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

Percentage Accurate: 95.6% → 98.2%

Time: 18.0s

Alternatives: 23

Speedup: 0.5×

• 36.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - z \cdot \left(y + -1\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 61.3%

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

4. Final simplification 97.7%

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

Alternative 2: 97.9% 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 94.1%

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

   1. +-commutative 94.1%

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

   2. fma-define 96.5%

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

   3. associate--l+ 96.5%

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

   4. sub-neg 96.5%

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

   5. metadata-eval 96.5%

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

   6. sub-neg 96.5%

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

   7. associate-+l- 96.5%

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

   8. fma-neg 96.5%

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

   9. sub-neg 96.5%

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

   10. metadata-eval 96.5%

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

   11. remove-double-neg 96.5%

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

   12. sub-neg 96.5%

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

   13. metadata-eval 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 3: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := z \cdot \left(y + -1\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;t\_1 + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-105}:\\ \;\;\;\;\left(x + a\right) - t\_2\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+113}:\\ \;\;\;\;x - z \cdot \left(-1 + \left(y + \frac{t \cdot a}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))) (t_2 (* z (+ y -1.0))))
   (if (<= b -1.6e+18)
     (+ t_1 (* a (- 1.0 t)))
     (if (<= b -3.3e-105)
       (- (+ x a) t_2)
       (if (<= b 1.1e+113)
         (- x (* z (+ -1.0 (+ y (/ (* t a) z)))))
         (- t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = z * (y + -1.0);
	double tmp;
	if (b <= -1.6e+18) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= -3.3e-105) {
		tmp = (x + a) - t_2;
	} else if (b <= 1.1e+113) {
		tmp = x - (z * (-1.0 + (y + ((t * a) / z))));
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    t_2 = z * (y + (-1.0d0))
    if (b <= (-1.6d+18)) then
        tmp = t_1 + (a * (1.0d0 - t))
    else if (b <= (-3.3d-105)) then
        tmp = (x + a) - t_2
    else if (b <= 1.1d+113) then
        tmp = x - (z * ((-1.0d0) + (y + ((t * a) / z))))
    else
        tmp = t_1 - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = z * (y + -1.0);
	double tmp;
	if (b <= -1.6e+18) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= -3.3e-105) {
		tmp = (x + a) - t_2;
	} else if (b <= 1.1e+113) {
		tmp = x - (z * (-1.0 + (y + ((t * a) / z))));
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	t_2 = z * (y + -1.0)
	tmp = 0
	if b <= -1.6e+18:
		tmp = t_1 + (a * (1.0 - t))
	elif b <= -3.3e-105:
		tmp = (x + a) - t_2
	elif b <= 1.1e+113:
		tmp = x - (z * (-1.0 + (y + ((t * a) / z))))
	else:
		tmp = t_1 - t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_2 = Float64(z * Float64(y + -1.0))
	tmp = 0.0
	if (b <= -1.6e+18)
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	elseif (b <= -3.3e-105)
		tmp = Float64(Float64(x + a) - t_2);
	elseif (b <= 1.1e+113)
		tmp = Float64(x - Float64(z * Float64(-1.0 + Float64(y + Float64(Float64(t * a) / z)))));
	else
		tmp = Float64(t_1 - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	t_2 = z * (y + -1.0);
	tmp = 0.0;
	if (b <= -1.6e+18)
		tmp = t_1 + (a * (1.0 - t));
	elseif (b <= -3.3e-105)
		tmp = (x + a) - t_2;
	elseif (b <= 1.1e+113)
		tmp = x - (z * (-1.0 + (y + ((t * a) / z))));
	else
		tmp = t_1 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.6e+18], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.3e-105], N[(N[(x + a), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[b, 1.1e+113], N[(x - N[(z * N[(-1.0 + N[(y + N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.6e18

   1. Initial program 87.9%

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

   3. Taylor expanded in z around -inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. neg-mul-1 76.3%

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

      3. sub-neg 76.3%

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

      4. mul-1-neg 76.3%

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

      5. sub-neg 76.3%

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

      6. metadata-eval 76.3%

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

      7. sub-neg 76.3%

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

      8. metadata-eval 76.3%

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

      9. mul-1-neg 76.3%

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

      10. remove-double-neg 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in a around -inf 81.6%

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

      1. sub-neg 81.6%

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

      2. metadata-eval 81.6%

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

      3. neg-mul-1 81.6%

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

      4. distribute-rgt-neg-in 81.6%

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

      5. +-commutative 81.6%

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

      6. distribute-neg-in 81.6%

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

      7. metadata-eval 81.6%

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

      8. sub-neg 81.6%

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

   8. Simplified 81.6%

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

   if -1.6e18 < b < -3.2999999999999999e-105

   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. Add Preprocessing

   3. Taylor expanded in b around 0 89.9%

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

   4. Taylor expanded in t around 0 83.7%

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

      1. associate--r+ 83.7%

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

      2. sub-neg 83.7%

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

      3. neg-mul-1 83.7%

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

      4. remove-double-neg 83.7%

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

      5. sub-neg 83.7%

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

      6. metadata-eval 83.7%

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

      7. +-commutative 83.7%

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

   6. Simplified 83.7%

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

   if -3.2999999999999999e-105 < b < 1.10000000000000005e113

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0 90.0%

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

   4. Taylor expanded in z around inf 81.0%

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

   5. Taylor expanded in t around inf 74.9%

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

   if 1.10000000000000005e113 < b

   1. Initial program 86.4%

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

   3. Taylor expanded in z around -inf 73.5%

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

      1. associate-*r* 73.5%

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

      2. neg-mul-1 73.5%

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

      3. sub-neg 73.5%

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

      4. mul-1-neg 73.5%

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

      5. sub-neg 73.5%

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

      6. metadata-eval 73.5%

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

      7. sub-neg 73.5%

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

      8. metadata-eval 73.5%

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

      9. mul-1-neg 73.5%

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

      10. remove-double-neg 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in z around inf 80.1%

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

      1. sub-neg 80.1%

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

      2. metadata-eval 80.1%

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

      3. +-commutative 80.1%

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

      4. neg-mul-1 80.1%

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

      5. distribute-rgt-neg-in 80.1%

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

      6. distribute-neg-in 80.1%

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

      7. metadata-eval 80.1%

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

      8. sub-neg 80.1%

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

   8. Simplified 80.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-105}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+113}:\\ \;\;\;\;x - z \cdot \left(-1 + \left(y + \frac{t \cdot a}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - z \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-88}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -1.15e+165)
     t_2
     (if (<= t -8.2e-25)
       t_1
       (if (<= t 8e-88) (+ x a) (if (<= t 5.9e+50) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.15e+165) {
		tmp = t_2;
	} else if (t <= -8.2e-25) {
		tmp = t_1;
	} else if (t <= 8e-88) {
		tmp = x + a;
	} else if (t <= 5.9e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-1.15d+165)) then
        tmp = t_2
    else if (t <= (-8.2d-25)) then
        tmp = t_1
    else if (t <= 8d-88) then
        tmp = x + a
    else if (t <= 5.9d+50) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.15e+165) {
		tmp = t_2;
	} else if (t <= -8.2e-25) {
		tmp = t_1;
	} else if (t <= 8e-88) {
		tmp = x + a;
	} else if (t <= 5.9e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1.15e+165:
		tmp = t_2
	elif t <= -8.2e-25:
		tmp = t_1
	elif t <= 8e-88:
		tmp = x + a
	elif t <= 5.9e+50:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.15e+165)
		tmp = t_2;
	elseif (t <= -8.2e-25)
		tmp = t_1;
	elseif (t <= 8e-88)
		tmp = Float64(x + a);
	elseif (t <= 5.9e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.15e+165)
		tmp = t_2;
	elseif (t <= -8.2e-25)
		tmp = t_1;
	elseif (t <= 8e-88)
		tmp = x + a;
	elseif (t <= 5.9e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+165], t$95$2, If[LessEqual[t, -8.2e-25], t$95$1, If[LessEqual[t, 8e-88], N[(x + a), $MachinePrecision], If[LessEqual[t, 5.9e+50], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15000000000000008e165 or 5.8999999999999998e50 < t

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 68.5%

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

   if -1.15000000000000008e165 < t < -8.19999999999999974e-25 or 7.99999999999999947e-88 < t < 5.8999999999999998e50

   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. Add Preprocessing

   3. Taylor expanded in y around inf 51.6%

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

   if -8.19999999999999974e-25 < t < 7.99999999999999947e-88

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0 66.4%

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

   4. Taylor expanded in a around inf 48.9%

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

   5. Taylor expanded in t around 0 48.9%

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

      1. cancel-sign-sub-inv 48.9%

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

      2. metadata-eval 48.9%

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

      3. *-lft-identity 48.9%

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

   7. Simplified 48.9%

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

Alternative 5: 39.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+94}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))))
   (if (<= b -1.25e+245)
     t_1
     (if (<= b -1.15e+50)
       (* b (- y 2.0))
       (if (<= b 1.1e+20) (* a (- 1.0 t)) (if (<= b 2.2e+94) (+ x a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -1.25e+245) {
		tmp = t_1;
	} else if (b <= -1.15e+50) {
		tmp = b * (y - 2.0);
	} else if (b <= 1.1e+20) {
		tmp = a * (1.0 - t);
	} else if (b <= 2.2e+94) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    if (b <= (-1.25d+245)) then
        tmp = t_1
    else if (b <= (-1.15d+50)) then
        tmp = b * (y - 2.0d0)
    else if (b <= 1.1d+20) then
        tmp = a * (1.0d0 - t)
    else if (b <= 2.2d+94) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -1.25e+245) {
		tmp = t_1;
	} else if (b <= -1.15e+50) {
		tmp = b * (y - 2.0);
	} else if (b <= 1.1e+20) {
		tmp = a * (1.0 - t);
	} else if (b <= 2.2e+94) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	tmp = 0
	if b <= -1.25e+245:
		tmp = t_1
	elif b <= -1.15e+50:
		tmp = b * (y - 2.0)
	elif b <= 1.1e+20:
		tmp = a * (1.0 - t)
	elif b <= 2.2e+94:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -1.25e+245)
		tmp = t_1;
	elseif (b <= -1.15e+50)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= 1.1e+20)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 2.2e+94)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -1.25e+245)
		tmp = t_1;
	elseif (b <= -1.15e+50)
		tmp = b * (y - 2.0);
	elseif (b <= 1.1e+20)
		tmp = a * (1.0 - t);
	elseif (b <= 2.2e+94)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+245], t$95$1, If[LessEqual[b, -1.15e+50], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+20], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e+94], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.25000000000000009e245 or 2.20000000000000012e94 < b

   1. Initial program 83.6%

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

   3. Taylor expanded in b around inf 74.4%

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

   4. Taylor expanded in y around 0 59.4%

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

   if -1.25000000000000009e245 < b < -1.14999999999999998e50

   1. Initial program 89.5%

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

   3. Taylor expanded in t around 0 70.8%

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

   4. Taylor expanded in b around inf 61.0%

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

   if -1.14999999999999998e50 < b < 1.1e20

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf 40.5%

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

   if 1.1e20 < b < 2.20000000000000012e94

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 66.5%

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

   4. Taylor expanded in a around inf 56.6%

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

   5. Taylor expanded in t around 0 48.1%

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

      1. cancel-sign-sub-inv 48.1%

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

      2. metadata-eval 48.1%

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

      3. *-lft-identity 48.1%

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

   7. Simplified 48.1%

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

Alternative 6: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -31000000 \lor \neg \left(b \leq 68000000000\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -31000000.0) (not (<= b 68000000000.0)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* a (- 1.0 t)))
   (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -31000000.0) || !(b <= 68000000000.0)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-31000000.0d0)) .or. (.not. (b <= 68000000000.0d0))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (a * (1.0d0 - t))
    else
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -31000000.0) || !(b <= 68000000000.0)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -31000000.0) or not (b <= 68000000000.0):
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t))
	else:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -31000000.0) || !(b <= 68000000000.0))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -31000000.0) || ~((b <= 68000000000.0)))
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	else
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -31000000.0], N[Not[LessEqual[b, 68000000000.0]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.1e7 or 6.8e10 < b

   1. Initial program 88.6%

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

   3. Taylor expanded in z around 0 81.8%

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

   if -3.1e7 < b < 6.8e10

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0 93.4%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -31000000 \lor \neg \left(b \leq 68000000000\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -160:\\ \;\;\;\;t\_1 + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-77}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -160.0)
     (+ t_1 (* a (- 1.0 t)))
     (if (<= b 2.9e-77)
       (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))
       (+ t_1 (* z (- 1.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -160.0) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 2.9e-77) {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	} else {
		tmp = t_1 + (z * (1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-160.0d0)) then
        tmp = t_1 + (a * (1.0d0 - t))
    else if (b <= 2.9d-77) then
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    else
        tmp = t_1 + (z * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -160.0) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 2.9e-77) {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	} else {
		tmp = t_1 + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -160.0:
		tmp = t_1 + (a * (1.0 - t))
	elif b <= 2.9e-77:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	else:
		tmp = t_1 + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -160.0)
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	elseif (b <= 2.9e-77)
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -160.0)
		tmp = t_1 + (a * (1.0 - t));
	elseif (b <= 2.9e-77)
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	else
		tmp = t_1 + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -160.0], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e-77], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -160

   1. Initial program 88.7%

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

   3. Taylor expanded in z around 0 85.9%

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

   if -160 < b < 2.8999999999999999e-77

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0 97.4%

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

   if 2.8999999999999999e-77 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in a around 0 81.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -160:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-77}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-87}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-77}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -2.05e+18)
     t_1
     (if (<= b -5.5e-87)
       (+ x (+ z a))
       (if (<= b 4e-77) (+ x (* a (- 1.0 t))) t_1)))))

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 <= -2.05e+18) {
		tmp = t_1;
	} else if (b <= -5.5e-87) {
		tmp = x + (z + a);
	} else if (b <= 4e-77) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-2.05d+18)) then
        tmp = t_1
    else if (b <= (-5.5d-87)) then
        tmp = x + (z + a)
    else if (b <= 4d-77) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -2.05e+18) {
		tmp = t_1;
	} else if (b <= -5.5e-87) {
		tmp = x + (z + a);
	} else if (b <= 4e-77) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -2.05e+18:
		tmp = t_1
	elif b <= -5.5e-87:
		tmp = x + (z + a)
	elif b <= 4e-77:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	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 <= -2.05e+18)
		tmp = t_1;
	elseif (b <= -5.5e-87)
		tmp = Float64(x + Float64(z + a));
	elseif (b <= 4e-77)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -2.05e+18)
		tmp = t_1;
	elseif (b <= -5.5e-87)
		tmp = x + (z + a);
	elseif (b <= 4e-77)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+18], t$95$1, If[LessEqual[b, -5.5e-87], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e-77], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.05e18 or 3.9999999999999997e-77 < b

   1. Initial program 89.8%

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

   3. Taylor expanded in z around -inf 76.5%

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

      1. associate-*r* 76.5%

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

      2. neg-mul-1 76.5%

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

      3. sub-neg 76.5%

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

      4. mul-1-neg 76.5%

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

      5. sub-neg 76.5%

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

      6. metadata-eval 76.5%

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

      7. sub-neg 76.5%

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

      8. metadata-eval 76.5%

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

      9. mul-1-neg 76.5%

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

      10. remove-double-neg 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in x around inf 70.9%

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

   if -2.05e18 < b < -5.5000000000000004e-87

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0 88.6%

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

   4. Taylor expanded in y around 0 76.5%

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

      1. associate--l+ 76.5%

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

      2. *-commutative 76.5%

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

      3. distribute-lft-in 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in b around 0 76.7%

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

      1. cancel-sign-sub-inv 76.7%

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

      2. metadata-eval 76.7%

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

      3. +-commutative 76.7%

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

      4. *-lft-identity 76.7%

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

      5. +-commutative 76.7%

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

   9. Simplified 76.7%

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

   if -5.5000000000000004e-87 < b < 3.9999999999999997e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 99.0%

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

   4. Taylor expanded in a around inf 65.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+18}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-87}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-77}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 26.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -380:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-108}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+88}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -380.0)
   (* y b)
   (if (<= y -4.6e-108)
     z
     (if (<= y 1.9e-114) x (if (<= y 1.15e+88) (* t b) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -380.0) {
		tmp = y * b;
	} else if (y <= -4.6e-108) {
		tmp = z;
	} else if (y <= 1.9e-114) {
		tmp = x;
	} else if (y <= 1.15e+88) {
		tmp = t * b;
	} 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 <= (-380.0d0)) then
        tmp = y * b
    else if (y <= (-4.6d-108)) then
        tmp = z
    else if (y <= 1.9d-114) then
        tmp = x
    else if (y <= 1.15d+88) then
        tmp = t * b
    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 <= -380.0) {
		tmp = y * b;
	} else if (y <= -4.6e-108) {
		tmp = z;
	} else if (y <= 1.9e-114) {
		tmp = x;
	} else if (y <= 1.15e+88) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -380.0:
		tmp = y * b
	elif y <= -4.6e-108:
		tmp = z
	elif y <= 1.9e-114:
		tmp = x
	elif y <= 1.15e+88:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -380.0)
		tmp = Float64(y * b);
	elseif (y <= -4.6e-108)
		tmp = z;
	elseif (y <= 1.9e-114)
		tmp = x;
	elseif (y <= 1.15e+88)
		tmp = Float64(t * b);
	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 <= -380.0)
		tmp = y * b;
	elseif (y <= -4.6e-108)
		tmp = z;
	elseif (y <= 1.9e-114)
		tmp = x;
	elseif (y <= 1.15e+88)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -380.0], N[(y * b), $MachinePrecision], If[LessEqual[y, -4.6e-108], z, If[LessEqual[y, 1.9e-114], x, If[LessEqual[y, 1.15e+88], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -380 or 1.1500000000000001e88 < y

   1. Initial program 90.8%

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

   3. Taylor expanded in b around inf 42.7%

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

   4. Taylor expanded in y around inf 36.0%

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

      1. *-commutative 36.0%

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

   6. Simplified 36.0%

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

   if -380 < y < -4.59999999999999992e-108

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 41.5%

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

   4. Taylor expanded in y around 0 40.5%

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

   if -4.59999999999999992e-108 < y < 1.8999999999999999e-114

   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. Add Preprocessing

   3. Taylor expanded in x around inf 30.3%

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

   if 1.8999999999999999e-114 < y < 1.1500000000000001e88

   1. Initial program 93.5%

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

   3. Taylor expanded in t around inf 40.5%

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

   4. Taylor expanded in b around inf 33.9%

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

      1. *-commutative 33.9%

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

   6. Simplified 33.9%

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

Alternative 10: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+18}:\\ \;\;\;\;t\_1 + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+170}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -9.2e+18)
     (+ t_1 (* a (- 1.0 t)))
     (if (<= b 3.3e+170)
       (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))
       (+ x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9.2e+18) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 3.3e+170) {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-9.2d+18)) then
        tmp = t_1 + (a * (1.0d0 - t))
    else if (b <= 3.3d+170) then
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9.2e+18) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 3.3e+170) {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -9.2e+18:
		tmp = t_1 + (a * (1.0 - t))
	elif b <= 3.3e+170:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -9.2e+18)
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	elseif (b <= 3.3e+170)
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -9.2e+18)
		tmp = t_1 + (a * (1.0 - t));
	elseif (b <= 3.3e+170)
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+18], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e+170], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.2e18

   1. Initial program 87.9%

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

   3. Taylor expanded in z around -inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. neg-mul-1 76.3%

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

      3. sub-neg 76.3%

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

      4. mul-1-neg 76.3%

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

      5. sub-neg 76.3%

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

      6. metadata-eval 76.3%

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

      7. sub-neg 76.3%

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

      8. metadata-eval 76.3%

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

      9. mul-1-neg 76.3%

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

      10. remove-double-neg 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in a around -inf 81.6%

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

      1. sub-neg 81.6%

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

      2. metadata-eval 81.6%

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

      3. neg-mul-1 81.6%

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

      4. distribute-rgt-neg-in 81.6%

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

      5. +-commutative 81.6%

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

      6. distribute-neg-in 81.6%

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

      7. metadata-eval 81.6%

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

      8. sub-neg 81.6%

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

   8. Simplified 81.6%

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

   if -9.2e18 < b < 3.30000000000000023e170

   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. Add Preprocessing

   3. Taylor expanded in b around 0 88.3%

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

   if 3.30000000000000023e170 < b

   1. Initial program 87.9%

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

   3. Taylor expanded in z around -inf 73.3%

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

      1. associate-*r* 73.3%

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

      2. neg-mul-1 73.3%

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

      3. sub-neg 73.3%

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

      4. mul-1-neg 73.3%

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

      5. sub-neg 73.3%

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

      6. metadata-eval 73.3%

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

      7. sub-neg 73.3%

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

      8. metadata-eval 73.3%

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

      9. mul-1-neg 73.3%

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

      10. remove-double-neg 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in x around inf 85.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+170}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := z \cdot \left(y + -1\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;t\_1 + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-77}:\\ \;\;\;\;\left(x + a\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))) (t_2 (* z (+ y -1.0))))
   (if (<= b -5.2e+16)
     (+ t_1 (* a (- 1.0 t)))
     (if (<= b 3.4e-77) (- (+ x a) t_2) (- t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = z * (y + -1.0);
	double tmp;
	if (b <= -5.2e+16) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 3.4e-77) {
		tmp = (x + a) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    t_2 = z * (y + (-1.0d0))
    if (b <= (-5.2d+16)) then
        tmp = t_1 + (a * (1.0d0 - t))
    else if (b <= 3.4d-77) then
        tmp = (x + a) - t_2
    else
        tmp = t_1 - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = z * (y + -1.0);
	double tmp;
	if (b <= -5.2e+16) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 3.4e-77) {
		tmp = (x + a) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	t_2 = z * (y + -1.0)
	tmp = 0
	if b <= -5.2e+16:
		tmp = t_1 + (a * (1.0 - t))
	elif b <= 3.4e-77:
		tmp = (x + a) - t_2
	else:
		tmp = t_1 - t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_2 = Float64(z * Float64(y + -1.0))
	tmp = 0.0
	if (b <= -5.2e+16)
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	elseif (b <= 3.4e-77)
		tmp = Float64(Float64(x + a) - t_2);
	else
		tmp = Float64(t_1 - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	t_2 = z * (y + -1.0);
	tmp = 0.0;
	if (b <= -5.2e+16)
		tmp = t_1 + (a * (1.0 - t));
	elseif (b <= 3.4e-77)
		tmp = (x + a) - t_2;
	else
		tmp = t_1 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+16], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-77], N[(N[(x + a), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$1 - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.2e16

   1. Initial program 87.9%

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

   3. Taylor expanded in z around -inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. neg-mul-1 76.3%

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

      3. sub-neg 76.3%

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

      4. mul-1-neg 76.3%

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

      5. sub-neg 76.3%

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

      6. metadata-eval 76.3%

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

      7. sub-neg 76.3%

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

      8. metadata-eval 76.3%

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

      9. mul-1-neg 76.3%

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

      10. remove-double-neg 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in a around -inf 81.6%

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

      1. sub-neg 81.6%

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

      2. metadata-eval 81.6%

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

      3. neg-mul-1 81.6%

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

      4. distribute-rgt-neg-in 81.6%

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

      5. +-commutative 81.6%

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

      6. distribute-neg-in 81.6%

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

      7. metadata-eval 81.6%

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

      8. sub-neg 81.6%

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

   8. Simplified 81.6%

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

   if -5.2e16 < b < 3.39999999999999983e-77

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0 96.7%

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

   4. Taylor expanded in t around 0 76.4%

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

      1. associate--r+ 76.4%

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

      2. sub-neg 76.4%

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

      3. neg-mul-1 76.4%

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

      4. remove-double-neg 76.4%

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

      5. sub-neg 76.4%

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

      6. metadata-eval 76.4%

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

      7. +-commutative 76.4%

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

   6. Simplified 76.4%

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

   if 3.39999999999999983e-77 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in z around -inf 76.7%

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

      1. associate-*r* 76.7%

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

      2. neg-mul-1 76.7%

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

      3. sub-neg 76.7%

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

      4. mul-1-neg 76.7%

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

      5. sub-neg 76.7%

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

      6. metadata-eval 76.7%

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

      7. sub-neg 76.7%

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

      8. metadata-eval 76.7%

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

      9. mul-1-neg 76.7%

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

      10. remove-double-neg 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in z around inf 71.8%

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

      1. sub-neg 71.8%

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

      2. metadata-eval 71.8%

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

      3. +-commutative 71.8%

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

      4. neg-mul-1 71.8%

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

      5. distribute-rgt-neg-in 71.8%

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

      6. distribute-neg-in 71.8%

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

      7. metadata-eval 71.8%

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

      8. sub-neg 71.8%

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

   8. Simplified 71.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-77}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - z \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-89}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+92}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -2.8e+49)
     t_1
     (if (<= b -1.05e-89)
       (+ x (+ z a))
       (if (<= b 2.2e+92) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.8e+49) {
		tmp = t_1;
	} else if (b <= -1.05e-89) {
		tmp = x + (z + a);
	} else if (b <= 2.2e+92) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-2.8d+49)) then
        tmp = t_1
    else if (b <= (-1.05d-89)) then
        tmp = x + (z + a)
    else if (b <= 2.2d+92) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.8e+49) {
		tmp = t_1;
	} else if (b <= -1.05e-89) {
		tmp = x + (z + a);
	} else if (b <= 2.2e+92) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2.8e+49:
		tmp = t_1
	elif b <= -1.05e-89:
		tmp = x + (z + a)
	elif b <= 2.2e+92:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2.8e+49)
		tmp = t_1;
	elseif (b <= -1.05e-89)
		tmp = Float64(x + Float64(z + a));
	elseif (b <= 2.2e+92)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.8e+49)
		tmp = t_1;
	elseif (b <= -1.05e-89)
		tmp = x + (z + a);
	elseif (b <= 2.2e+92)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+49], t$95$1, If[LessEqual[b, -1.05e-89], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e+92], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.7999999999999998e49 or 2.19999999999999992e92 < b

   1. Initial program 85.9%

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

   3. Taylor expanded in b around inf 74.5%

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

   if -2.7999999999999998e49 < b < -1.05e-89

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0 87.2%

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

   4. Taylor expanded in y around 0 70.6%

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

      1. associate--l+ 70.6%

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

      2. *-commutative 70.6%

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

      3. distribute-lft-in 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in b around 0 70.7%

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

      1. cancel-sign-sub-inv 70.7%

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

      2. metadata-eval 70.7%

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

      3. +-commutative 70.7%

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

      4. *-lft-identity 70.7%

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

      5. +-commutative 70.7%

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

   9. Simplified 70.7%

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

   if -1.05e-89 < b < 2.19999999999999992e92

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 90.2%

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

   4. Taylor expanded in a around inf 57.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-89}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+92}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-110}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 3700000000:\\ \;\;\;\;z + b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -5.8e+85)
     t_1
     (if (<= y 6.5e-110)
       (+ x (+ z a))
       (if (<= y 3700000000.0) (+ z (* b (- t 2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -5.8e+85) {
		tmp = t_1;
	} else if (y <= 6.5e-110) {
		tmp = x + (z + a);
	} else if (y <= 3700000000.0) {
		tmp = z + (b * (t - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-5.8d+85)) then
        tmp = t_1
    else if (y <= 6.5d-110) then
        tmp = x + (z + a)
    else if (y <= 3700000000.0d0) then
        tmp = z + (b * (t - 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -5.8e+85) {
		tmp = t_1;
	} else if (y <= 6.5e-110) {
		tmp = x + (z + a);
	} else if (y <= 3700000000.0) {
		tmp = z + (b * (t - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -5.8e+85:
		tmp = t_1
	elif y <= 6.5e-110:
		tmp = x + (z + a)
	elif y <= 3700000000.0:
		tmp = z + (b * (t - 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -5.8e+85)
		tmp = t_1;
	elseif (y <= 6.5e-110)
		tmp = Float64(x + Float64(z + a));
	elseif (y <= 3700000000.0)
		tmp = Float64(z + Float64(b * Float64(t - 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -5.8e+85)
		tmp = t_1;
	elseif (y <= 6.5e-110)
		tmp = x + (z + a);
	elseif (y <= 3700000000.0)
		tmp = z + (b * (t - 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+85], t$95$1, If[LessEqual[y, 6.5e-110], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3700000000.0], N[(z + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999995e85 or 3.7e9 < y

   1. Initial program 89.4%

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

   3. Taylor expanded in y around inf 65.4%

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

   if -5.79999999999999995e85 < y < 6.4999999999999996e-110

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 71.7%

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

   4. Taylor expanded in y around 0 68.4%

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

      1. associate--l+ 68.4%

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

      2. *-commutative 68.4%

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

      3. distribute-lft-in 68.4%

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

   6. Simplified 68.4%

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

   7. Taylor expanded in b around 0 59.0%

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

      1. cancel-sign-sub-inv 59.0%

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

      2. metadata-eval 59.0%

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

      3. +-commutative 59.0%

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

      4. *-lft-identity 59.0%

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

      5. +-commutative 59.0%

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

   9. Simplified 59.0%

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

   if 6.4999999999999996e-110 < y < 3.7e9

   1. Initial program 95.7%

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

   3. Taylor expanded in z around -inf 91.8%

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

      1. associate-*r* 91.8%

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

      2. neg-mul-1 91.8%

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

      3. sub-neg 91.8%

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

      4. mul-1-neg 91.8%

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

      5. sub-neg 91.8%

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

      6. metadata-eval 91.8%

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

      7. sub-neg 91.8%

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

      8. metadata-eval 91.8%

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

      9. mul-1-neg 91.8%

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

      10. remove-double-neg 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in z around inf 69.0%

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

      1. sub-neg 69.0%

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

      2. metadata-eval 69.0%

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

      3. +-commutative 69.0%

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

      4. neg-mul-1 69.0%

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

      5. distribute-rgt-neg-in 69.0%

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

      6. distribute-neg-in 69.0%

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

      7. metadata-eval 69.0%

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

      8. sub-neg 69.0%

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

   8. Simplified 69.0%

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

   9. Taylor expanded in y around 0 69.0%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-110}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 3700000000:\\ \;\;\;\;z + b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+49} \lor \neg \left(b \leq 14000000000\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.3e+49) (not (<= b 14000000000.0)))
   (+ x (* b (- (+ y t) 2.0)))
   (- (+ x a) (* z (+ y -1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e+49) || !(b <= 14000000000.0)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + a) - (z * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.3d+49)) .or. (.not. (b <= 14000000000.0d0))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = (x + a) - (z * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e+49) || !(b <= 14000000000.0)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + a) - (z * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.3e+49) or not (b <= 14000000000.0):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = (x + a) - (z * (y + -1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.3e+49) || !(b <= 14000000000.0))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(Float64(x + a) - Float64(z * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.3e+49) || ~((b <= 14000000000.0)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = (x + a) - (z * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.3e+49], N[Not[LessEqual[b, 14000000000.0]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + a), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.29999999999999994e49 or 1.4e10 < b

   1. Initial program 87.7%

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

   3. Taylor expanded in z around -inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

      3. sub-neg 72.6%

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

      4. mul-1-neg 72.6%

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

      5. sub-neg 72.6%

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

      6. metadata-eval 72.6%

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

      7. sub-neg 72.6%

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

      8. metadata-eval 72.6%

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

      9. mul-1-neg 72.6%

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

      10. remove-double-neg 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in x around inf 78.3%

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

   if -1.29999999999999994e49 < b < 1.4e10

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 91.7%

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

   4. Taylor expanded in t around 0 72.7%

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

      1. associate--r+ 72.7%

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

      2. sub-neg 72.7%

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

      3. neg-mul-1 72.7%

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

      4. remove-double-neg 72.7%

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

      5. sub-neg 72.7%

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

      6. metadata-eval 72.7%

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

      7. +-commutative 72.7%

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

   6. Simplified 72.7%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+49} \lor \neg \left(b \leq 14000000000\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+16}:\\ \;\;\;\;t\_1 + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 106000000000:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -4e+16)
     (+ t_1 (* a (- 1.0 t)))
     (if (<= b 106000000000.0) (- (+ x a) (* z (+ y -1.0))) (+ x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4e+16) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 106000000000.0) {
		tmp = (x + a) - (z * (y + -1.0));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-4d+16)) then
        tmp = t_1 + (a * (1.0d0 - t))
    else if (b <= 106000000000.0d0) then
        tmp = (x + a) - (z * (y + (-1.0d0)))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4e+16) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 106000000000.0) {
		tmp = (x + a) - (z * (y + -1.0));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -4e+16:
		tmp = t_1 + (a * (1.0 - t))
	elif b <= 106000000000.0:
		tmp = (x + a) - (z * (y + -1.0))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -4e+16)
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	elseif (b <= 106000000000.0)
		tmp = Float64(Float64(x + a) - Float64(z * Float64(y + -1.0)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -4e+16)
		tmp = t_1 + (a * (1.0 - t));
	elseif (b <= 106000000000.0)
		tmp = (x + a) - (z * (y + -1.0));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+16], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 106000000000.0], N[(N[(x + a), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4e16

   1. Initial program 87.9%

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

   3. Taylor expanded in z around -inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. neg-mul-1 76.3%

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

      3. sub-neg 76.3%

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

      4. mul-1-neg 76.3%

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

      5. sub-neg 76.3%

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

      6. metadata-eval 76.3%

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

      7. sub-neg 76.3%

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

      8. metadata-eval 76.3%

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

      9. mul-1-neg 76.3%

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

      10. remove-double-neg 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in a around -inf 81.6%

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

      1. sub-neg 81.6%

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

      2. metadata-eval 81.6%

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

      3. neg-mul-1 81.6%

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

      4. distribute-rgt-neg-in 81.6%

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

      5. +-commutative 81.6%

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

      6. distribute-neg-in 81.6%

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

      7. metadata-eval 81.6%

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

      8. sub-neg 81.6%

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

   8. Simplified 81.6%

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

   if -4e16 < b < 1.06e11

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0 92.9%

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

   4. Taylor expanded in t around 0 73.2%

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

      1. associate--r+ 73.2%

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

      2. sub-neg 73.2%

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

      3. neg-mul-1 73.2%

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

      4. remove-double-neg 73.2%

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

      5. sub-neg 73.2%

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

      6. metadata-eval 73.2%

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

      7. +-commutative 73.2%

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

   6. Simplified 73.2%

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

   if 1.06e11 < b

   1. Initial program 88.5%

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

   3. Taylor expanded in z around -inf 71.4%

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

      1. associate-*r* 71.4%

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

      2. neg-mul-1 71.4%

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

      3. sub-neg 71.4%

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

      4. mul-1-neg 71.4%

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

      5. sub-neg 71.4%

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

      6. metadata-eval 71.4%

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

      7. sub-neg 71.4%

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

      8. metadata-eval 71.4%

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

      9. mul-1-neg 71.4%

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

      10. remove-double-neg 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in x around inf 73.7%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 106000000000:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+258}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 6400000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.8e+258)
   (* t b)
   (if (<= t -1.95e+24)
     (* t (- a))
     (if (<= t 6400000000000.0) (+ x a) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+258) {
		tmp = t * b;
	} else if (t <= -1.95e+24) {
		tmp = t * -a;
	} else if (t <= 6400000000000.0) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.8d+258)) then
        tmp = t * b
    else if (t <= (-1.95d+24)) then
        tmp = t * -a
    else if (t <= 6400000000000.0d0) then
        tmp = x + a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+258) {
		tmp = t * b;
	} else if (t <= -1.95e+24) {
		tmp = t * -a;
	} else if (t <= 6400000000000.0) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.8e+258:
		tmp = t * b
	elif t <= -1.95e+24:
		tmp = t * -a
	elif t <= 6400000000000.0:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.8e+258)
		tmp = Float64(t * b);
	elseif (t <= -1.95e+24)
		tmp = Float64(t * Float64(-a));
	elseif (t <= 6400000000000.0)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.8e+258)
		tmp = t * b;
	elseif (t <= -1.95e+24)
		tmp = t * -a;
	elseif (t <= 6400000000000.0)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.8e+258], N[(t * b), $MachinePrecision], If[LessEqual[t, -1.95e+24], N[(t * (-a)), $MachinePrecision], If[LessEqual[t, 6400000000000.0], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7999999999999999e258 or 6.4e12 < t

   1. Initial program 84.3%

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

   3. Taylor expanded in t around inf 66.5%

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

   4. Taylor expanded in b around inf 44.4%

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

      1. *-commutative 44.4%

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

   6. Simplified 44.4%

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

   if -4.7999999999999999e258 < t < -1.9499999999999999e24

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 54.3%

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

   4. Taylor expanded in b around 0 47.8%

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

      1. neg-mul-1 47.8%

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

   6. Simplified 47.8%

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

   if -1.9499999999999999e24 < t < 6.4e12

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 68.8%

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

   4. Taylor expanded in a around inf 45.7%

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

   5. Taylor expanded in t around 0 45.1%

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

      1. cancel-sign-sub-inv 45.1%

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

      2. metadata-eval 45.1%

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

      3. *-lft-identity 45.1%

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

   7. Simplified 45.1%

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

Alternative 17: 33.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+245}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+95}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+245)
   (* t b)
   (if (<= b -4.8e+49) (* y b) (if (<= b 4e+95) (+ x a) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+245) {
		tmp = t * b;
	} else if (b <= -4.8e+49) {
		tmp = y * b;
	} else if (b <= 4e+95) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2d+245)) then
        tmp = t * b
    else if (b <= (-4.8d+49)) then
        tmp = y * b
    else if (b <= 4d+95) then
        tmp = x + a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+245) {
		tmp = t * b;
	} else if (b <= -4.8e+49) {
		tmp = y * b;
	} else if (b <= 4e+95) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e+245:
		tmp = t * b
	elif b <= -4.8e+49:
		tmp = y * b
	elif b <= 4e+95:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+245)
		tmp = Float64(t * b);
	elseif (b <= -4.8e+49)
		tmp = Float64(y * b);
	elseif (b <= 4e+95)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e+245)
		tmp = t * b;
	elseif (b <= -4.8e+49)
		tmp = y * b;
	elseif (b <= 4e+95)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+245], N[(t * b), $MachinePrecision], If[LessEqual[b, -4.8e+49], N[(y * b), $MachinePrecision], If[LessEqual[b, 4e+95], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.00000000000000009e245 or 4.00000000000000008e95 < b

   1. Initial program 83.6%

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

   3. Taylor expanded in t around inf 48.1%

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

   4. Taylor expanded in b around inf 43.3%

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

      1. *-commutative 43.3%

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

   6. Simplified 43.3%

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

   if -2.00000000000000009e245 < b < -4.8e49

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf 74.7%

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

   4. Taylor expanded in y around inf 50.5%

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

      1. *-commutative 50.5%

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

   6. Simplified 50.5%

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

   if -4.8e49 < b < 4.00000000000000008e95

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 88.9%

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

   4. Taylor expanded in a around inf 57.3%

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

   5. Taylor expanded in t around 0 38.0%

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

      1. cancel-sign-sub-inv 38.0%

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

      2. metadata-eval 38.0%

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

      3. *-lft-identity 38.0%

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

   7. Simplified 38.0%

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

Alternative 18: 56.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+51} \lor \neg \left(b \leq 3.6 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7e+51) (not (<= b 3.6e+103)))
   (* b (- (+ y t) 2.0))
   (+ x (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7e+51) || !(b <= 3.6e+103)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (z + 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 <= (-7d+51)) .or. (.not. (b <= 3.6d+103))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = x + (z + 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 <= -7e+51) || !(b <= 3.6e+103)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7e+51) or not (b <= 3.6e+103):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = x + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7e+51) || !(b <= 3.6e+103))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(x + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7e+51) || ~((b <= 3.6e+103)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = x + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7e+51], N[Not[LessEqual[b, 3.6e+103]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7e51 or 3.60000000000000017e103 < b

   1. Initial program 86.6%

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

   3. Taylor expanded in b around inf 76.0%

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

   if -7e51 < b < 3.60000000000000017e103

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0 77.4%

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

   4. Taylor expanded in y around 0 52.2%

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

      1. associate--l+ 52.2%

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

      2. *-commutative 52.2%

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

      3. distribute-lft-in 52.2%

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

   6. Simplified 52.2%

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

   7. Taylor expanded in b around 0 51.7%

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

      1. cancel-sign-sub-inv 51.7%

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

      2. metadata-eval 51.7%

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

      3. +-commutative 51.7%

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

      4. *-lft-identity 51.7%

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

      5. +-commutative 51.7%

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

   9. Simplified 51.7%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+51} \lor \neg \left(b \leq 3.6 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+35} \lor \neg \left(t \leq 900000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.5e+35) (not (<= t 900000000000.0)))
   (* t (- b a))
   (+ x (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.5e+35) || !(t <= 900000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.5d+35)) .or. (.not. (t <= 900000000000.0d0))) then
        tmp = t * (b - a)
    else
        tmp = x + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.5e+35) || !(t <= 900000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.5e+35) or not (t <= 900000000000.0):
		tmp = t * (b - a)
	else:
		tmp = x + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.5e+35) || !(t <= 900000000000.0))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.5e+35) || ~((t <= 900000000000.0)))
		tmp = t * (b - a);
	else
		tmp = x + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.5e+35], N[Not[LessEqual[t, 900000000000.0]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999995e35 or 9e11 < t

   1. Initial program 89.0%

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

   3. Taylor expanded in t around inf 62.9%

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

   if -1.49999999999999995e35 < t < 9e11

   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. Add Preprocessing

   3. Taylor expanded in t around 0 96.8%

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

   4. Taylor expanded in y around 0 69.9%

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

      1. associate--l+ 69.9%

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

      2. *-commutative 69.9%

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

      3. distribute-lft-in 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in b around 0 58.7%

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

      1. cancel-sign-sub-inv 58.7%

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

      2. metadata-eval 58.7%

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

      3. +-commutative 58.7%

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

      4. *-lft-identity 58.7%

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

      5. +-commutative 58.7%

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

   9. Simplified 58.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+35} \lor \neg \left(t \leq 900000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+24} \lor \neg \left(t \leq 1700000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.2e+24) (not (<= t 1700000000000.0))) (* t (- b a)) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e+24) || !(t <= 1700000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.2d+24)) .or. (.not. (t <= 1700000000000.0d0))) then
        tmp = t * (b - a)
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e+24) || !(t <= 1700000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.2e+24) or not (t <= 1700000000000.0):
		tmp = t * (b - a)
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.2e+24) || !(t <= 1700000000000.0))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.2e+24) || ~((t <= 1700000000000.0)))
		tmp = t * (b - a);
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.2e+24], N[Not[LessEqual[t, 1700000000000.0]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e24 or 1.7e12 < t

   1. Initial program 89.4%

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

   3. Taylor expanded in t around inf 61.2%

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

   if -1.2e24 < t < 1.7e12

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 68.8%

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

   4. Taylor expanded in a around inf 45.7%

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

   5. Taylor expanded in t around 0 45.1%

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

      1. cancel-sign-sub-inv 45.1%

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

      2. metadata-eval 45.1%

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

      3. *-lft-identity 45.1%

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

   7. Simplified 45.1%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+24} \lor \neg \left(t \leq 1700000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 26.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+67} \lor \neg \left(t \leq 0.056\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.06e+67) (not (<= t 0.056))) (* t b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.06e+67) || !(t <= 0.056)) {
		tmp = t * b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.06d+67)) .or. (.not. (t <= 0.056d0))) then
        tmp = t * b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.06e+67) || !(t <= 0.056)) {
		tmp = t * b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.06e+67) or not (t <= 0.056):
		tmp = t * b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.06e+67) || !(t <= 0.056))
		tmp = Float64(t * b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.06e+67) || ~((t <= 0.056)))
		tmp = t * b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.06e+67], N[Not[LessEqual[t, 0.056]], $MachinePrecision]], N[(t * b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if t < -1.0599999999999999e67 or 0.0560000000000000012 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 61.1%

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

   4. Taylor expanded in b around inf 32.7%

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

      1. *-commutative 32.7%

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

   6. Simplified 32.7%

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

   if -1.0599999999999999e67 < t < 0.0560000000000000012

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0 94.3%

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

   4. Taylor expanded in a around inf 24.1%

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

4. Final simplification 28.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+67} \lor \neg \left(t \leq 0.056\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+106}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.6e+106) a (if (<= a 1.16e+96) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.6e+106) {
		tmp = a;
	} else if (a <= 1.16e+96) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-6.6d+106)) then
        tmp = a
    else if (a <= 1.16d+96) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.6e+106) {
		tmp = a;
	} else if (a <= 1.16e+96) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.6e+106:
		tmp = a
	elif a <= 1.16e+96:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.6e+106)
		tmp = a;
	elseif (a <= 1.16e+96)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.6e+106)
		tmp = a;
	elseif (a <= 1.16e+96)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.6e+106], a, If[LessEqual[a, 1.16e+96], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -6.60000000000000015e106 or 1.16000000000000005e96 < a

   1. Initial program 93.0%

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

   3. Taylor expanded in t around 0 60.9%

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

   4. Taylor expanded in a around inf 34.6%

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

   if -6.60000000000000015e106 < a < 1.16000000000000005e96

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 21.9%

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

Alternative 23: 11.3% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in t around 0 71.7%

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

4. Taylor expanded in a around inf 14.3%

   \[\leadsto \color{blue}{a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024137 
(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)))