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

Percentage Accurate: 94.9% → 97.9%

Time: 21.1s

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%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]
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: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) - b \cdot \left(2 - t\right)\\ t_2 := x + \left(a - t \cdot a\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-161}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ x z) (* b (- 2.0 t)))) (t_2 (+ x (- a (* t a)))))
   (if (<= a -1e+54)
     t_2
     (if (<= a -3.2e-78)
       t_1
       (if (<= a -3.1e-161)
         (+ x (* b (- (+ y t) 2.0)))
         (if (<= a 2.3e-248)
           t_1
           (if (<= a 4e-184) (* y (- b z)) (if (<= a 1.32e+150) 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 * (2.0 - t));
	double t_2 = x + (a - (t * a));
	double tmp;
	if (a <= -1e+54) {
		tmp = t_2;
	} else if (a <= -3.2e-78) {
		tmp = t_1;
	} else if (a <= -3.1e-161) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (a <= 2.3e-248) {
		tmp = t_1;
	} else if (a <= 4e-184) {
		tmp = y * (b - z);
	} else if (a <= 1.32e+150) {
		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 * (2.0d0 - t))
    t_2 = x + (a - (t * a))
    if (a <= (-1d+54)) then
        tmp = t_2
    else if (a <= (-3.2d-78)) then
        tmp = t_1
    else if (a <= (-3.1d-161)) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else if (a <= 2.3d-248) then
        tmp = t_1
    else if (a <= 4d-184) then
        tmp = y * (b - z)
    else if (a <= 1.32d+150) 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 * (2.0 - t));
	double t_2 = x + (a - (t * a));
	double tmp;
	if (a <= -1e+54) {
		tmp = t_2;
	} else if (a <= -3.2e-78) {
		tmp = t_1;
	} else if (a <= -3.1e-161) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (a <= 2.3e-248) {
		tmp = t_1;
	} else if (a <= 4e-184) {
		tmp = y * (b - z);
	} else if (a <= 1.32e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) - (b * (2.0 - t))
	t_2 = x + (a - (t * a))
	tmp = 0
	if a <= -1e+54:
		tmp = t_2
	elif a <= -3.2e-78:
		tmp = t_1
	elif a <= -3.1e-161:
		tmp = x + (b * ((y + t) - 2.0))
	elif a <= 2.3e-248:
		tmp = t_1
	elif a <= 4e-184:
		tmp = y * (b - z)
	elif a <= 1.32e+150:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) - Float64(b * Float64(2.0 - t)))
	t_2 = Float64(x + Float64(a - Float64(t * a)))
	tmp = 0.0
	if (a <= -1e+54)
		tmp = t_2;
	elseif (a <= -3.2e-78)
		tmp = t_1;
	elseif (a <= -3.1e-161)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	elseif (a <= 2.3e-248)
		tmp = t_1;
	elseif (a <= 4e-184)
		tmp = Float64(y * Float64(b - z));
	elseif (a <= 1.32e+150)
		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 * (2.0 - t));
	t_2 = x + (a - (t * a));
	tmp = 0.0;
	if (a <= -1e+54)
		tmp = t_2;
	elseif (a <= -3.2e-78)
		tmp = t_1;
	elseif (a <= -3.1e-161)
		tmp = x + (b * ((y + t) - 2.0));
	elseif (a <= 2.3e-248)
		tmp = t_1;
	elseif (a <= 4e-184)
		tmp = y * (b - z);
	elseif (a <= 1.32e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + z), $MachinePrecision] - N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+54], t$95$2, If[LessEqual[a, -3.2e-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, 2.3e-248], t$95$1, If[LessEqual[a, 4e-184], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.32e+150], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.0000000000000001e54 or 1.32e150 < 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 y around 0 96.6%

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

      1. mul-1-neg 96.6%

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

      2. unsub-neg 96.6%

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

   4. Simplified 96.6%

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

   5. Taylor expanded in b around 0 85.4%

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

   6. Taylor expanded in z around 0 75.7%

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

      1. sub-neg 75.7%

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

      2. metadata-eval 75.7%

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

      3. *-commutative 75.7%

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

      4. distribute-rgt-in 75.7%

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

      5. mul-1-neg 75.7%

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

      6. unsub-neg 75.7%

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

   8. Simplified 75.7%

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

   if -1.0000000000000001e54 < a < -3.2e-78 or -3.0999999999999999e-161 < a < 2.3e-248 or 4.0000000000000002e-184 < a < 1.32e150

   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 97.6%

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

      1. mul-1-neg 97.6%

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

      2. unsub-neg 97.6%

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

   4. Simplified 97.6%

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

   5. Taylor expanded in y around 0 76.2%

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

   6. Taylor expanded in a around 0 66.0%

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

   if -3.2e-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 a around 0 89.2%

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

   3. Taylor expanded in z around 0 80.7%

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

   if 2.3e-248 < 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%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+54}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-78}:\\ \;\;\;\;\left(x + z\right) - b \cdot \left(2 - t\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-161}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-248}:\\ \;\;\;\;\left(x + z\right) - b \cdot \left(2 - t\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+150}:\\ \;\;\;\;\left(x + z\right) - b \cdot \left(2 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \end{array} \]

Alternative 4: 82.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+131}:\\ \;\;\;\;a + \left(z + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y)))))
        (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -1.1e+132)
     t_2
     (if (<= b 2.7e+31)
       t_1
       (if (<= b 2.1e+131)
         (+ a (+ z (+ x (* b (- y 2.0)))))
         (if (<= b 1.1e+149) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.1e+132) {
		tmp = t_2;
	} else if (b <= 2.7e+31) {
		tmp = t_1;
	} else if (b <= 2.1e+131) {
		tmp = a + (z + (x + (b * (y - 2.0))));
	} else if (b <= 1.1e+149) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-1.1d+132)) then
        tmp = t_2
    else if (b <= 2.7d+31) then
        tmp = t_1
    else if (b <= 2.1d+131) then
        tmp = a + (z + (x + (b * (y - 2.0d0))))
    else if (b <= 1.1d+149) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.1e+132) {
		tmp = t_2;
	} else if (b <= 2.7e+31) {
		tmp = t_1;
	} else if (b <= 2.1e+131) {
		tmp = a + (z + (x + (b * (y - 2.0))));
	} else if (b <= 1.1e+149) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -1.1e+132:
		tmp = t_2
	elif b <= 2.7e+31:
		tmp = t_1
	elif b <= 2.1e+131:
		tmp = a + (z + (x + (b * (y - 2.0))))
	elif b <= 1.1e+149:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -1.1e+132)
		tmp = t_2;
	elseif (b <= 2.7e+31)
		tmp = t_1;
	elseif (b <= 2.1e+131)
		tmp = Float64(a + Float64(z + Float64(x + Float64(b * Float64(y - 2.0)))));
	elseif (b <= 1.1e+149)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -1.1e+132)
		tmp = t_2;
	elseif (b <= 2.7e+31)
		tmp = t_1;
	elseif (b <= 2.1e+131)
		tmp = a + (z + (x + (b * (y - 2.0))));
	elseif (b <= 1.1e+149)
		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[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e+132], t$95$2, If[LessEqual[b, 2.7e+31], t$95$1, If[LessEqual[b, 2.1e+131], N[(a + N[(z + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+149], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.09999999999999994e132 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 a around 0 88.9%

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

   3. Taylor expanded in z around 0 89.3%

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

   if -1.09999999999999994e132 < b < 2.69999999999999986e31 or 2.09999999999999985e131 < b < 1.1e149

   1. Initial program 98.7%

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

   2. Taylor expanded in b around 0 86.1%

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

   if 2.69999999999999986e31 < b < 2.09999999999999985e131

   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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. sub-neg 88.9%

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

      3. metadata-eval 88.9%

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

      4. mul-1-neg 88.9%

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

      5. unsub-neg 88.9%

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

      6. *-commutative 88.9%

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

      7. distribute-lft-in 88.9%

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

      8. *-commutative 88.9%

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

      9. neg-mul-1 88.9%

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

      10. unsub-neg 88.9%

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

      11. *-commutative 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in t around 0 75.9%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+132}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+31}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+131}:\\ \;\;\;\;a + \left(z + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+149}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 5: 85.8% accurate, 1.0× speedup

Math

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

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)
         (+ (+ z (+ x (* b (- t 2.0)))) 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 = (z + (x + (b * (t - 2.0)))) + 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 = (z + (x + (b * (t - 2.0d0)))) + 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 = (z + (x + (b * (t - 2.0)))) + 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 = (z + (x + (b * (t - 2.0)))) + 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(z + Float64(x + Float64(b * Float64(t - 2.0)))) + 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 = (z + (x + (b * (t - 2.0)))) + 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[(z + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $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%

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

   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%

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

   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%

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

      1. mul-1-neg 99.2%

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

      2. 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%

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

   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%

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

4. Final simplification 92.1%

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

Alternative 6: 59.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-138}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (* a (- 1.0 t))))
   (if (<= b -3.4e+117)
     t_2
     (if (<= b -1.65e-79)
       t_1
       (if (<= b -9.8e-138)
         t_3
         (if (<= b 1.42e-213)
           t_1
           (if (<= b 4e-184) t_3 (if (<= b 8e+86) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = a * (1.0 - t);
	double tmp;
	if (b <= -3.4e+117) {
		tmp = t_2;
	} else if (b <= -1.65e-79) {
		tmp = t_1;
	} else if (b <= -9.8e-138) {
		tmp = t_3;
	} else if (b <= 1.42e-213) {
		tmp = t_1;
	} else if (b <= 4e-184) {
		tmp = t_3;
	} else if (b <= 8e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = a * (1.0d0 - t)
    if (b <= (-3.4d+117)) then
        tmp = t_2
    else if (b <= (-1.65d-79)) then
        tmp = t_1
    else if (b <= (-9.8d-138)) then
        tmp = t_3
    else if (b <= 1.42d-213) then
        tmp = t_1
    else if (b <= 4d-184) then
        tmp = t_3
    else if (b <= 8d+86) 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 * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = a * (1.0 - t);
	double tmp;
	if (b <= -3.4e+117) {
		tmp = t_2;
	} else if (b <= -1.65e-79) {
		tmp = t_1;
	} else if (b <= -9.8e-138) {
		tmp = t_3;
	} else if (b <= 1.42e-213) {
		tmp = t_1;
	} else if (b <= 4e-184) {
		tmp = t_3;
	} else if (b <= 8e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = b * ((y + t) - 2.0)
	t_3 = a * (1.0 - t)
	tmp = 0
	if b <= -3.4e+117:
		tmp = t_2
	elif b <= -1.65e-79:
		tmp = t_1
	elif b <= -9.8e-138:
		tmp = t_3
	elif b <= 1.42e-213:
		tmp = t_1
	elif b <= 4e-184:
		tmp = t_3
	elif b <= 8e+86:
		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(1.0 - y)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -3.4e+117)
		tmp = t_2;
	elseif (b <= -1.65e-79)
		tmp = t_1;
	elseif (b <= -9.8e-138)
		tmp = t_3;
	elseif (b <= 1.42e-213)
		tmp = t_1;
	elseif (b <= 4e-184)
		tmp = t_3;
	elseif (b <= 8e+86)
		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 * (1.0 - y));
	t_2 = b * ((y + t) - 2.0);
	t_3 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -3.4e+117)
		tmp = t_2;
	elseif (b <= -1.65e-79)
		tmp = t_1;
	elseif (b <= -9.8e-138)
		tmp = t_3;
	elseif (b <= 1.42e-213)
		tmp = t_1;
	elseif (b <= 4e-184)
		tmp = t_3;
	elseif (b <= 8e+86)
		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[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+117], t$95$2, If[LessEqual[b, -1.65e-79], t$95$1, If[LessEqual[b, -9.8e-138], t$95$3, If[LessEqual[b, 1.42e-213], t$95$1, If[LessEqual[b, 4e-184], t$95$3, If[LessEqual[b, 8e+86], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4000000000000001e117 or 8.0000000000000001e86 < b

   1. Initial program 92.3%

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

   2. Taylor expanded in b around inf 75.4%

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

   if -3.4000000000000001e117 < b < -1.6499999999999999e-79 or -9.80000000000000033e-138 < b < 1.42000000000000002e-213 or 4.0000000000000002e-184 < b < 8.0000000000000001e86

   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 a around 0 68.1%

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

   3. Taylor expanded in b around 0 53.8%

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

   if -1.6499999999999999e-79 < b < -9.80000000000000033e-138 or 1.42000000000000002e-213 < b < 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 a around inf 77.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-79}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-138}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-213}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-184}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+86}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 7: 61.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - t \cdot a\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-223}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- a (* t a))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (+ x (* z (- 1.0 y)))))
   (if (<= b -2.8e+56)
     t_2
     (if (<= b -2.15e-138)
       t_1
       (if (<= b -1.05e-223)
         t_3
         (if (<= b 1.22e-144)
           t_1
           (if (<= b 2.05e-76) t_3 (if (<= b 4.2e+84) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (t * a));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -2.8e+56) {
		tmp = t_2;
	} else if (b <= -2.15e-138) {
		tmp = t_1;
	} else if (b <= -1.05e-223) {
		tmp = t_3;
	} else if (b <= 1.22e-144) {
		tmp = t_1;
	} else if (b <= 2.05e-76) {
		tmp = t_3;
	} else if (b <= 4.2e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a - (t * a))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x + (z * (1.0d0 - y))
    if (b <= (-2.8d+56)) then
        tmp = t_2
    else if (b <= (-2.15d-138)) then
        tmp = t_1
    else if (b <= (-1.05d-223)) then
        tmp = t_3
    else if (b <= 1.22d-144) then
        tmp = t_1
    else if (b <= 2.05d-76) then
        tmp = t_3
    else if (b <= 4.2d+84) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (t * a));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -2.8e+56) {
		tmp = t_2;
	} else if (b <= -2.15e-138) {
		tmp = t_1;
	} else if (b <= -1.05e-223) {
		tmp = t_3;
	} else if (b <= 1.22e-144) {
		tmp = t_1;
	} else if (b <= 2.05e-76) {
		tmp = t_3;
	} else if (b <= 4.2e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a - (t * a))
	t_2 = b * ((y + t) - 2.0)
	t_3 = x + (z * (1.0 - y))
	tmp = 0
	if b <= -2.8e+56:
		tmp = t_2
	elif b <= -2.15e-138:
		tmp = t_1
	elif b <= -1.05e-223:
		tmp = t_3
	elif b <= 1.22e-144:
		tmp = t_1
	elif b <= 2.05e-76:
		tmp = t_3
	elif b <= 4.2e+84:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -2.8e+56)
		tmp = t_2;
	elseif (b <= -2.15e-138)
		tmp = t_1;
	elseif (b <= -1.05e-223)
		tmp = t_3;
	elseif (b <= 1.22e-144)
		tmp = t_1;
	elseif (b <= 2.05e-76)
		tmp = t_3;
	elseif (b <= 4.2e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a - (t * a));
	t_2 = b * ((y + t) - 2.0);
	t_3 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -2.8e+56)
		tmp = t_2;
	elseif (b <= -2.15e-138)
		tmp = t_1;
	elseif (b <= -1.05e-223)
		tmp = t_3;
	elseif (b <= 1.22e-144)
		tmp = t_1;
	elseif (b <= 2.05e-76)
		tmp = t_3;
	elseif (b <= 4.2e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+56], t$95$2, If[LessEqual[b, -2.15e-138], t$95$1, If[LessEqual[b, -1.05e-223], t$95$3, If[LessEqual[b, 1.22e-144], t$95$1, If[LessEqual[b, 2.05e-76], t$95$3, If[LessEqual[b, 4.2e+84], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.80000000000000008e56 or 4.20000000000000037e84 < 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%

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

   if -2.80000000000000008e56 < b < -2.15e-138 or -1.04999999999999991e-223 < b < 1.22e-144 or 2.0499999999999999e-76 < b < 4.20000000000000037e84

   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%

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

      1. mul-1-neg 100.0%

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

      2. 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 89.4%

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

   6. Taylor expanded in z around 0 63.2%

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

      1. sub-neg 63.2%

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

      2. metadata-eval 63.2%

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

      3. *-commutative 63.2%

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

      4. distribute-rgt-in 63.2%

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

      5. mul-1-neg 63.2%

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

      6. unsub-neg 63.2%

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

   8. Simplified 63.2%

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

   if -2.15e-138 < b < -1.04999999999999991e-223 or 1.22e-144 < b < 2.0499999999999999e-76

   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 a around 0 77.5%

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

   3. Taylor expanded in b around 0 64.6%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-138}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-223}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{-144}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-76}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+84}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 8: 72.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-231}:\\ \;\;\;\;\left(x + z\right) - \left(y \cdot z - a\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ z (+ x (* b (- y 2.0)))))) (t_2 (* t (- b a))))
   (if (<= t -4.6e+106)
     t_2
     (if (<= t 2.3e-301)
       t_1
       (if (<= t 5.5e-231)
         (- (+ x z) (- (* y z) a))
         (if (<= t 7e+48) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z + (x + (b * (y - 2.0))));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.6e+106) {
		tmp = t_2;
	} else if (t <= 2.3e-301) {
		tmp = t_1;
	} else if (t <= 5.5e-231) {
		tmp = (x + z) - ((y * z) - a);
	} else if (t <= 7e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (z + (x + (b * (y - 2.0d0))))
    t_2 = t * (b - a)
    if (t <= (-4.6d+106)) then
        tmp = t_2
    else if (t <= 2.3d-301) then
        tmp = t_1
    else if (t <= 5.5d-231) then
        tmp = (x + z) - ((y * z) - a)
    else if (t <= 7d+48) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z + (x + (b * (y - 2.0))));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.6e+106) {
		tmp = t_2;
	} else if (t <= 2.3e-301) {
		tmp = t_1;
	} else if (t <= 5.5e-231) {
		tmp = (x + z) - ((y * z) - a);
	} else if (t <= 7e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z + (x + (b * (y - 2.0))))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -4.6e+106:
		tmp = t_2
	elif t <= 2.3e-301:
		tmp = t_1
	elif t <= 5.5e-231:
		tmp = (x + z) - ((y * z) - a)
	elif t <= 7e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z + Float64(x + Float64(b * Float64(y - 2.0)))))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.6e+106)
		tmp = t_2;
	elseif (t <= 2.3e-301)
		tmp = t_1;
	elseif (t <= 5.5e-231)
		tmp = Float64(Float64(x + z) - Float64(Float64(y * z) - a));
	elseif (t <= 7e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z + (x + (b * (y - 2.0))));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.6e+106)
		tmp = t_2;
	elseif (t <= 2.3e-301)
		tmp = t_1;
	elseif (t <= 5.5e-231)
		tmp = (x + z) - ((y * z) - a);
	elseif (t <= 7e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e+106], t$95$2, If[LessEqual[t, 2.3e-301], t$95$1, If[LessEqual[t, 5.5e-231], N[(N[(x + z), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+48], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.6000000000000004e106 or 6.9999999999999995e48 < t

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 73.0%

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

   if -4.6000000000000004e106 < t < 2.3000000000000002e-301 or 5.49999999999999951e-231 < t < 6.9999999999999995e48

   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. Step-by-step derivation

      1. +-commutative 98.5%

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

      2. fma-def 99.3%

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

      3. associate--l+ 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

      6. sub-neg 99.3%

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

      7. associate-+l- 99.3%

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

      8. fma-neg 99.3%

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

      9. sub-neg 99.3%

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

      10. metadata-eval 99.3%

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

      11. remove-double-neg 99.3%

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

      12. sub-neg 99.3%

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

      13. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 87.7%

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

      1. +-commutative 87.7%

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

      2. sub-neg 87.7%

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

      3. metadata-eval 87.7%

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

      4. mul-1-neg 87.7%

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

      5. unsub-neg 87.7%

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

      6. *-commutative 87.7%

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

      7. distribute-lft-in 87.7%

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

      8. *-commutative 87.7%

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

      9. neg-mul-1 87.7%

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

      10. unsub-neg 87.7%

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

      11. *-commutative 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in t around 0 79.7%

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

   if 2.3000000000000002e-301 < t < 5.49999999999999951e-231

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in b around 0 89.6%

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

   6. Taylor expanded in t around 0 89.6%

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

      1. neg-mul-1 89.6%

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

   8. Simplified 89.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-301}:\\ \;\;\;\;a + \left(z + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-231}:\\ \;\;\;\;\left(x + z\right) - \left(y \cdot z - a\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+48}:\\ \;\;\;\;a + \left(z + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 9: 73.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.06 \cdot 10^{-224}:\\ \;\;\;\;\left(x + z\right) - \left(y \cdot z - a\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ z (+ x (* b (- y 2.0))))))
        (t_2 (- (* b (- (+ y t) 2.0)) (* t a))))
   (if (<= t -1.12e+17)
     t_2
     (if (<= t 1.15e-303)
       t_1
       (if (<= t 2.06e-224)
         (- (+ x z) (- (* y z) a))
         (if (<= t 2.6e+45) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z + (x + (b * (y - 2.0))));
	double t_2 = (b * ((y + t) - 2.0)) - (t * a);
	double tmp;
	if (t <= -1.12e+17) {
		tmp = t_2;
	} else if (t <= 1.15e-303) {
		tmp = t_1;
	} else if (t <= 2.06e-224) {
		tmp = (x + z) - ((y * z) - a);
	} else if (t <= 2.6e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (z + (x + (b * (y - 2.0d0))))
    t_2 = (b * ((y + t) - 2.0d0)) - (t * a)
    if (t <= (-1.12d+17)) then
        tmp = t_2
    else if (t <= 1.15d-303) then
        tmp = t_1
    else if (t <= 2.06d-224) then
        tmp = (x + z) - ((y * z) - a)
    else if (t <= 2.6d+45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z + (x + (b * (y - 2.0))));
	double t_2 = (b * ((y + t) - 2.0)) - (t * a);
	double tmp;
	if (t <= -1.12e+17) {
		tmp = t_2;
	} else if (t <= 1.15e-303) {
		tmp = t_1;
	} else if (t <= 2.06e-224) {
		tmp = (x + z) - ((y * z) - a);
	} else if (t <= 2.6e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z + (x + (b * (y - 2.0))))
	t_2 = (b * ((y + t) - 2.0)) - (t * a)
	tmp = 0
	if t <= -1.12e+17:
		tmp = t_2
	elif t <= 1.15e-303:
		tmp = t_1
	elif t <= 2.06e-224:
		tmp = (x + z) - ((y * z) - a)
	elif t <= 2.6e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z + Float64(x + Float64(b * Float64(y - 2.0)))))
	t_2 = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(t * a))
	tmp = 0.0
	if (t <= -1.12e+17)
		tmp = t_2;
	elseif (t <= 1.15e-303)
		tmp = t_1;
	elseif (t <= 2.06e-224)
		tmp = Float64(Float64(x + z) - Float64(Float64(y * z) - a));
	elseif (t <= 2.6e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z + (x + (b * (y - 2.0))));
	t_2 = (b * ((y + t) - 2.0)) - (t * a);
	tmp = 0.0;
	if (t <= -1.12e+17)
		tmp = t_2;
	elseif (t <= 1.15e-303)
		tmp = t_1;
	elseif (t <= 2.06e-224)
		tmp = (x + z) - ((y * z) - a);
	elseif (t <= 2.6e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.12e+17], t$95$2, If[LessEqual[t, 1.15e-303], t$95$1, If[LessEqual[t, 2.06e-224], N[(N[(x + z), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.12e17 or 2.60000000000000007e45 < t

   1. Initial program 94.9%

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

   2. Taylor expanded in y around 0 95.0%

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

      1. mul-1-neg 95.0%

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

      2. unsub-neg 95.0%

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

   4. Simplified 95.0%

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

   5. Taylor expanded in t around inf 72.9%

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

      1. associate-*r* 72.9%

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

      2. neg-mul-1 72.9%

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

   7. Simplified 72.9%

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

   if -1.12e17 < t < 1.14999999999999998e-303 or 2.0599999999999999e-224 < t < 2.60000000000000007e45

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 87.3%

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

      1. +-commutative 87.3%

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

      2. sub-neg 87.3%

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

      3. metadata-eval 87.3%

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

      4. mul-1-neg 87.3%

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

      5. unsub-neg 87.3%

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

      6. *-commutative 87.3%

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

      7. distribute-lft-in 87.3%

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

      8. *-commutative 87.3%

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

      9. neg-mul-1 87.3%

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

      10. unsub-neg 87.3%

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

      11. *-commutative 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in t around 0 83.9%

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

   if 1.14999999999999998e-303 < t < 2.0599999999999999e-224

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in b around 0 89.6%

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

   6. Taylor expanded in t around 0 89.6%

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

      1. neg-mul-1 89.6%

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

   8. Simplified 89.6%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-303}:\\ \;\;\;\;a + \left(z + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.06 \cdot 10^{-224}:\\ \;\;\;\;\left(x + z\right) - \left(y \cdot z - a\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+45}:\\ \;\;\;\;a + \left(z + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \end{array} \]

Alternative 10: 83.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+87} \lor \neg \left(y \leq 6.2 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.35e+87) (not (<= y 6.2e+84)))
   (* y (- b z))
   (+ (+ z (+ x (* b (- t 2.0)))) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.35e+87) || !(y <= 6.2e+84)) {
		tmp = y * (b - z);
	} else {
		tmp = (z + (x + (b * (t - 2.0)))) + (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 ((y <= (-2.35d+87)) .or. (.not. (y <= 6.2d+84))) then
        tmp = y * (b - z)
    else
        tmp = (z + (x + (b * (t - 2.0d0)))) + (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 ((y <= -2.35e+87) || !(y <= 6.2e+84)) {
		tmp = y * (b - z);
	} else {
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.35e+87) or not (y <= 6.2e+84):
		tmp = y * (b - z)
	else:
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.35e+87) || !(y <= 6.2e+84))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(Float64(z + Float64(x + Float64(b * Float64(t - 2.0)))) + 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 ((y <= -2.35e+87) || ~((y <= 6.2e+84)))
		tmp = y * (b - z);
	else
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.35e+87], N[Not[LessEqual[y, 6.2e+84]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3500000000000002e87 or 6.20000000000000006e84 < 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 y around inf 74.0%

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

   if -2.3500000000000002e87 < y < 6.20000000000000006e84

   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 98.8%

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

      1. mul-1-neg 98.8%

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

      2. unsub-neg 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in y around 0 94.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+87} \lor \neg \left(y \leq 6.2 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 11: 85.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+88} \lor \neg \left(y \leq 6.8 \cdot 10^{+69}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.06e+88) (not (<= y 6.8e+69)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* z (- 1.0 y)))
   (+ (+ z (+ x (* b (- t 2.0)))) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.06e+88) || !(y <= 6.8e+69)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	} else {
		tmp = (z + (x + (b * (t - 2.0)))) + (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 ((y <= (-1.06d+88)) .or. (.not. (y <= 6.8d+69))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (z * (1.0d0 - y))
    else
        tmp = (z + (x + (b * (t - 2.0d0)))) + (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 ((y <= -1.06e+88) || !(y <= 6.8e+69)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	} else {
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.06e+88) or not (y <= 6.8e+69):
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y))
	else:
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.06e+88) || !(y <= 6.8e+69))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(Float64(z + Float64(x + Float64(b * Float64(t - 2.0)))) + 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 ((y <= -1.06e+88) || ~((y <= 6.8e+69)))
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	else
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.06e+88], N[Not[LessEqual[y, 6.8e+69]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06000000000000001e88 or 6.79999999999999973e69 < 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 a around 0 81.9%

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

   if -1.06000000000000001e88 < y < 6.79999999999999973e69

   1. Initial program 98.7%

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

   2. Taylor expanded in y around 0 98.7%

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

      1. mul-1-neg 98.7%

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

      2. 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 y around 0 95.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+88} \lor \neg \left(y \leq 6.8 \cdot 10^{+69}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 12: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -9 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-239}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-184}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+24}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+146}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -9e-35)
     t_1
     (if (<= a 1.5e-239)
       (+ x z)
       (if (<= a 6e-184)
         (* y b)
         (if (<= a 4.5e+24)
           (+ x z)
           (if (<= a 3.4e+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 <= -9e-35) {
		tmp = t_1;
	} else if (a <= 1.5e-239) {
		tmp = x + z;
	} else if (a <= 6e-184) {
		tmp = y * b;
	} else if (a <= 4.5e+24) {
		tmp = x + z;
	} else if (a <= 3.4e+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 <= (-9d-35)) then
        tmp = t_1
    else if (a <= 1.5d-239) then
        tmp = x + z
    else if (a <= 6d-184) then
        tmp = y * b
    else if (a <= 4.5d+24) then
        tmp = x + z
    else if (a <= 3.4d+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 <= -9e-35) {
		tmp = t_1;
	} else if (a <= 1.5e-239) {
		tmp = x + z;
	} else if (a <= 6e-184) {
		tmp = y * b;
	} else if (a <= 4.5e+24) {
		tmp = x + z;
	} else if (a <= 3.4e+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 <= -9e-35:
		tmp = t_1
	elif a <= 1.5e-239:
		tmp = x + z
	elif a <= 6e-184:
		tmp = y * b
	elif a <= 4.5e+24:
		tmp = x + z
	elif a <= 3.4e+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 <= -9e-35)
		tmp = t_1;
	elseif (a <= 1.5e-239)
		tmp = Float64(x + z);
	elseif (a <= 6e-184)
		tmp = Float64(y * b);
	elseif (a <= 4.5e+24)
		tmp = Float64(x + z);
	elseif (a <= 3.4e+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 <= -9e-35)
		tmp = t_1;
	elseif (a <= 1.5e-239)
		tmp = x + z;
	elseif (a <= 6e-184)
		tmp = y * b;
	elseif (a <= 4.5e+24)
		tmp = x + z;
	elseif (a <= 3.4e+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, -9e-35], t$95$1, If[LessEqual[a, 1.5e-239], N[(x + z), $MachinePrecision], If[LessEqual[a, 6e-184], N[(y * b), $MachinePrecision], If[LessEqual[a, 4.5e+24], N[(x + z), $MachinePrecision], If[LessEqual[a, 3.4e+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 < -9.0000000000000002e-35 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 -9.0000000000000002e-35 < a < 1.4999999999999999e-239 or 5.99999999999999982e-184 < a < 4.50000000000000019e24

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0 90.2%

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

   3. Taylor expanded in b around 0 53.8%

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

   4. Taylor expanded in y around 0 38.5%

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

      1. sub-neg 38.5%

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

      2. neg-mul-1 38.5%

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

      3. remove-double-neg 38.5%

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

   6. Simplified 38.5%

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

   if 1.4999999999999999e-239 < a < 5.99999999999999982e-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 90.3%

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

   3. Taylor expanded in b around inf 55.1%

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

   if 4.50000000000000019e24 < a < 3.39999999999999991e146

   1. Initial program 95.2%

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

   2. Taylor expanded in a around 0 86.1%

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

   3. Taylor expanded in t around inf 44.0%

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

   if 3.39999999999999991e146 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-239}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-184}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+24}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+146}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 13: 46.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-95}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 170000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9200000000000:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* t (- b a))))
   (if (<= t -6.6e+16)
     t_2
     (if (<= t -1.6e-95)
       (+ x z)
       (if (<= t -9.5e-188)
         t_1
         (if (<= t 1.5e-50)
           (+ x z)
           (if (<= t 170000.0)
             t_1
             (if (<= t 9200000000000.0) (+ x z) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6.6e+16) {
		tmp = t_2;
	} else if (t <= -1.6e-95) {
		tmp = x + z;
	} else if (t <= -9.5e-188) {
		tmp = t_1;
	} else if (t <= 1.5e-50) {
		tmp = x + z;
	} else if (t <= 170000.0) {
		tmp = t_1;
	} else if (t <= 9200000000000.0) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = t * (b - a)
    if (t <= (-6.6d+16)) then
        tmp = t_2
    else if (t <= (-1.6d-95)) then
        tmp = x + z
    else if (t <= (-9.5d-188)) then
        tmp = t_1
    else if (t <= 1.5d-50) then
        tmp = x + z
    else if (t <= 170000.0d0) then
        tmp = t_1
    else if (t <= 9200000000000.0d0) then
        tmp = x + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6.6e+16) {
		tmp = t_2;
	} else if (t <= -1.6e-95) {
		tmp = x + z;
	} else if (t <= -9.5e-188) {
		tmp = t_1;
	} else if (t <= 1.5e-50) {
		tmp = x + z;
	} else if (t <= 170000.0) {
		tmp = t_1;
	} else if (t <= 9200000000000.0) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -6.6e+16:
		tmp = t_2
	elif t <= -1.6e-95:
		tmp = x + z
	elif t <= -9.5e-188:
		tmp = t_1
	elif t <= 1.5e-50:
		tmp = x + z
	elif t <= 170000.0:
		tmp = t_1
	elif t <= 9200000000000.0:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6.6e+16)
		tmp = t_2;
	elseif (t <= -1.6e-95)
		tmp = Float64(x + z);
	elseif (t <= -9.5e-188)
		tmp = t_1;
	elseif (t <= 1.5e-50)
		tmp = Float64(x + z);
	elseif (t <= 170000.0)
		tmp = t_1;
	elseif (t <= 9200000000000.0)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -6.6e+16)
		tmp = t_2;
	elseif (t <= -1.6e-95)
		tmp = x + z;
	elseif (t <= -9.5e-188)
		tmp = t_1;
	elseif (t <= 1.5e-50)
		tmp = x + z;
	elseif (t <= 170000.0)
		tmp = t_1;
	elseif (t <= 9200000000000.0)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.6e+16], t$95$2, If[LessEqual[t, -1.6e-95], N[(x + z), $MachinePrecision], If[LessEqual[t, -9.5e-188], t$95$1, If[LessEqual[t, 1.5e-50], N[(x + z), $MachinePrecision], If[LessEqual[t, 170000.0], t$95$1, If[LessEqual[t, 9200000000000.0], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.6e16 or 9.2e12 < t

   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 t around inf 66.0%

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

   if -6.6e16 < t < -1.5999999999999999e-95 or -9.50000000000000063e-188 < t < 1.49999999999999995e-50 or 1.7e5 < t < 9.2e12

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 86.8%

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

   3. Taylor expanded in b around 0 54.2%

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

   4. Taylor expanded in y around 0 38.6%

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

      1. sub-neg 38.6%

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

      2. neg-mul-1 38.6%

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

      3. remove-double-neg 38.6%

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

   6. Simplified 38.6%

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

   if -1.5999999999999999e-95 < t < -9.50000000000000063e-188 or 1.49999999999999995e-50 < t < 1.7e5

   1. Initial program 97.4%

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

   2. Taylor expanded in a around inf 38.7%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-95}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 170000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 9200000000000:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 14: 49.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-20}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-224}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+70}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -1.2e+87)
     t_2
     (if (<= y -4.1e+14)
       t_1
       (if (<= y -1.02e-20)
         (+ x z)
         (if (<= y -1.9e-70)
           t_1
           (if (<= y 8.2e-224)
             (+ x z)
             (if (<= y 2.35e+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 <= -1.2e+87) {
		tmp = t_2;
	} else if (y <= -4.1e+14) {
		tmp = t_1;
	} else if (y <= -1.02e-20) {
		tmp = x + z;
	} else if (y <= -1.9e-70) {
		tmp = t_1;
	} else if (y <= 8.2e-224) {
		tmp = x + z;
	} else if (y <= 2.35e+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 <= (-1.2d+87)) then
        tmp = t_2
    else if (y <= (-4.1d+14)) then
        tmp = t_1
    else if (y <= (-1.02d-20)) then
        tmp = x + z
    else if (y <= (-1.9d-70)) then
        tmp = t_1
    else if (y <= 8.2d-224) then
        tmp = x + z
    else if (y <= 2.35d+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 <= -1.2e+87) {
		tmp = t_2;
	} else if (y <= -4.1e+14) {
		tmp = t_1;
	} else if (y <= -1.02e-20) {
		tmp = x + z;
	} else if (y <= -1.9e-70) {
		tmp = t_1;
	} else if (y <= 8.2e-224) {
		tmp = x + z;
	} else if (y <= 2.35e+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 <= -1.2e+87:
		tmp = t_2
	elif y <= -4.1e+14:
		tmp = t_1
	elif y <= -1.02e-20:
		tmp = x + z
	elif y <= -1.9e-70:
		tmp = t_1
	elif y <= 8.2e-224:
		tmp = x + z
	elif y <= 2.35e+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 <= -1.2e+87)
		tmp = t_2;
	elseif (y <= -4.1e+14)
		tmp = t_1;
	elseif (y <= -1.02e-20)
		tmp = Float64(x + z);
	elseif (y <= -1.9e-70)
		tmp = t_1;
	elseif (y <= 8.2e-224)
		tmp = Float64(x + z);
	elseif (y <= 2.35e+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 <= -1.2e+87)
		tmp = t_2;
	elseif (y <= -4.1e+14)
		tmp = t_1;
	elseif (y <= -1.02e-20)
		tmp = x + z;
	elseif (y <= -1.9e-70)
		tmp = t_1;
	elseif (y <= 8.2e-224)
		tmp = x + z;
	elseif (y <= 2.35e+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, -1.2e+87], t$95$2, If[LessEqual[y, -4.1e+14], t$95$1, If[LessEqual[y, -1.02e-20], N[(x + z), $MachinePrecision], If[LessEqual[y, -1.9e-70], t$95$1, If[LessEqual[y, 8.2e-224], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.35e+70], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.19999999999999991e87 or 2.3499999999999999e70 < 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%

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

   if -1.19999999999999991e87 < y < -4.1e14 or -1.02000000000000001e-20 < y < -1.8999999999999999e-70

   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 t around inf 63.7%

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

   if -4.1e14 < y < -1.02000000000000001e-20 or -1.8999999999999999e-70 < y < 8.19999999999999972e-224

   1. Initial program 98.7%

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

   2. Taylor expanded in a around 0 74.7%

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

   3. Taylor expanded in b around 0 52.9%

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

   4. Taylor expanded in y around 0 51.3%

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

      1. sub-neg 51.3%

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

      2. neg-mul-1 51.3%

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

      3. remove-double-neg 51.3%

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

   6. Simplified 51.3%

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

   if 8.19999999999999972e-224 < y < 2.3499999999999999e70

   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 4 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-20}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-224}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+70}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 15: 71.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;\left(x + z\right) - \left(y \cdot z - a\right)\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+38} \lor \neg \left(b \leq 9.5 \cdot 10^{+45}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -8.5e+56)
     t_1
     (if (<= b -3.5e+43)
       (- (+ x z) (- (* y z) a))
       (if (or (<= b -2.55e+38) (not (<= b 9.5e+45)))
         t_1
         (- (+ x (+ z a)) (* t a)))))))

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 (b <= -8.5e+56) {
		tmp = t_1;
	} else if (b <= -3.5e+43) {
		tmp = (x + z) - ((y * z) - a);
	} else if ((b <= -2.55e+38) || !(b <= 9.5e+45)) {
		tmp = t_1;
	} else {
		tmp = (x + (z + a)) - (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-8.5d+56)) then
        tmp = t_1
    else if (b <= (-3.5d+43)) then
        tmp = (x + z) - ((y * z) - a)
    else if ((b <= (-2.55d+38)) .or. (.not. (b <= 9.5d+45))) then
        tmp = t_1
    else
        tmp = (x + (z + a)) - (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -8.5e+56) {
		tmp = t_1;
	} else if (b <= -3.5e+43) {
		tmp = (x + z) - ((y * z) - a);
	} else if ((b <= -2.55e+38) || !(b <= 9.5e+45)) {
		tmp = t_1;
	} else {
		tmp = (x + (z + a)) - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -8.5e+56:
		tmp = t_1
	elif b <= -3.5e+43:
		tmp = (x + z) - ((y * z) - a)
	elif (b <= -2.55e+38) or not (b <= 9.5e+45):
		tmp = t_1
	else:
		tmp = (x + (z + a)) - (t * a)
	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 (b <= -8.5e+56)
		tmp = t_1;
	elseif (b <= -3.5e+43)
		tmp = Float64(Float64(x + z) - Float64(Float64(y * z) - a));
	elseif ((b <= -2.55e+38) || !(b <= 9.5e+45))
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(z + a)) - Float64(t * a));
	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 (b <= -8.5e+56)
		tmp = t_1;
	elseif (b <= -3.5e+43)
		tmp = (x + z) - ((y * z) - a);
	elseif ((b <= -2.55e+38) || ~((b <= 9.5e+45)))
		tmp = t_1;
	else
		tmp = (x + (z + a)) - (t * a);
	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[LessEqual[b, -8.5e+56], t$95$1, If[LessEqual[b, -3.5e+43], N[(N[(x + z), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -2.55e+38], N[Not[LessEqual[b, 9.5e+45]], $MachinePrecision]], t$95$1, N[(N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.4999999999999998e56 or -3.5000000000000001e43 < b < -2.5500000000000001e38 or 9.4999999999999998e45 < 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 a around 0 83.8%

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

   3. Taylor expanded in z around 0 75.8%

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

   if -8.4999999999999998e56 < b < -3.5000000000000001e43

   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%

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

      1. mul-1-neg 100.0%

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

      2. 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 0 100.0%

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

   6. Taylor expanded in t around 0 100.0%

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

      1. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   if -2.5500000000000001e38 < b < 9.4999999999999998e45

   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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. sub-neg 84.9%

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

      3. metadata-eval 84.9%

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

      4. mul-1-neg 84.9%

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

      5. unsub-neg 84.9%

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

      6. *-commutative 84.9%

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

      7. distribute-lft-in 84.9%

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

      8. *-commutative 84.9%

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

      9. neg-mul-1 84.9%

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

      10. unsub-neg 84.9%

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

      11. *-commutative 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in b around 0 75.6%

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

      1. associate-+r+ 75.6%

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

   9. Simplified 75.6%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+56}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;\left(x + z\right) - \left(y \cdot z - a\right)\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+38} \lor \neg \left(b \leq 9.5 \cdot 10^{+45}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - t \cdot a\\ \end{array} \]

Alternative 16: 57.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) - b \cdot \left(2 - t\right)\\ t_2 := x + \left(a - t \cdot a\right)\\ \mathbf{if}\;a \leq -1.18 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ x z) (* b (- 2.0 t)))) (t_2 (+ x (- a (* t a)))))
   (if (<= a -1.18e+54)
     t_2
     (if (<= a 1.7e-247)
       t_1
       (if (<= a 4e-184) (* y (- b z)) (if (<= a 8.2e+152) 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 * (2.0 - t));
	double t_2 = x + (a - (t * a));
	double tmp;
	if (a <= -1.18e+54) {
		tmp = t_2;
	} else if (a <= 1.7e-247) {
		tmp = t_1;
	} else if (a <= 4e-184) {
		tmp = y * (b - z);
	} else if (a <= 8.2e+152) {
		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 * (2.0d0 - t))
    t_2 = x + (a - (t * a))
    if (a <= (-1.18d+54)) then
        tmp = t_2
    else if (a <= 1.7d-247) then
        tmp = t_1
    else if (a <= 4d-184) then
        tmp = y * (b - z)
    else if (a <= 8.2d+152) 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 * (2.0 - t));
	double t_2 = x + (a - (t * a));
	double tmp;
	if (a <= -1.18e+54) {
		tmp = t_2;
	} else if (a <= 1.7e-247) {
		tmp = t_1;
	} else if (a <= 4e-184) {
		tmp = y * (b - z);
	} else if (a <= 8.2e+152) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) - (b * (2.0 - t))
	t_2 = x + (a - (t * a))
	tmp = 0
	if a <= -1.18e+54:
		tmp = t_2
	elif a <= 1.7e-247:
		tmp = t_1
	elif a <= 4e-184:
		tmp = y * (b - z)
	elif a <= 8.2e+152:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) - Float64(b * Float64(2.0 - t)))
	t_2 = Float64(x + Float64(a - Float64(t * a)))
	tmp = 0.0
	if (a <= -1.18e+54)
		tmp = t_2;
	elseif (a <= 1.7e-247)
		tmp = t_1;
	elseif (a <= 4e-184)
		tmp = Float64(y * Float64(b - z));
	elseif (a <= 8.2e+152)
		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 * (2.0 - t));
	t_2 = x + (a - (t * a));
	tmp = 0.0;
	if (a <= -1.18e+54)
		tmp = t_2;
	elseif (a <= 1.7e-247)
		tmp = t_1;
	elseif (a <= 4e-184)
		tmp = y * (b - z);
	elseif (a <= 8.2e+152)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + z), $MachinePrecision] - N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.18e+54], t$95$2, If[LessEqual[a, 1.7e-247], t$95$1, If[LessEqual[a, 4e-184], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+152], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1799999999999999e54 or 8.1999999999999996e152 < 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 y around 0 96.6%

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

      1. mul-1-neg 96.6%

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

      2. unsub-neg 96.6%

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

   4. Simplified 96.6%

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

   5. Taylor expanded in b around 0 85.4%

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

   6. Taylor expanded in z around 0 75.7%

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

      1. sub-neg 75.7%

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

      2. metadata-eval 75.7%

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

      3. *-commutative 75.7%

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

      4. distribute-rgt-in 75.7%

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

      5. mul-1-neg 75.7%

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

      6. unsub-neg 75.7%

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

   8. Simplified 75.7%

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

   if -1.1799999999999999e54 < a < 1.7000000000000001e-247 or 4.0000000000000002e-184 < a < 8.1999999999999996e152

   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 97.3%

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

      1. mul-1-neg 97.3%

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

      2. unsub-neg 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in y around 0 74.7%

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

   6. Taylor expanded in a around 0 65.1%

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

   if 1.7000000000000001e-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%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{+54}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-247}:\\ \;\;\;\;\left(x + z\right) - b \cdot \left(2 - t\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+152}:\\ \;\;\;\;\left(x + z\right) - b \cdot \left(2 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \end{array} \]

Alternative 17: 33.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+87}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4000000000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-222}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= y -1.2e+87)
     (* y b)
     (if (<= y -3.2e+19)
       t_1
       (if (<= y -4000000000000.0)
         (* t b)
         (if (<= y 3.5e-222) (+ x z) (if (<= y 1.7e+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 <= -1.2e+87) {
		tmp = y * b;
	} else if (y <= -3.2e+19) {
		tmp = t_1;
	} else if (y <= -4000000000000.0) {
		tmp = t * b;
	} else if (y <= 3.5e-222) {
		tmp = x + z;
	} else if (y <= 1.7e+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 <= (-1.2d+87)) then
        tmp = y * b
    else if (y <= (-3.2d+19)) then
        tmp = t_1
    else if (y <= (-4000000000000.0d0)) then
        tmp = t * b
    else if (y <= 3.5d-222) then
        tmp = x + z
    else if (y <= 1.7d+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 <= -1.2e+87) {
		tmp = y * b;
	} else if (y <= -3.2e+19) {
		tmp = t_1;
	} else if (y <= -4000000000000.0) {
		tmp = t * b;
	} else if (y <= 3.5e-222) {
		tmp = x + z;
	} else if (y <= 1.7e+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 <= -1.2e+87:
		tmp = y * b
	elif y <= -3.2e+19:
		tmp = t_1
	elif y <= -4000000000000.0:
		tmp = t * b
	elif y <= 3.5e-222:
		tmp = x + z
	elif y <= 1.7e+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 <= -1.2e+87)
		tmp = Float64(y * b);
	elseif (y <= -3.2e+19)
		tmp = t_1;
	elseif (y <= -4000000000000.0)
		tmp = Float64(t * b);
	elseif (y <= 3.5e-222)
		tmp = Float64(x + z);
	elseif (y <= 1.7e+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 <= -1.2e+87)
		tmp = y * b;
	elseif (y <= -3.2e+19)
		tmp = t_1;
	elseif (y <= -4000000000000.0)
		tmp = t * b;
	elseif (y <= 3.5e-222)
		tmp = x + z;
	elseif (y <= 1.7e+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, -1.2e+87], N[(y * b), $MachinePrecision], If[LessEqual[y, -3.2e+19], t$95$1, If[LessEqual[y, -4000000000000.0], N[(t * b), $MachinePrecision], If[LessEqual[y, 3.5e-222], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.7e+84], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.19999999999999991e87 or 1.6999999999999999e84 < 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 y around inf 74.0%

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

   3. Taylor expanded in b around inf 44.2%

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

   if -1.19999999999999991e87 < y < -3.2e19 or 3.50000000000000024e-222 < y < 1.6999999999999999e84

   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%

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

      1. mul-1-neg 98.6%

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

      2. unsub-neg 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in b around 0 69.6%

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

   6. Taylor expanded in t around inf 34.1%

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

      1. associate-*r* 34.1%

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

      2. mul-1-neg 34.1%

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

   8. Simplified 34.1%

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

   if -3.2e19 < y < -4e12

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 100.0%

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

   3. Taylor expanded in t around inf 66.7%

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

   if -4e12 < y < 3.50000000000000024e-222

   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 a around 0 72.5%

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

   3. Taylor expanded in b around 0 49.0%

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

   4. Taylor expanded in y around 0 47.5%

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

      1. sub-neg 47.5%

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

      2. neg-mul-1 47.5%

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

      3. remove-double-neg 47.5%

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

   6. Simplified 47.5%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+87}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq -4000000000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-222}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 18: 47.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* t (- b a))))
   (if (<= t -7.2e+15)
     t_2
     (if (<= t 9.5e-66)
       t_1
       (if (<= t 3.6e+31) (* a (- 1.0 t)) (if (<= t 4.2e+42) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.2e+15) {
		tmp = t_2;
	} else if (t <= 9.5e-66) {
		tmp = t_1;
	} else if (t <= 3.6e+31) {
		tmp = a * (1.0 - t);
	} else if (t <= 4.2e+42) {
		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 * (1.0d0 - y)
    t_2 = t * (b - a)
    if (t <= (-7.2d+15)) then
        tmp = t_2
    else if (t <= 9.5d-66) then
        tmp = t_1
    else if (t <= 3.6d+31) then
        tmp = a * (1.0d0 - t)
    else if (t <= 4.2d+42) 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 * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.2e+15) {
		tmp = t_2;
	} else if (t <= 9.5e-66) {
		tmp = t_1;
	} else if (t <= 3.6e+31) {
		tmp = a * (1.0 - t);
	} else if (t <= 4.2e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -7.2e+15:
		tmp = t_2
	elif t <= 9.5e-66:
		tmp = t_1
	elif t <= 3.6e+31:
		tmp = a * (1.0 - t)
	elif t <= 4.2e+42:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.2e+15)
		tmp = t_2;
	elseif (t <= 9.5e-66)
		tmp = t_1;
	elseif (t <= 3.6e+31)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (t <= 4.2e+42)
		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 * (1.0 - y);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.2e+15)
		tmp = t_2;
	elseif (t <= 9.5e-66)
		tmp = t_1;
	elseif (t <= 3.6e+31)
		tmp = a * (1.0 - t);
	elseif (t <= 4.2e+42)
		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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+15], t$95$2, If[LessEqual[t, 9.5e-66], t$95$1, If[LessEqual[t, 3.6e+31], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+42], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2e15 or 4.19999999999999991e42 < t

   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 t around inf 67.0%

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

   if -7.2e15 < t < 9.5000000000000004e-66 or 3.59999999999999996e31 < t < 4.19999999999999991e42

   1. Initial program 99.1%

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

   2. Taylor expanded in z around inf 37.4%

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

   if 9.5000000000000004e-66 < t < 3.59999999999999996e31

   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 39.8%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 19: 71.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+38} \lor \neg \left(b \leq 4 \cdot 10^{+46}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.9e+38) (not (<= b 4e+46)))
   (+ x (* b (- (+ y t) 2.0)))
   (- (+ x (+ z a)) (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+38) || !(b <= 4e+46)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + (z + a)) - (t * 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 ((b <= (-1.9d+38)) .or. (.not. (b <= 4d+46))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = (x + (z + a)) - (t * 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 ((b <= -1.9e+38) || !(b <= 4e+46)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + (z + a)) - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.9e+38) or not (b <= 4e+46):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = (x + (z + a)) - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.9e+38) || !(b <= 4e+46))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(Float64(x + Float64(z + a)) - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.9e+38) || ~((b <= 4e+46)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = (x + (z + a)) - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.9e+38], N[Not[LessEqual[b, 4e+46]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8999999999999999e38 or 4e46 < 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 a around 0 82.9%

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

   3. Taylor expanded in z around 0 72.7%

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

   if -1.8999999999999999e38 < b < 4e46

   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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. sub-neg 84.9%

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

      3. metadata-eval 84.9%

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

      4. mul-1-neg 84.9%

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

      5. unsub-neg 84.9%

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

      6. *-commutative 84.9%

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

      7. distribute-lft-in 84.9%

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

      8. *-commutative 84.9%

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

      9. neg-mul-1 84.9%

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

      10. unsub-neg 84.9%

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

      11. *-commutative 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in b around 0 75.6%

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

      1. associate-+r+ 75.6%

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

   9. Simplified 75.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+38} \lor \neg \left(b \leq 4 \cdot 10^{+46}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - t \cdot a\\ \end{array} \]

Alternative 20: 21.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+198}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq -3.85 \cdot 10^{-236}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-230}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 10^{+35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4e+198)
   x
   (if (<= x -3.8e+24)
     (* t b)
     (if (<= x -3.85e-236) z (if (<= x 4.7e-230) a (if (<= x 1e+35) z x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4e+198) {
		tmp = x;
	} else if (x <= -3.8e+24) {
		tmp = t * b;
	} else if (x <= -3.85e-236) {
		tmp = z;
	} else if (x <= 4.7e-230) {
		tmp = a;
	} else if (x <= 1e+35) {
		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 <= (-4d+198)) then
        tmp = x
    else if (x <= (-3.8d+24)) then
        tmp = t * b
    else if (x <= (-3.85d-236)) then
        tmp = z
    else if (x <= 4.7d-230) then
        tmp = a
    else if (x <= 1d+35) 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 <= -4e+198) {
		tmp = x;
	} else if (x <= -3.8e+24) {
		tmp = t * b;
	} else if (x <= -3.85e-236) {
		tmp = z;
	} else if (x <= 4.7e-230) {
		tmp = a;
	} else if (x <= 1e+35) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4e+198:
		tmp = x
	elif x <= -3.8e+24:
		tmp = t * b
	elif x <= -3.85e-236:
		tmp = z
	elif x <= 4.7e-230:
		tmp = a
	elif x <= 1e+35:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4e+198)
		tmp = x;
	elseif (x <= -3.8e+24)
		tmp = Float64(t * b);
	elseif (x <= -3.85e-236)
		tmp = z;
	elseif (x <= 4.7e-230)
		tmp = a;
	elseif (x <= 1e+35)
		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 <= -4e+198)
		tmp = x;
	elseif (x <= -3.8e+24)
		tmp = t * b;
	elseif (x <= -3.85e-236)
		tmp = z;
	elseif (x <= 4.7e-230)
		tmp = a;
	elseif (x <= 1e+35)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4e+198], x, If[LessEqual[x, -3.8e+24], N[(t * b), $MachinePrecision], If[LessEqual[x, -3.85e-236], z, If[LessEqual[x, 4.7e-230], a, If[LessEqual[x, 1e+35], z, x]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.00000000000000007e198 or 9.9999999999999997e34 < x

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 36.7%

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

   if -4.00000000000000007e198 < x < -3.80000000000000015e24

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 77.3%

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

   3. Taylor expanded in t around inf 33.3%

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

   if -3.80000000000000015e24 < x < -3.85e-236 or 4.7e-230 < x < 9.9999999999999997e34

   1. Initial program 96.3%

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

      1. +-commutative 96.3%

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

      2. fma-def 98.2%

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

      3. associate--l+ 98.2%

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

      4. sub-neg 98.2%

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

      5. metadata-eval 98.2%

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

      6. sub-neg 98.2%

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

      7. associate-+l- 98.2%

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

      8. fma-neg 98.2%

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

      9. sub-neg 98.2%

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

      10. metadata-eval 98.2%

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

      11. remove-double-neg 98.2%

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

      12. sub-neg 98.2%

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

      13. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around 0 86.3%

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

      1. +-commutative 86.3%

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

      2. sub-neg 86.3%

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

      3. metadata-eval 86.3%

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

      4. mul-1-neg 86.3%

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

      5. unsub-neg 86.3%

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

      6. *-commutative 86.3%

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

      7. distribute-lft-in 86.3%

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

      8. *-commutative 86.3%

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

      9. neg-mul-1 86.3%

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

      10. unsub-neg 86.3%

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

      11. *-commutative 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in z around inf 22.5%

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

   if -3.85e-236 < x < 4.7e-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 4 regimes into one program.

4. Final simplification 28.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+198}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq -3.85 \cdot 10^{-236}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-230}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 10^{+35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 25.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+51}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-95}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-207}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.32e+51)
   (* y b)
   (if (<= y -9.6e-95)
     (* t b)
     (if (<= y 1.22e-207) z (if (<= y 2.5e+25) a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.32e+51) {
		tmp = y * b;
	} else if (y <= -9.6e-95) {
		tmp = t * b;
	} else if (y <= 1.22e-207) {
		tmp = z;
	} else if (y <= 2.5e+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 <= (-1.32d+51)) then
        tmp = y * b
    else if (y <= (-9.6d-95)) then
        tmp = t * b
    else if (y <= 1.22d-207) then
        tmp = z
    else if (y <= 2.5d+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 <= -1.32e+51) {
		tmp = y * b;
	} else if (y <= -9.6e-95) {
		tmp = t * b;
	} else if (y <= 1.22e-207) {
		tmp = z;
	} else if (y <= 2.5e+25) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.32e+51:
		tmp = y * b
	elif y <= -9.6e-95:
		tmp = t * b
	elif y <= 1.22e-207:
		tmp = z
	elif y <= 2.5e+25:
		tmp = a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.32e+51)
		tmp = Float64(y * b);
	elseif (y <= -9.6e-95)
		tmp = Float64(t * b);
	elseif (y <= 1.22e-207)
		tmp = z;
	elseif (y <= 2.5e+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 <= -1.32e+51)
		tmp = y * b;
	elseif (y <= -9.6e-95)
		tmp = t * b;
	elseif (y <= 1.22e-207)
		tmp = z;
	elseif (y <= 2.5e+25)
		tmp = a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.32e+51], N[(y * b), $MachinePrecision], If[LessEqual[y, -9.6e-95], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.22e-207], z, If[LessEqual[y, 2.5e+25], a, N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.32e51 or 2.50000000000000012e25 < 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 y around inf 67.8%

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

   3. Taylor expanded in b around inf 39.8%

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

   if -1.32e51 < y < -9.6e-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 a around 0 69.6%

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

   3. Taylor expanded in t around inf 29.2%

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

   if -9.6e-95 < y < 1.22e-207

   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. Step-by-step derivation

      1. +-commutative 98.5%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. mul-1-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-lft-in 100.0%

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

      8. *-commutative 100.0%

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

      9. neg-mul-1 100.0%

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

      10. unsub-neg 100.0%

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

      11. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around inf 35.6%

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

   if 1.22e-207 < y < 2.50000000000000012e25

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+51}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-95}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-207}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 22: 20.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-239}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-229}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.55e+129)
   x
   (if (<= x -1.1e-239) z (if (<= x 2.5e-229) a (if (<= x 1.12e+35) z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.55e+129) {
		tmp = x;
	} else if (x <= -1.1e-239) {
		tmp = z;
	} else if (x <= 2.5e-229) {
		tmp = a;
	} else if (x <= 1.12e+35) {
		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 <= (-1.55d+129)) then
        tmp = x
    else if (x <= (-1.1d-239)) then
        tmp = z
    else if (x <= 2.5d-229) then
        tmp = a
    else if (x <= 1.12d+35) 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 <= -1.55e+129) {
		tmp = x;
	} else if (x <= -1.1e-239) {
		tmp = z;
	} else if (x <= 2.5e-229) {
		tmp = a;
	} else if (x <= 1.12e+35) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.55e+129:
		tmp = x
	elif x <= -1.1e-239:
		tmp = z
	elif x <= 2.5e-229:
		tmp = a
	elif x <= 1.12e+35:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.55e+129)
		tmp = x;
	elseif (x <= -1.1e-239)
		tmp = z;
	elseif (x <= 2.5e-229)
		tmp = a;
	elseif (x <= 1.12e+35)
		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 <= -1.55e+129)
		tmp = x;
	elseif (x <= -1.1e-239)
		tmp = z;
	elseif (x <= 2.5e-229)
		tmp = a;
	elseif (x <= 1.12e+35)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.55e+129], x, If[LessEqual[x, -1.1e-239], z, If[LessEqual[x, 2.5e-229], a, If[LessEqual[x, 1.12e+35], z, x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e129 or 1.12000000000000003e35 < 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 -1.55e129 < x < -1.09999999999999991e-239 or 2.50000000000000008e-229 < x < 1.12000000000000003e35

   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. Step-by-step derivation

      1. +-commutative 96.9%

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

      2. fma-def 98.5%

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

      3. associate--l+ 98.5%

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

      4. sub-neg 98.5%

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

      5. metadata-eval 98.5%

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

      6. sub-neg 98.5%

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

      7. associate-+l- 98.5%

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

      8. fma-neg 98.5%

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

      9. sub-neg 98.5%

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

      10. metadata-eval 98.5%

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

      11. remove-double-neg 98.5%

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

      12. sub-neg 98.5%

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

      13. metadata-eval 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 85.5%

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

      1. +-commutative 85.5%

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

      2. sub-neg 85.5%

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

      3. metadata-eval 85.5%

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

      4. mul-1-neg 85.5%

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

      5. unsub-neg 85.5%

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

      6. *-commutative 85.5%

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

      7. distribute-lft-in 85.5%

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

      8. *-commutative 85.5%

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

      9. neg-mul-1 85.5%

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

      10. unsub-neg 85.5%

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

      11. *-commutative 85.5%

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

   6. Simplified 85.5%

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

   7. Taylor expanded in z around inf 20.7%

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

   if -1.09999999999999991e-239 < x < 2.50000000000000008e-229

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-239}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-229}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 33.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+87}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+87) (* t b) (if (<= b 2.05e+108) (+ x z) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+87) {
		tmp = t * b;
	} else if (b <= 2.05e+108) {
		tmp = x + z;
	} 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 <= (-3.5d+87)) then
        tmp = t * b
    else if (b <= 2.05d+108) then
        tmp = x + z
    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 <= -3.5e+87) {
		tmp = t * b;
	} else if (b <= 2.05e+108) {
		tmp = x + z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+87:
		tmp = t * b
	elif b <= 2.05e+108:
		tmp = x + z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+87)
		tmp = Float64(t * b);
	elseif (b <= 2.05e+108)
		tmp = Float64(x + z);
	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 <= -3.5e+87)
		tmp = t * b;
	elseif (b <= 2.05e+108)
		tmp = x + z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+87], N[(t * b), $MachinePrecision], If[LessEqual[b, 2.05e+108], N[(x + z), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.49999999999999986e87

   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 a around 0 83.5%

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

   3. Taylor expanded in t around inf 46.0%

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

   if -3.49999999999999986e87 < b < 2.05e108

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 62.9%

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

   3. Taylor expanded in b around 0 49.4%

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

   4. Taylor expanded in y around 0 33.8%

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

      1. sub-neg 33.8%

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

      2. neg-mul-1 33.8%

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

      3. remove-double-neg 33.8%

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

   6. Simplified 33.8%

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

   if 2.05e108 < b

   1. Initial program 92.5%

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

   2. Taylor expanded in y around inf 42.5%

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

   3. Taylor expanded in b around inf 37.3%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+87}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 24: 20.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+34}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.8e+66) x (if (<= x 1.45e+34) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.8e+66) {
		tmp = x;
	} else if (x <= 1.45e+34) {
		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 <= (-5.8d+66)) then
        tmp = x
    else if (x <= 1.45d+34) 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 <= -5.8e+66) {
		tmp = x;
	} else if (x <= 1.45e+34) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.8e+66:
		tmp = x
	elif x <= 1.45e+34:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.8e+66)
		tmp = x;
	elseif (x <= 1.45e+34)
		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 <= -5.8e+66)
		tmp = x;
	elseif (x <= 1.45e+34)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.8e+66], x, If[LessEqual[x, 1.45e+34], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.79999999999999972e66 or 1.4500000000000001e34 < 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 -5.79999999999999972e66 < x < 1.4500000000000001e34

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+34}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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)))