23]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * a), $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 < -9.59999999999999993e54 or 1.89999999999999987e23 < 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 85.9%

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

   3. Taylor expanded in t around inf 80.7%

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

      1. *-commutative 20.6%

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

   5. Simplified 80.7%

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

   if -9.59999999999999993e54 < b < 1.89999999999999987e23

   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 89.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.6 \cdot 10^{+54} \lor \neg \left(b \leq 1.9 \cdot 10^{+23}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 14: 34.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1300000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-207}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-74}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= y -1.05e+88)
     (* y b)
     (if (<= y -3.1e+19)
       t_1
       (if (<= y -1300000000.0)
         (* t b)
         (if (<= y 2.6e-207)
           (+ x z)
           (if (<= y 1.35e-74) (+ x a) (if (<= y 7e+84) t_1 (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (y <= -1.05e+88) {
		tmp = y * b;
	} else if (y <= -3.1e+19) {
		tmp = t_1;
	} else if (y <= -1300000000.0) {
		tmp = t * b;
	} else if (y <= 2.6e-207) {
		tmp = x + z;
	} else if (y <= 1.35e-74) {
		tmp = x + a;
	} else if (y <= 7e+84) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (y <= (-1.05d+88)) then
        tmp = y * b
    else if (y <= (-3.1d+19)) then
        tmp = t_1
    else if (y <= (-1300000000.0d0)) then
        tmp = t * b
    else if (y <= 2.6d-207) then
        tmp = x + z
    else if (y <= 1.35d-74) then
        tmp = x + a
    else if (y <= 7d+84) then
        tmp = t_1
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (y <= -1.05e+88) {
		tmp = y * b;
	} else if (y <= -3.1e+19) {
		tmp = t_1;
	} else if (y <= -1300000000.0) {
		tmp = t * b;
	} else if (y <= 2.6e-207) {
		tmp = x + z;
	} else if (y <= 1.35e-74) {
		tmp = x + a;
	} else if (y <= 7e+84) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if y <= -1.05e+88:
		tmp = y * b
	elif y <= -3.1e+19:
		tmp = t_1
	elif y <= -1300000000.0:
		tmp = t * b
	elif y <= 2.6e-207:
		tmp = x + z
	elif y <= 1.35e-74:
		tmp = x + a
	elif y <= 7e+84:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (y <= -1.05e+88)
		tmp = Float64(y * b);
	elseif (y <= -3.1e+19)
		tmp = t_1;
	elseif (y <= -1300000000.0)
		tmp = Float64(t * b);
	elseif (y <= 2.6e-207)
		tmp = Float64(x + z);
	elseif (y <= 1.35e-74)
		tmp = Float64(x + a);
	elseif (y <= 7e+84)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (y <= -1.05e+88)
		tmp = y * b;
	elseif (y <= -3.1e+19)
		tmp = t_1;
	elseif (y <= -1300000000.0)
		tmp = t * b;
	elseif (y <= 2.6e-207)
		tmp = x + z;
	elseif (y <= 1.35e-74)
		tmp = x + a;
	elseif (y <= 7e+84)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[y, -1.05e+88], N[(y * b), $MachinePrecision], If[LessEqual[y, -3.1e+19], t$95$1, If[LessEqual[y, -1300000000.0], N[(t * b), $MachinePrecision], If[LessEqual[y, 2.6e-207], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.35e-74], N[(x + a), $MachinePrecision], If[LessEqual[y, 7e+84], t$95$1, N[(y * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.05e88 or 6.9999999999999998e84 < y

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 68.6%

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

   3. Taylor expanded in y around inf 44.2%

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

   if -1.05e88 < y < -3.1e19 or 1.35000000000000009e-74 < y < 6.9999999999999998e84

   1. Initial program 97.6%

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

   2. Taylor expanded in a around inf 47.1%

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

   3. Taylor expanded in t around inf 39.6%

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

      1. associate-*r* 39.6%

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

      2. neg-mul-1 39.6%

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

   5. Simplified 39.6%

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

   if -3.1e19 < y < -1.3e9

   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 0 100.0%

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

   3. Taylor expanded in a around 0 100.0%

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

   4. Taylor expanded in t around inf 69.1%

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

   5. Taylor expanded in x around 0 66.7%

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

      1. *-commutative 66.7%

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

   7. Simplified 66.7%

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

   if -1.3e9 < y < 2.5999999999999999e-207

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 97.4%

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

      1. associate--l+ 97.4%

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

      2. fma-neg 98.5%

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

      3. sub-neg 98.5%

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

      4. metadata-eval 98.5%

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

      5. sub-neg 98.5%

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

      6. metadata-eval 98.5%

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

      7. *-commutative 98.5%

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

      8. distribute-neg-in 98.5%

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

      9. mul-1-neg 98.5%

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

      10. remove-double-neg 98.5%

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

      11. *-commutative 98.5%

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

      12. distribute-rgt-neg-in 98.5%

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

      13. +-commutative 98.5%

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

      14. distribute-neg-in 98.5%

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

      15. metadata-eval 98.5%

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

      16. sub-neg 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in z around inf 46.5%

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

   if 2.5999999999999999e-207 < y < 1.35000000000000009e-74

   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 96.2%

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

   3. Taylor expanded in b around 0 68.3%

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

   4. Taylor expanded in t around 0 48.5%

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

      1. cancel-sign-sub-inv 48.5%

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

      2. metadata-eval 48.5%

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

      3. *-lft-identity 48.5%

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

      4. +-commutative 48.5%

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

   6. Simplified 48.5%

      \[\leadsto \color{blue}{a + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq -1300000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-207}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-74}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 15: 52.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot a\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* t a))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.3e+39)
     t_2
     (if (<= b -1.05e-252)
       t_1
       (if (<= b 3.2e-173) (* a (- 1.0 t)) (if (<= b 3.1e+68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (t * a);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.3e+39) {
		tmp = t_2;
	} else if (b <= -1.05e-252) {
		tmp = t_1;
	} else if (b <= 3.2e-173) {
		tmp = a * (1.0 - t);
	} else if (b <= 3.1e+68) {
		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 - (t * a)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.3d+39)) then
        tmp = t_2
    else if (b <= (-1.05d-252)) then
        tmp = t_1
    else if (b <= 3.2d-173) then
        tmp = a * (1.0d0 - t)
    else if (b <= 3.1d+68) 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 - (t * a);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.3e+39) {
		tmp = t_2;
	} else if (b <= -1.05e-252) {
		tmp = t_1;
	} else if (b <= 3.2e-173) {
		tmp = a * (1.0 - t);
	} else if (b <= 3.1e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (t * a)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.3e+39:
		tmp = t_2
	elif b <= -1.05e-252:
		tmp = t_1
	elif b <= 3.2e-173:
		tmp = a * (1.0 - t)
	elif b <= 3.1e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(t * a))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.3e+39)
		tmp = t_2;
	elseif (b <= -1.05e-252)
		tmp = t_1;
	elseif (b <= 3.2e-173)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 3.1e+68)
		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 - (t * a);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.3e+39)
		tmp = t_2;
	elseif (b <= -1.05e-252)
		tmp = t_1;
	elseif (b <= 3.2e-173)
		tmp = a * (1.0 - t);
	elseif (b <= 3.1e+68)
		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[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+39], t$95$2, If[LessEqual[b, -1.05e-252], t$95$1, If[LessEqual[b, 3.2e-173], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3e39 or 3.0999999999999998e68 < 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 66.4%

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

   if -1.3e39 < b < -1.05e-252 or 3.2e-173 < b < 3.0999999999999998e68

   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 71.7%

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

   3. Taylor expanded in b around 0 58.6%

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

   4. Taylor expanded in t around inf 50.0%

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

      1. *-commutative 50.0%

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

   6. Simplified 50.0%

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

   if -1.05e-252 < b < 3.2e-173

   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 52.5%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-252}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+68}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 16: 35.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+50}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+14}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+14}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-205}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+84}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.5e+50)
   (* y b)
   (if (<= y -3e+14)
     (* t b)
     (if (<= y -2.2e+14)
       (* y b)
       (if (<= y 4.8e-205) (+ x z) (if (<= y 6.5e+84) (+ x a) (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e+50) {
		tmp = y * b;
	} else if (y <= -3e+14) {
		tmp = t * b;
	} else if (y <= -2.2e+14) {
		tmp = y * b;
	} else if (y <= 4.8e-205) {
		tmp = x + z;
	} else if (y <= 6.5e+84) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8.5d+50)) then
        tmp = y * b
    else if (y <= (-3d+14)) then
        tmp = t * b
    else if (y <= (-2.2d+14)) then
        tmp = y * b
    else if (y <= 4.8d-205) then
        tmp = x + z
    else if (y <= 6.5d+84) then
        tmp = x + a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e+50) {
		tmp = y * b;
	} else if (y <= -3e+14) {
		tmp = t * b;
	} else if (y <= -2.2e+14) {
		tmp = y * b;
	} else if (y <= 4.8e-205) {
		tmp = x + z;
	} else if (y <= 6.5e+84) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.5e+50:
		tmp = y * b
	elif y <= -3e+14:
		tmp = t * b
	elif y <= -2.2e+14:
		tmp = y * b
	elif y <= 4.8e-205:
		tmp = x + z
	elif y <= 6.5e+84:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.5e+50)
		tmp = Float64(y * b);
	elseif (y <= -3e+14)
		tmp = Float64(t * b);
	elseif (y <= -2.2e+14)
		tmp = Float64(y * b);
	elseif (y <= 4.8e-205)
		tmp = Float64(x + z);
	elseif (y <= 6.5e+84)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.5e+50)
		tmp = y * b;
	elseif (y <= -3e+14)
		tmp = t * b;
	elseif (y <= -2.2e+14)
		tmp = y * b;
	elseif (y <= 4.8e-205)
		tmp = x + z;
	elseif (y <= 6.5e+84)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.5e+50], N[(y * b), $MachinePrecision], If[LessEqual[y, -3e+14], N[(t * b), $MachinePrecision], If[LessEqual[y, -2.2e+14], N[(y * b), $MachinePrecision], If[LessEqual[y, 4.8e-205], N[(x + z), $MachinePrecision], If[LessEqual[y, 6.5e+84], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.49999999999999961e50 or -3e14 < y < -2.2e14 or 6.50000000000000027e84 < y

   1. Initial program 95.0%

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

   2. Taylor expanded in z around 0 70.4%

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

   3. Taylor expanded in y around inf 42.4%

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

   if -8.49999999999999961e50 < y < -3e14

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in a around 0 59.4%

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

   4. Taylor expanded in t around inf 52.6%

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

   5. Taylor expanded in x around 0 44.8%

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

      1. *-commutative 44.8%

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

   7. Simplified 44.8%

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

   if -2.2e14 < y < 4.8000000000000004e-205

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 97.4%

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

      1. associate--l+ 97.4%

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

      2. fma-neg 98.5%

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

      3. sub-neg 98.5%

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

      4. metadata-eval 98.5%

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

      5. sub-neg 98.5%

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

      6. metadata-eval 98.5%

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

      7. *-commutative 98.5%

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

      8. distribute-neg-in 98.5%

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

      9. mul-1-neg 98.5%

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

      10. remove-double-neg 98.5%

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

      11. *-commutative 98.5%

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

      12. distribute-rgt-neg-in 98.5%

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

      13. +-commutative 98.5%

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

      14. distribute-neg-in 98.5%

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

      15. metadata-eval 98.5%

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

      16. sub-neg 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in z around inf 46.5%

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

   if 4.8000000000000004e-205 < y < 6.50000000000000027e84

   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 91.7%

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

   3. Taylor expanded in b around 0 62.1%

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

   4. Taylor expanded in t around 0 32.9%

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

      1. cancel-sign-sub-inv 32.9%

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

      2. metadata-eval 32.9%

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

      3. *-lft-identity 32.9%

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

      4. +-commutative 32.9%

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

   6. Simplified 32.9%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+50}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+14}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+14}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-205}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+84}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 17: 64.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+37} \lor \neg \left(b \leq 8.2 \cdot 10^{+43}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.85e+37) (not (<= b 8.2e+43)))
   (+ x (* 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 <= -1.85e+37) || !(b <= 8.2e+43)) {
		tmp = x + (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 <= (-1.85d+37)) .or. (.not. (b <= 8.2d+43))) then
        tmp = x + (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 <= -1.85e+37) || !(b <= 8.2e+43)) {
		tmp = x + (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 <= -1.85e+37) or not (b <= 8.2e+43):
		tmp = x + (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 <= -1.85e+37) || !(b <= 8.2e+43))
		tmp = Float64(x + 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 <= -1.85e+37) || ~((b <= 8.2e+43)))
		tmp = x + (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, -1.85e+37], N[Not[LessEqual[b, 8.2e+43]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.85e37 or 8.2000000000000001e43 < 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 z around 0 83.8%

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

   3. Taylor expanded in a around 0 72.7%

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

   if -1.85e37 < b < 8.2000000000000001e43

   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 68.1%

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

   3. Taylor expanded in b around 0 59.6%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+37} \lor \neg \left(b \leq 8.2 \cdot 10^{+43}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 18: 25.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-95}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-204}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.05e+51)
   (* y b)
   (if (<= y -1.25e-95)
     (* t b)
     (if (<= y 1.56e-204) z (if (<= y 1.62e+25) a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.05e+51) {
		tmp = y * b;
	} else if (y <= -1.25e-95) {
		tmp = t * b;
	} else if (y <= 1.56e-204) {
		tmp = z;
	} else if (y <= 1.62e+25) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.05d+51)) then
        tmp = y * b
    else if (y <= (-1.25d-95)) then
        tmp = t * b
    else if (y <= 1.56d-204) then
        tmp = z
    else if (y <= 1.62d+25) then
        tmp = a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.05e+51) {
		tmp = y * b;
	} else if (y <= -1.25e-95) {
		tmp = t * b;
	} else if (y <= 1.56e-204) {
		tmp = z;
	} else if (y <= 1.62e+25) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.05e+51:
		tmp = y * b
	elif y <= -1.25e-95:
		tmp = t * b
	elif y <= 1.56e-204:
		tmp = z
	elif y <= 1.62e+25:
		tmp = a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.05e+51)
		tmp = Float64(y * b);
	elseif (y <= -1.25e-95)
		tmp = Float64(t * b);
	elseif (y <= 1.56e-204)
		tmp = z;
	elseif (y <= 1.62e+25)
		tmp = a;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.05e+51)
		tmp = y * b;
	elseif (y <= -1.25e-95)
		tmp = t * b;
	elseif (y <= 1.56e-204)
		tmp = z;
	elseif (y <= 1.62e+25)
		tmp = a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.05e+51], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.25e-95], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.56e-204], z, If[LessEqual[y, 1.62e+25], a, N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0500000000000001e51 or 1.62e25 < y

   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 z around 0 71.5%

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

   3. Taylor expanded in y around inf 39.8%

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

   if -1.0500000000000001e51 < y < -1.2499999999999999e-95

   1. Initial program 97.5%

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

   2. Taylor expanded in z around 0 90.5%

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

   3. Taylor expanded in a around 0 62.4%

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

   4. Taylor expanded in t around inf 48.3%

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

   5. Taylor expanded in x around 0 29.2%

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

      1. *-commutative 29.2%

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

   7. Simplified 29.2%

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

   if -1.2499999999999999e-95 < y < 1.56000000000000007e-204

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 35.6%

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

   3. Taylor expanded in y around 0 35.6%

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

   if 1.56000000000000007e-204 < y < 1.62e25

   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 49.3%

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

   3. Taylor expanded in t around 0 23.6%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-95}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-204}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 19: 31.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+83}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-305}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-212}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.8e+83)
   (* t b)
   (if (<= b 2.1e-305)
     (+ x a)
     (if (<= b 1.65e-212) z (if (<= b 2.35e+111) (+ x a) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.8e+83) {
		tmp = t * b;
	} else if (b <= 2.1e-305) {
		tmp = x + a;
	} else if (b <= 1.65e-212) {
		tmp = z;
	} else if (b <= 2.35e+111) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.8d+83)) then
        tmp = t * b
    else if (b <= 2.1d-305) then
        tmp = x + a
    else if (b <= 1.65d-212) then
        tmp = z
    else if (b <= 2.35d+111) then
        tmp = x + a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.8e+83) {
		tmp = t * b;
	} else if (b <= 2.1e-305) {
		tmp = x + a;
	} else if (b <= 1.65e-212) {
		tmp = z;
	} else if (b <= 2.35e+111) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.8e+83:
		tmp = t * b
	elif b <= 2.1e-305:
		tmp = x + a
	elif b <= 1.65e-212:
		tmp = z
	elif b <= 2.35e+111:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.8e+83)
		tmp = Float64(t * b);
	elseif (b <= 2.1e-305)
		tmp = Float64(x + a);
	elseif (b <= 1.65e-212)
		tmp = z;
	elseif (b <= 2.35e+111)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.8e+83)
		tmp = t * b;
	elseif (b <= 2.1e-305)
		tmp = x + a;
	elseif (b <= 1.65e-212)
		tmp = z;
	elseif (b <= 2.35e+111)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.8e+83], N[(t * b), $MachinePrecision], If[LessEqual[b, 2.1e-305], N[(x + a), $MachinePrecision], If[LessEqual[b, 1.65e-212], z, If[LessEqual[b, 2.35e+111], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.8000000000000003e83

   1. Initial program 92.6%

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

   2. Taylor expanded in z around 0 87.5%

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

   3. Taylor expanded in a around 0 78.5%

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

   4. Taylor expanded in t around inf 51.3%

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

   5. Taylor expanded in x around 0 46.0%

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

      1. *-commutative 46.0%

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

   7. Simplified 46.0%

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

   if -7.8000000000000003e83 < b < 2.1e-305 or 1.6500000000000001e-212 < b < 2.35000000000000004e111

   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 70.8%

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

   3. Taylor expanded in b around 0 55.3%

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

   4. Taylor expanded in t around 0 32.4%

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

      1. cancel-sign-sub-inv 32.4%

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

      2. metadata-eval 32.4%

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

      3. *-lft-identity 32.4%

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

      4. +-commutative 32.4%

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

   6. Simplified 32.4%

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

   if 2.1e-305 < b < 1.6500000000000001e-212

   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 48.8%

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

   3. Taylor expanded in y around 0 42.2%

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

   if 2.35000000000000004e111 < b

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 87.2%

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

   3. Taylor expanded in y around inf 39.0%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+83}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-305}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-212}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 20: 61.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+57} \lor \neg \left(b \leq 1.2 \cdot 10^{+87}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.45e+57) (not (<= b 1.2e+87)))
   (* 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 <= -1.45e+57) || !(b <= 1.2e+87)) {
		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 <= (-1.45d+57)) .or. (.not. (b <= 1.2d+87))) 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 <= -1.45e+57) || !(b <= 1.2e+87)) {
		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 <= -1.45e+57) or not (b <= 1.2e+87):
		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 <= -1.45e+57) || !(b <= 1.2e+87))
		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 <= -1.45e+57) || ~((b <= 1.2e+87)))
		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, -1.45e+57], N[Not[LessEqual[b, 1.2e+87]], $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 < -1.4500000000000001e57 or 1.19999999999999991e87 < b

   1. Initial program 93.4%

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

   2. Taylor expanded in b around inf 70.1%

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

   if -1.4500000000000001e57 < b < 1.19999999999999991e87

   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 67.9%

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

   3. Taylor expanded in b around 0 57.4%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+57} \lor \neg \left(b \leq 1.2 \cdot 10^{+87}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 21: 20.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-241}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-230}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+38}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.65e+130)
   x
   (if (<= x -4.7e-241) z (if (<= x 3.25e-230) a (if (<= x 1.12e+38) z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.65e+130) {
		tmp = x;
	} else if (x <= -4.7e-241) {
		tmp = z;
	} else if (x <= 3.25e-230) {
		tmp = a;
	} else if (x <= 1.12e+38) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.65d+130)) then
        tmp = x
    else if (x <= (-4.7d-241)) then
        tmp = z
    else if (x <= 3.25d-230) then
        tmp = a
    else if (x <= 1.12d+38) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.65e+130) {
		tmp = x;
	} else if (x <= -4.7e-241) {
		tmp = z;
	} else if (x <= 3.25e-230) {
		tmp = a;
	} else if (x <= 1.12e+38) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.65e+130:
		tmp = x
	elif x <= -4.7e-241:
		tmp = z
	elif x <= 3.25e-230:
		tmp = a
	elif x <= 1.12e+38:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.65e+130)
		tmp = x;
	elseif (x <= -4.7e-241)
		tmp = z;
	elseif (x <= 3.25e-230)
		tmp = a;
	elseif (x <= 1.12e+38)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.65e+130)
		tmp = x;
	elseif (x <= -4.7e-241)
		tmp = z;
	elseif (x <= 3.25e-230)
		tmp = a;
	elseif (x <= 1.12e+38)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.65e+130], x, If[LessEqual[x, -4.7e-241], z, If[LessEqual[x, 3.25e-230], a, If[LessEqual[x, 1.12e+38], z, x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e130 or 1.1199999999999999e38 < x

   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 x around inf 35.1%

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

   if -1.65e130 < x < -4.6999999999999999e-241 or 3.2500000000000002e-230 < x < 1.1199999999999999e38

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 37.7%

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

   3. Taylor expanded in y around 0 20.7%

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

   if -4.6999999999999999e-241 < x < 3.2500000000000002e-230

   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 51.5%

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

   3. Taylor expanded in t around 0 24.5%

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

4. Final simplification 26.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-241}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-230}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+38}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 25.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1500000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-202}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1500000.0)
   (* y b)
   (if (<= y 6.1e-202) z (if (<= y 7.6e+25) a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1500000.0) {
		tmp = y * b;
	} else if (y <= 6.1e-202) {
		tmp = z;
	} else if (y <= 7.6e+25) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1500000.0d0)) then
        tmp = y * b
    else if (y <= 6.1d-202) then
        tmp = z
    else if (y <= 7.6d+25) then
        tmp = a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1500000.0) {
		tmp = y * b;
	} else if (y <= 6.1e-202) {
		tmp = z;
	} else if (y <= 7.6e+25) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1500000.0:
		tmp = y * b
	elif y <= 6.1e-202:
		tmp = z
	elif y <= 7.6e+25:
		tmp = a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1500000.0)
		tmp = Float64(y * b);
	elseif (y <= 6.1e-202)
		tmp = z;
	elseif (y <= 7.6e+25)
		tmp = a;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1500000.0)
		tmp = y * b;
	elseif (y <= 6.1e-202)
		tmp = z;
	elseif (y <= 7.6e+25)
		tmp = a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1500000.0], N[(y * b), $MachinePrecision], If[LessEqual[y, 6.1e-202], z, If[LessEqual[y, 7.6e+25], a, N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5e6 or 7.6000000000000001e25 < y

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 75.0%

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

   3. Taylor expanded in y around inf 36.9%

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

   if -1.5e6 < y < 6.10000000000000045e-202

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 30.7%

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

   3. Taylor expanded in y around 0 29.2%

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

   if 6.10000000000000045e-202 < y < 7.6000000000000001e25

   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 49.3%

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

   3. Taylor expanded in t around 0 23.6%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1500000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-202}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 23: 50.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -12000 \lor \neg \left(t \leq 14500000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -12000.0) (not (<= t 14500000.0))) (* t (- b a)) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -12000.0) || !(t <= 14500000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-12000.0d0)) .or. (.not. (t <= 14500000.0d0))) then
        tmp = t * (b - a)
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -12000.0) || !(t <= 14500000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -12000.0) or not (t <= 14500000.0):
		tmp = t * (b - a)
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -12000.0) || !(t <= 14500000.0))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -12000.0) || ~((t <= 14500000.0)))
		tmp = t * (b - a);
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -12000.0], N[Not[LessEqual[t, 14500000.0]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -12000 or 1.45e7 < t

   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 t around inf 64.7%

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

   if -12000 < t < 1.45e7

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 69.0%

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

   3. Taylor expanded in b around 0 37.4%

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

   4. Taylor expanded in t around 0 36.6%

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

      1. cancel-sign-sub-inv 36.6%

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

      2. metadata-eval 36.6%

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

      3. *-lft-identity 36.6%

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

      4. +-commutative 36.6%

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

   6. Simplified 36.6%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -12000 \lor \neg \left(t \leq 14500000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]

Alternative 24: 20.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+33}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.2e+61) x (if (<= x 2.35e+33) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.2e+61) {
		tmp = x;
	} else if (x <= 2.35e+33) {
		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 <= (-3.2d+61)) then
        tmp = x
    else if (x <= 2.35d+33) 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 <= -3.2e+61) {
		tmp = x;
	} else if (x <= 2.35e+33) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.2e+61:
		tmp = x
	elif x <= 2.35e+33:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.2e+61)
		tmp = x;
	elseif (x <= 2.35e+33)
		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 <= -3.2e+61)
		tmp = x;
	elseif (x <= 2.35e+33)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.2e+61], x, If[LessEqual[x, 2.35e+33], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1999999999999998e61 or 2.3499999999999999e33 < x

   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 x around inf 31.2%

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

   if -3.1999999999999998e61 < x < 2.3499999999999999e33

   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 35.3%

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

   3. Taylor expanded in t around 0 16.2%

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

4. Final simplification 22.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+33}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25: 10.8% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 30.3%

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

3. Taylor expanded in t around 0 11.5%

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

4. Final simplification 11.5%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023279 
(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)))