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

Percentage Accurate: 94.8% → 97.2%

Time: 18.8s

Alternatives: 23

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.62 \cdot 10^{+212}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.62e+212)
   (fma (+ y (+ t -2.0)) b (- x (fma (+ y -1.0) z (* a (+ t -1.0)))))
   (* b (- (+ y t) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.62e+212) {
		tmp = fma((y + (t + -2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
	} else {
		tmp = b * ((y + t) - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.62e+212)
		tmp = fma(Float64(y + Float64(t + -2.0)), b, Float64(x - fma(Float64(y + -1.0), z, Float64(a * Float64(t + -1.0)))));
	else
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.62e+212], 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], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.61999999999999994e212

   1. Initial program 95.2%

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

      1. +-commutative 95.2%

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

      2. fma-def 97.8%

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

      3. associate--l+ 97.8%

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

      4. sub-neg 97.8%

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

      5. metadata-eval 97.8%

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

      6. sub-neg 97.8%

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

      7. associate-+l- 97.8%

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

      8. fma-neg 98.2%

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

      9. sub-neg 98.2%

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

      10. metadata-eval 98.2%

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

      11. remove-double-neg 98.2%

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

      12. sub-neg 98.2%

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

      13. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   if 1.61999999999999994e212 < b

   1. Initial program 81.5%

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

   3. Taylor expanded in b around inf 96.5%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.62 \cdot 10^{+212}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 42.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7400:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-229}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-131}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4800:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))) (t_2 (* t (- b a))))
   (if (<= t -7400.0)
     t_2
     (if (<= t -3.8e-134)
       x
       (if (<= t -1.3e-307)
         t_1
         (if (<= t 2.05e-229)
           x
           (if (<= t 2.2e-131)
             (* b y)
             (if (<= t 2.2e-64)
               x
               (if (<= t 1.05e-34)
                 t_1
                 (if (<= t 4800.0)
                   (* a (- 1.0 t))
                   (if (<= t 4.4e+18) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7400.0) {
		tmp = t_2;
	} else if (t <= -3.8e-134) {
		tmp = x;
	} else if (t <= -1.3e-307) {
		tmp = t_1;
	} else if (t <= 2.05e-229) {
		tmp = x;
	} else if (t <= 2.2e-131) {
		tmp = b * y;
	} else if (t <= 2.2e-64) {
		tmp = x;
	} else if (t <= 1.05e-34) {
		tmp = t_1;
	} else if (t <= 4800.0) {
		tmp = a * (1.0 - t);
	} else if (t <= 4.4e+18) {
		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 * -z
    t_2 = t * (b - a)
    if (t <= (-7400.0d0)) then
        tmp = t_2
    else if (t <= (-3.8d-134)) then
        tmp = x
    else if (t <= (-1.3d-307)) then
        tmp = t_1
    else if (t <= 2.05d-229) then
        tmp = x
    else if (t <= 2.2d-131) then
        tmp = b * y
    else if (t <= 2.2d-64) then
        tmp = x
    else if (t <= 1.05d-34) then
        tmp = t_1
    else if (t <= 4800.0d0) then
        tmp = a * (1.0d0 - t)
    else if (t <= 4.4d+18) 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 * -z;
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7400.0) {
		tmp = t_2;
	} else if (t <= -3.8e-134) {
		tmp = x;
	} else if (t <= -1.3e-307) {
		tmp = t_1;
	} else if (t <= 2.05e-229) {
		tmp = x;
	} else if (t <= 2.2e-131) {
		tmp = b * y;
	} else if (t <= 2.2e-64) {
		tmp = x;
	} else if (t <= 1.05e-34) {
		tmp = t_1;
	} else if (t <= 4800.0) {
		tmp = a * (1.0 - t);
	} else if (t <= 4.4e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	t_2 = t * (b - a)
	tmp = 0
	if t <= -7400.0:
		tmp = t_2
	elif t <= -3.8e-134:
		tmp = x
	elif t <= -1.3e-307:
		tmp = t_1
	elif t <= 2.05e-229:
		tmp = x
	elif t <= 2.2e-131:
		tmp = b * y
	elif t <= 2.2e-64:
		tmp = x
	elif t <= 1.05e-34:
		tmp = t_1
	elif t <= 4800.0:
		tmp = a * (1.0 - t)
	elif t <= 4.4e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7400.0)
		tmp = t_2;
	elseif (t <= -3.8e-134)
		tmp = x;
	elseif (t <= -1.3e-307)
		tmp = t_1;
	elseif (t <= 2.05e-229)
		tmp = x;
	elseif (t <= 2.2e-131)
		tmp = Float64(b * y);
	elseif (t <= 2.2e-64)
		tmp = x;
	elseif (t <= 1.05e-34)
		tmp = t_1;
	elseif (t <= 4800.0)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (t <= 4.4e+18)
		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 * -z;
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -7400.0)
		tmp = t_2;
	elseif (t <= -3.8e-134)
		tmp = x;
	elseif (t <= -1.3e-307)
		tmp = t_1;
	elseif (t <= 2.05e-229)
		tmp = x;
	elseif (t <= 2.2e-131)
		tmp = b * y;
	elseif (t <= 2.2e-64)
		tmp = x;
	elseif (t <= 1.05e-34)
		tmp = t_1;
	elseif (t <= 4800.0)
		tmp = a * (1.0 - t);
	elseif (t <= 4.4e+18)
		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 * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7400.0], t$95$2, If[LessEqual[t, -3.8e-134], x, If[LessEqual[t, -1.3e-307], t$95$1, If[LessEqual[t, 2.05e-229], x, If[LessEqual[t, 2.2e-131], N[(b * y), $MachinePrecision], If[LessEqual[t, 2.2e-64], x, If[LessEqual[t, 1.05e-34], t$95$1, If[LessEqual[t, 4800.0], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+18], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7400 or 4.4e18 < t

   1. Initial program 91.9%

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

   3. Taylor expanded in t around inf 69.3%

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

   if -7400 < t < -3.80000000000000003e-134 or -1.29999999999999998e-307 < t < 2.05e-229 or 2.2e-131 < t < 2.2e-64

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 38.2%

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

   if -3.80000000000000003e-134 < t < -1.29999999999999998e-307 or 2.2e-64 < t < 1.05e-34 or 4800 < t < 4.4e18

   1. Initial program 94.3%

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

   3. Taylor expanded in z around inf 42.7%

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

   4. Taylor expanded in y around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. distribute-lft-neg-out 39.1%

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

      3. *-commutative 39.1%

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

   6. Simplified 39.1%

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

   if 2.05e-229 < t < 2.2e-131

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 72.8%

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

   4. Taylor expanded in y around inf 43.1%

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

   if 1.05e-34 < t < 4800

   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 a around inf 46.1%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7400:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-229}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-131}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 4800:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 57.1%

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

4. Final simplification 97.3%

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

Alternative 4: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := x - y \cdot z\\ t_3 := y \cdot \left(b - z\right)\\ t_4 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-298}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-131}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 35000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z a)))
        (t_2 (- x (* y z)))
        (t_3 (* y (- b z)))
        (t_4 (* t (- b a))))
   (if (<= t -8.5e+34)
     t_4
     (if (<= t -5.5e-152)
       t_1
       (if (<= t -1.45e-298)
         t_3
         (if (<= t 1.4e-245)
           t_1
           (if (<= t 9.2e-131)
             t_3
             (if (<= t 1.65e-41)
               t_2
               (if (<= t 35000.0) t_1 (if (<= t 2.7e+19) t_2 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = x - (y * z);
	double t_3 = y * (b - z);
	double t_4 = t * (b - a);
	double tmp;
	if (t <= -8.5e+34) {
		tmp = t_4;
	} else if (t <= -5.5e-152) {
		tmp = t_1;
	} else if (t <= -1.45e-298) {
		tmp = t_3;
	} else if (t <= 1.4e-245) {
		tmp = t_1;
	} else if (t <= 9.2e-131) {
		tmp = t_3;
	} else if (t <= 1.65e-41) {
		tmp = t_2;
	} else if (t <= 35000.0) {
		tmp = t_1;
	} else if (t <= 2.7e+19) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x + (z + a)
    t_2 = x - (y * z)
    t_3 = y * (b - z)
    t_4 = t * (b - a)
    if (t <= (-8.5d+34)) then
        tmp = t_4
    else if (t <= (-5.5d-152)) then
        tmp = t_1
    else if (t <= (-1.45d-298)) then
        tmp = t_3
    else if (t <= 1.4d-245) then
        tmp = t_1
    else if (t <= 9.2d-131) then
        tmp = t_3
    else if (t <= 1.65d-41) then
        tmp = t_2
    else if (t <= 35000.0d0) then
        tmp = t_1
    else if (t <= 2.7d+19) then
        tmp = t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = x - (y * z);
	double t_3 = y * (b - z);
	double t_4 = t * (b - a);
	double tmp;
	if (t <= -8.5e+34) {
		tmp = t_4;
	} else if (t <= -5.5e-152) {
		tmp = t_1;
	} else if (t <= -1.45e-298) {
		tmp = t_3;
	} else if (t <= 1.4e-245) {
		tmp = t_1;
	} else if (t <= 9.2e-131) {
		tmp = t_3;
	} else if (t <= 1.65e-41) {
		tmp = t_2;
	} else if (t <= 35000.0) {
		tmp = t_1;
	} else if (t <= 2.7e+19) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + a)
	t_2 = x - (y * z)
	t_3 = y * (b - z)
	t_4 = t * (b - a)
	tmp = 0
	if t <= -8.5e+34:
		tmp = t_4
	elif t <= -5.5e-152:
		tmp = t_1
	elif t <= -1.45e-298:
		tmp = t_3
	elif t <= 1.4e-245:
		tmp = t_1
	elif t <= 9.2e-131:
		tmp = t_3
	elif t <= 1.65e-41:
		tmp = t_2
	elif t <= 35000.0:
		tmp = t_1
	elif t <= 2.7e+19:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + a))
	t_2 = Float64(x - Float64(y * z))
	t_3 = Float64(y * Float64(b - z))
	t_4 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.5e+34)
		tmp = t_4;
	elseif (t <= -5.5e-152)
		tmp = t_1;
	elseif (t <= -1.45e-298)
		tmp = t_3;
	elseif (t <= 1.4e-245)
		tmp = t_1;
	elseif (t <= 9.2e-131)
		tmp = t_3;
	elseif (t <= 1.65e-41)
		tmp = t_2;
	elseif (t <= 35000.0)
		tmp = t_1;
	elseif (t <= 2.7e+19)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + a);
	t_2 = x - (y * z);
	t_3 = y * (b - z);
	t_4 = t * (b - a);
	tmp = 0.0;
	if (t <= -8.5e+34)
		tmp = t_4;
	elseif (t <= -5.5e-152)
		tmp = t_1;
	elseif (t <= -1.45e-298)
		tmp = t_3;
	elseif (t <= 1.4e-245)
		tmp = t_1;
	elseif (t <= 9.2e-131)
		tmp = t_3;
	elseif (t <= 1.65e-41)
		tmp = t_2;
	elseif (t <= 35000.0)
		tmp = t_1;
	elseif (t <= 2.7e+19)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+34], t$95$4, If[LessEqual[t, -5.5e-152], t$95$1, If[LessEqual[t, -1.45e-298], t$95$3, If[LessEqual[t, 1.4e-245], t$95$1, If[LessEqual[t, 9.2e-131], t$95$3, If[LessEqual[t, 1.65e-41], t$95$2, If[LessEqual[t, 35000.0], t$95$1, If[LessEqual[t, 2.7e+19], t$95$2, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.5000000000000003e34 or 2.7e19 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf 71.2%

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

   if -8.5000000000000003e34 < t < -5.4999999999999998e-152 or -1.45000000000000007e-298 < t < 1.4000000000000001e-245 or 1.65000000000000012e-41 < t < 35000

   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 b around 0 75.7%

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

   4. Taylor expanded in y around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. sub-neg 67.0%

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

      3. metadata-eval 67.0%

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

      4. neg-mul-1 67.0%

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

      5. unsub-neg 67.0%

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

   6. Simplified 67.0%

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

   7. Taylor expanded in t around 0 61.6%

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

      1. neg-mul-1 61.6%

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

   9. Simplified 61.6%

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

   if -5.4999999999999998e-152 < t < -1.45000000000000007e-298 or 1.4000000000000001e-245 < t < 9.20000000000000087e-131

   1. Initial program 92.2%

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

   3. Taylor expanded in y around inf 59.8%

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

   if 9.20000000000000087e-131 < t < 1.65000000000000012e-41 or 35000 < t < 2.7e19

   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 b around 0 86.2%

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

   4. Taylor expanded in y around inf 70.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-152}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-298}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-245}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-41}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 35000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+19}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 26.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ t_2 := t \cdot \left(-a\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.4:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+139}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))) (t_2 (* t (- a))))
   (if (<= x -1.05e+157)
     x
     (if (<= x -5.8e-59)
       t_2
       (if (<= x 4.2e-186)
         t_1
         (if (<= x 6.2e-90)
           t_2
           (if (<= x 2.4) t_1 (if (<= x 3.5e+139) t_2 x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = t * -a;
	double tmp;
	if (x <= -1.05e+157) {
		tmp = x;
	} else if (x <= -5.8e-59) {
		tmp = t_2;
	} else if (x <= 4.2e-186) {
		tmp = t_1;
	} else if (x <= 6.2e-90) {
		tmp = t_2;
	} else if (x <= 2.4) {
		tmp = t_1;
	} else if (x <= 3.5e+139) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * -z
    t_2 = t * -a
    if (x <= (-1.05d+157)) then
        tmp = x
    else if (x <= (-5.8d-59)) then
        tmp = t_2
    else if (x <= 4.2d-186) then
        tmp = t_1
    else if (x <= 6.2d-90) then
        tmp = t_2
    else if (x <= 2.4d0) then
        tmp = t_1
    else if (x <= 3.5d+139) then
        tmp = t_2
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = t * -a;
	double tmp;
	if (x <= -1.05e+157) {
		tmp = x;
	} else if (x <= -5.8e-59) {
		tmp = t_2;
	} else if (x <= 4.2e-186) {
		tmp = t_1;
	} else if (x <= 6.2e-90) {
		tmp = t_2;
	} else if (x <= 2.4) {
		tmp = t_1;
	} else if (x <= 3.5e+139) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	t_2 = t * -a
	tmp = 0
	if x <= -1.05e+157:
		tmp = x
	elif x <= -5.8e-59:
		tmp = t_2
	elif x <= 4.2e-186:
		tmp = t_1
	elif x <= 6.2e-90:
		tmp = t_2
	elif x <= 2.4:
		tmp = t_1
	elif x <= 3.5e+139:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	t_2 = Float64(t * Float64(-a))
	tmp = 0.0
	if (x <= -1.05e+157)
		tmp = x;
	elseif (x <= -5.8e-59)
		tmp = t_2;
	elseif (x <= 4.2e-186)
		tmp = t_1;
	elseif (x <= 6.2e-90)
		tmp = t_2;
	elseif (x <= 2.4)
		tmp = t_1;
	elseif (x <= 3.5e+139)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	t_2 = t * -a;
	tmp = 0.0;
	if (x <= -1.05e+157)
		tmp = x;
	elseif (x <= -5.8e-59)
		tmp = t_2;
	elseif (x <= 4.2e-186)
		tmp = t_1;
	elseif (x <= 6.2e-90)
		tmp = t_2;
	elseif (x <= 2.4)
		tmp = t_1;
	elseif (x <= 3.5e+139)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[x, -1.05e+157], x, If[LessEqual[x, -5.8e-59], t$95$2, If[LessEqual[x, 4.2e-186], t$95$1, If[LessEqual[x, 6.2e-90], t$95$2, If[LessEqual[x, 2.4], t$95$1, If[LessEqual[x, 3.5e+139], t$95$2, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e157 or 3.49999999999999978e139 < x

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 52.8%

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

   if -1.05e157 < x < -5.80000000000000033e-59 or 4.2000000000000004e-186 < x < 6.2000000000000003e-90 or 2.39999999999999991 < x < 3.49999999999999978e139

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf 49.5%

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

   4. Taylor expanded in b around 0 33.0%

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

      1. mul-1-neg 33.0%

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

      2. distribute-rgt-neg-in 33.0%

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

   6. Simplified 33.0%

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

   if -5.80000000000000033e-59 < x < 4.2000000000000004e-186 or 6.2000000000000003e-90 < x < 2.39999999999999991

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 38.4%

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

   4. Taylor expanded in y around inf 33.4%

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

      1. mul-1-neg 33.4%

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

      2. distribute-lft-neg-out 33.4%

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

      3. *-commutative 33.4%

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

   6. Simplified 33.4%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;x \leq 2.4:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-64}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 30000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+20}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2.9e+35)
     t_1
     (if (<= t 5.8e-64)
       (+ x (* b (- y 2.0)))
       (if (<= t 2.4e-35)
         (* y (- b z))
         (if (<= t 30000.0)
           (+ x (+ z a))
           (if (<= t 1.12e+20) (- x (* y z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.9e+35) {
		tmp = t_1;
	} else if (t <= 5.8e-64) {
		tmp = x + (b * (y - 2.0));
	} else if (t <= 2.4e-35) {
		tmp = y * (b - z);
	} else if (t <= 30000.0) {
		tmp = x + (z + a);
	} else if (t <= 1.12e+20) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-2.9d+35)) then
        tmp = t_1
    else if (t <= 5.8d-64) then
        tmp = x + (b * (y - 2.0d0))
    else if (t <= 2.4d-35) then
        tmp = y * (b - z)
    else if (t <= 30000.0d0) then
        tmp = x + (z + a)
    else if (t <= 1.12d+20) then
        tmp = x - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.9e+35) {
		tmp = t_1;
	} else if (t <= 5.8e-64) {
		tmp = x + (b * (y - 2.0));
	} else if (t <= 2.4e-35) {
		tmp = y * (b - z);
	} else if (t <= 30000.0) {
		tmp = x + (z + a);
	} else if (t <= 1.12e+20) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2.9e+35:
		tmp = t_1
	elif t <= 5.8e-64:
		tmp = x + (b * (y - 2.0))
	elif t <= 2.4e-35:
		tmp = y * (b - z)
	elif t <= 30000.0:
		tmp = x + (z + a)
	elif t <= 1.12e+20:
		tmp = x - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.9e+35)
		tmp = t_1;
	elseif (t <= 5.8e-64)
		tmp = Float64(x + Float64(b * Float64(y - 2.0)));
	elseif (t <= 2.4e-35)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 30000.0)
		tmp = Float64(x + Float64(z + a));
	elseif (t <= 1.12e+20)
		tmp = Float64(x - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.9e+35)
		tmp = t_1;
	elseif (t <= 5.8e-64)
		tmp = x + (b * (y - 2.0));
	elseif (t <= 2.4e-35)
		tmp = y * (b - z);
	elseif (t <= 30000.0)
		tmp = x + (z + a);
	elseif (t <= 1.12e+20)
		tmp = x - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+35], t$95$1, If[LessEqual[t, 5.8e-64], N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-35], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 30000.0], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+20], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.89999999999999995e35 or 1.12e20 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf 71.2%

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

   if -2.89999999999999995e35 < t < 5.7999999999999998e-64

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 73.9%

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

   4. Taylor expanded in a around 0 59.5%

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

   5. Taylor expanded in t around 0 59.5%

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

   if 5.7999999999999998e-64 < t < 2.4000000000000001e-35

   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 y around inf 73.2%

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

   if 2.4000000000000001e-35 < t < 3e4

   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 82.9%

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

   4. Taylor expanded in y around 0 78.3%

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

      1. +-commutative 78.3%

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

      2. sub-neg 78.3%

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

      3. metadata-eval 78.3%

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

      4. neg-mul-1 78.3%

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

      5. unsub-neg 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in t around 0 66.0%

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

      1. neg-mul-1 66.0%

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

   9. Simplified 66.0%

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

   if 3e4 < t < 1.12e20

   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 0 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-64}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 30000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+20}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 25.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-251}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-187}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= x -4.2e+157)
     x
     (if (<= x -6e-68)
       t_1
       (if (<= x 1.7e-251)
         (* b y)
         (if (<= x 4.5e-187) a (if (<= x 9.5e+139) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (x <= -4.2e+157) {
		tmp = x;
	} else if (x <= -6e-68) {
		tmp = t_1;
	} else if (x <= 1.7e-251) {
		tmp = b * y;
	} else if (x <= 4.5e-187) {
		tmp = a;
	} else if (x <= 9.5e+139) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (x <= (-4.2d+157)) then
        tmp = x
    else if (x <= (-6d-68)) then
        tmp = t_1
    else if (x <= 1.7d-251) then
        tmp = b * y
    else if (x <= 4.5d-187) then
        tmp = a
    else if (x <= 9.5d+139) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (x <= -4.2e+157) {
		tmp = x;
	} else if (x <= -6e-68) {
		tmp = t_1;
	} else if (x <= 1.7e-251) {
		tmp = b * y;
	} else if (x <= 4.5e-187) {
		tmp = a;
	} else if (x <= 9.5e+139) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if x <= -4.2e+157:
		tmp = x
	elif x <= -6e-68:
		tmp = t_1
	elif x <= 1.7e-251:
		tmp = b * y
	elif x <= 4.5e-187:
		tmp = a
	elif x <= 9.5e+139:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (x <= -4.2e+157)
		tmp = x;
	elseif (x <= -6e-68)
		tmp = t_1;
	elseif (x <= 1.7e-251)
		tmp = Float64(b * y);
	elseif (x <= 4.5e-187)
		tmp = a;
	elseif (x <= 9.5e+139)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (x <= -4.2e+157)
		tmp = x;
	elseif (x <= -6e-68)
		tmp = t_1;
	elseif (x <= 1.7e-251)
		tmp = b * y;
	elseif (x <= 4.5e-187)
		tmp = a;
	elseif (x <= 9.5e+139)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[x, -4.2e+157], x, If[LessEqual[x, -6e-68], t$95$1, If[LessEqual[x, 1.7e-251], N[(b * y), $MachinePrecision], If[LessEqual[x, 4.5e-187], a, If[LessEqual[x, 9.5e+139], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2e157 or 9.5000000000000002e139 < x

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 52.8%

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

   if -4.2e157 < x < -6e-68 or 4.4999999999999998e-187 < x < 9.5000000000000002e139

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 47.5%

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

   4. Taylor expanded in b around 0 32.7%

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

      1. mul-1-neg 32.7%

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

      2. distribute-rgt-neg-in 32.7%

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

   6. Simplified 32.7%

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

   if -6e-68 < x < 1.70000000000000008e-251

   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 0 72.8%

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

   4. Taylor expanded in y around inf 26.0%

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

   if 1.70000000000000008e-251 < x < 4.4999999999999998e-187

   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 a around inf 39.7%

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

   4. Taylor expanded in t around 0 34.4%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-251}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-187}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-46}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ x (* b (+ y -2.0))))) (t_2 (* t (- b a))))
   (if (<= t -5.1e+35)
     t_2
     (if (<= t 5.8e-64)
       t_1
       (if (<= t 2.6e-46) (* z (- 1.0 y)) (if (<= t 5.3e+20) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + (b * (y + -2.0)));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -5.1e+35) {
		tmp = t_2;
	} else if (t <= 5.8e-64) {
		tmp = t_1;
	} else if (t <= 2.6e-46) {
		tmp = z * (1.0 - y);
	} else if (t <= 5.3e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (x + (b * (y + (-2.0d0))))
    t_2 = t * (b - a)
    if (t <= (-5.1d+35)) then
        tmp = t_2
    else if (t <= 5.8d-64) then
        tmp = t_1
    else if (t <= 2.6d-46) then
        tmp = z * (1.0d0 - y)
    else if (t <= 5.3d+20) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + (b * (y + -2.0)));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -5.1e+35) {
		tmp = t_2;
	} else if (t <= 5.8e-64) {
		tmp = t_1;
	} else if (t <= 2.6e-46) {
		tmp = z * (1.0 - y);
	} else if (t <= 5.3e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (x + (b * (y + -2.0)))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -5.1e+35:
		tmp = t_2
	elif t <= 5.8e-64:
		tmp = t_1
	elif t <= 2.6e-46:
		tmp = z * (1.0 - y)
	elif t <= 5.3e+20:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(x + Float64(b * Float64(y + -2.0))))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -5.1e+35)
		tmp = t_2;
	elseif (t <= 5.8e-64)
		tmp = t_1;
	elseif (t <= 2.6e-46)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 5.3e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (x + (b * (y + -2.0)));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -5.1e+35)
		tmp = t_2;
	elseif (t <= 5.8e-64)
		tmp = t_1;
	elseif (t <= 2.6e-46)
		tmp = z * (1.0 - y);
	elseif (t <= 5.3e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.1e+35], t$95$2, If[LessEqual[t, 5.8e-64], t$95$1, If[LessEqual[t, 2.6e-46], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e+20], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.10000000000000017e35 or 5.3e20 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf 71.2%

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

   if -5.10000000000000017e35 < t < 5.7999999999999998e-64 or 2.6000000000000002e-46 < t < 5.3e20

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0 74.0%

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

   4. Taylor expanded in t around 0 71.5%

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

      1. sub-neg 71.5%

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

      2. sub-neg 71.5%

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

      3. metadata-eval 71.5%

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

      4. neg-mul-1 71.5%

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

      5. remove-double-neg 71.5%

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

   6. Simplified 71.5%

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

   if 5.7999999999999998e-64 < t < 2.6000000000000002e-46

   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 z around inf 86.0%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-64}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-46}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+20}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -9e-15)
     t_2
     (if (<= b -2e-297)
       t_1
       (if (<= b 8.5e-294) (- x (* y z)) (if (<= b 3.7e-25) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -9e-15) {
		tmp = t_2;
	} else if (b <= -2e-297) {
		tmp = t_1;
	} else if (b <= 8.5e-294) {
		tmp = x - (y * z);
	} else if (b <= 3.7e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z + (a * (1.0d0 - t)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-9d-15)) then
        tmp = t_2
    else if (b <= (-2d-297)) then
        tmp = t_1
    else if (b <= 8.5d-294) then
        tmp = x - (y * z)
    else if (b <= 3.7d-25) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -9e-15) {
		tmp = t_2;
	} else if (b <= -2e-297) {
		tmp = t_1;
	} else if (b <= 8.5e-294) {
		tmp = x - (y * z);
	} else if (b <= 3.7e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -9e-15:
		tmp = t_2
	elif b <= -2e-297:
		tmp = t_1
	elif b <= 8.5e-294:
		tmp = x - (y * z)
	elif b <= 3.7e-25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -9e-15)
		tmp = t_2;
	elseif (b <= -2e-297)
		tmp = t_1;
	elseif (b <= 8.5e-294)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= 3.7e-25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a * (1.0 - t)));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -9e-15)
		tmp = t_2;
	elseif (b <= -2e-297)
		tmp = t_1;
	elseif (b <= 8.5e-294)
		tmp = x - (y * z);
	elseif (b <= 3.7e-25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e-15], t$95$2, If[LessEqual[b, -2e-297], t$95$1, If[LessEqual[b, 8.5e-294], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-25], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.9999999999999995e-15 or 3.70000000000000009e-25 < b

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in a around 0 76.2%

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

   if -8.9999999999999995e-15 < b < -2.00000000000000008e-297 or 8.4999999999999999e-294 < b < 3.70000000000000009e-25

   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 92.5%

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

   4. Taylor expanded in y around 0 70.4%

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

      1. +-commutative 70.4%

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

      2. sub-neg 70.4%

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

      3. metadata-eval 70.4%

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

      4. neg-mul-1 70.4%

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

      5. unsub-neg 70.4%

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

   6. Simplified 70.4%

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

   if -2.00000000000000008e-297 < b < 8.4999999999999999e-294

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in y around inf 97.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-297}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-25}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(1 - y\right) - t \cdot a\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -8e-15)
     t_2
     (if (<= b -1.5e-207)
       t_1
       (if (<= b 9.6e-294)
         (- (* z (- 1.0 y)) (* t a))
         (if (<= b 8e-25) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -8e-15) {
		tmp = t_2;
	} else if (b <= -1.5e-207) {
		tmp = t_1;
	} else if (b <= 9.6e-294) {
		tmp = (z * (1.0 - y)) - (t * a);
	} else if (b <= 8e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z + (a * (1.0d0 - t)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-8d-15)) then
        tmp = t_2
    else if (b <= (-1.5d-207)) then
        tmp = t_1
    else if (b <= 9.6d-294) then
        tmp = (z * (1.0d0 - y)) - (t * a)
    else if (b <= 8d-25) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -8e-15) {
		tmp = t_2;
	} else if (b <= -1.5e-207) {
		tmp = t_1;
	} else if (b <= 9.6e-294) {
		tmp = (z * (1.0 - y)) - (t * a);
	} else if (b <= 8e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -8e-15:
		tmp = t_2
	elif b <= -1.5e-207:
		tmp = t_1
	elif b <= 9.6e-294:
		tmp = (z * (1.0 - y)) - (t * a)
	elif b <= 8e-25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -8e-15)
		tmp = t_2;
	elseif (b <= -1.5e-207)
		tmp = t_1;
	elseif (b <= 9.6e-294)
		tmp = Float64(Float64(z * Float64(1.0 - y)) - Float64(t * a));
	elseif (b <= 8e-25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a * (1.0 - t)));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -8e-15)
		tmp = t_2;
	elseif (b <= -1.5e-207)
		tmp = t_1;
	elseif (b <= 9.6e-294)
		tmp = (z * (1.0 - y)) - (t * a);
	elseif (b <= 8e-25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e-15], t$95$2, If[LessEqual[b, -1.5e-207], t$95$1, If[LessEqual[b, 9.6e-294], N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-25], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.0000000000000006e-15 or 8.00000000000000031e-25 < b

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in a around 0 76.2%

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

   if -8.0000000000000006e-15 < b < -1.5e-207 or 9.59999999999999988e-294 < b < 8.00000000000000031e-25

   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 92.4%

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

   4. Taylor expanded in y around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. sub-neg 71.1%

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

      3. metadata-eval 71.1%

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

      4. neg-mul-1 71.1%

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

      5. unsub-neg 71.1%

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

   6. Simplified 71.1%

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

   if -1.5e-207 < b < 9.59999999999999988e-294

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 95.1%

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

   4. Taylor expanded in t around inf 85.4%

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

      1. *-commutative 85.4%

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

   6. Simplified 85.4%

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

   7. Taylor expanded in x around 0 80.4%

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

      1. distribute-lft-in 80.4%

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

      2. mul-1-neg 80.4%

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

      3. mul-1-neg 80.4%

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

      4. sub-neg 80.4%

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

      5. metadata-eval 80.4%

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

      6. +-commutative 80.4%

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

      7. distribute-rgt-neg-in 80.4%

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

      8. fma-udef 80.4%

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

      9. *-commutative 80.4%

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

      10. +-commutative 80.4%

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

      11. distribute-neg-in 80.4%

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

      12. metadata-eval 80.4%

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

      13. sub-neg 80.4%

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

      14. fma-neg 80.4%

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

      15. *-commutative 80.4%

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

   9. Simplified 80.4%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{-15}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-207}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(1 - y\right) - t \cdot a\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-25}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+57}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+39} \lor \neg \left(y \leq 1.4 \cdot 10^{+32}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.6e+126)
     t_1
     (if (<= y -3.7e+57)
       (- x (* t a))
       (if (or (<= y -1.35e+39) (not (<= y 1.4e+32))) t_1 (+ x (* b t)))))))

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 <= -2.6e+126) {
		tmp = t_1;
	} else if (y <= -3.7e+57) {
		tmp = x - (t * a);
	} else if ((y <= -1.35e+39) || !(y <= 1.4e+32)) {
		tmp = t_1;
	} else {
		tmp = x + (b * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-2.6d+126)) then
        tmp = t_1
    else if (y <= (-3.7d+57)) then
        tmp = x - (t * a)
    else if ((y <= (-1.35d+39)) .or. (.not. (y <= 1.4d+32))) then
        tmp = t_1
    else
        tmp = x + (b * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.6e+126) {
		tmp = t_1;
	} else if (y <= -3.7e+57) {
		tmp = x - (t * a);
	} else if ((y <= -1.35e+39) || !(y <= 1.4e+32)) {
		tmp = t_1;
	} else {
		tmp = x + (b * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2.6e+126:
		tmp = t_1
	elif y <= -3.7e+57:
		tmp = x - (t * a)
	elif (y <= -1.35e+39) or not (y <= 1.4e+32):
		tmp = t_1
	else:
		tmp = x + (b * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.6e+126)
		tmp = t_1;
	elseif (y <= -3.7e+57)
		tmp = Float64(x - Float64(t * a));
	elseif ((y <= -1.35e+39) || !(y <= 1.4e+32))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(b * t));
	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 <= -2.6e+126)
		tmp = t_1;
	elseif (y <= -3.7e+57)
		tmp = x - (t * a);
	elseif ((y <= -1.35e+39) || ~((y <= 1.4e+32)))
		tmp = t_1;
	else
		tmp = x + (b * t);
	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, -2.6e+126], t$95$1, If[LessEqual[y, -3.7e+57], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.35e+39], N[Not[LessEqual[y, 1.4e+32]], $MachinePrecision]], t$95$1, N[(x + N[(b * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e126 or -3.70000000000000006e57 < y < -1.35000000000000002e39 or 1.4e32 < y

   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 y around inf 75.0%

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

   if -2.6e126 < y < -3.70000000000000006e57

   1. Initial program 92.9%

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

   3. Taylor expanded in b around 0 78.2%

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

   4. Taylor expanded in t around inf 65.2%

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

      1. *-commutative 65.2%

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

   6. Simplified 65.2%

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

   7. Taylor expanded in t around inf 58.4%

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

   if -1.35000000000000002e39 < y < 1.4e32

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 85.6%

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

   4. Taylor expanded in a around 0 61.5%

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

   5. Taylor expanded in t around inf 48.7%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+57}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+39} \lor \neg \left(y \leq 1.4 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-289}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -5.8e+34)
     t_1
     (if (<= a -2.1e-110)
       x
       (if (<= a -5.2e-289) (* y (- z)) (if (<= a 3.15e+25) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -5.8e+34) {
		tmp = t_1;
	} else if (a <= -2.1e-110) {
		tmp = x;
	} else if (a <= -5.2e-289) {
		tmp = y * -z;
	} else if (a <= 3.15e+25) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-5.8d+34)) then
        tmp = t_1
    else if (a <= (-2.1d-110)) then
        tmp = x
    else if (a <= (-5.2d-289)) then
        tmp = y * -z
    else if (a <= 3.15d+25) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -5.8e+34) {
		tmp = t_1;
	} else if (a <= -2.1e-110) {
		tmp = x;
	} else if (a <= -5.2e-289) {
		tmp = y * -z;
	} else if (a <= 3.15e+25) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -5.8e+34:
		tmp = t_1
	elif a <= -2.1e-110:
		tmp = x
	elif a <= -5.2e-289:
		tmp = y * -z
	elif a <= 3.15e+25:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -5.8e+34)
		tmp = t_1;
	elseif (a <= -2.1e-110)
		tmp = x;
	elseif (a <= -5.2e-289)
		tmp = Float64(y * Float64(-z));
	elseif (a <= 3.15e+25)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -5.8e+34)
		tmp = t_1;
	elseif (a <= -2.1e-110)
		tmp = x;
	elseif (a <= -5.2e-289)
		tmp = y * -z;
	elseif (a <= 3.15e+25)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+34], t$95$1, If[LessEqual[a, -2.1e-110], x, If[LessEqual[a, -5.2e-289], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, 3.15e+25], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.8000000000000003e34 or 3.14999999999999987e25 < a

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf 47.6%

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

   if -5.8000000000000003e34 < a < -2.10000000000000002e-110 or -5.1999999999999998e-289 < a < 3.14999999999999987e25

   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 x around inf 33.2%

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

   if -2.10000000000000002e-110 < a < -5.1999999999999998e-289

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf 36.3%

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

   4. Taylor expanded in y around inf 30.2%

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

      1. mul-1-neg 30.2%

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

      2. distribute-lft-neg-out 30.2%

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

      3. *-commutative 30.2%

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

   6. Simplified 30.2%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-289}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.25 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -3.25e+35)
     t_2
     (if (<= t -2.2e-307)
       t_1
       (if (<= t 5.5e-248) x (if (<= t 1.52e+16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3.25e+35) {
		tmp = t_2;
	} else if (t <= -2.2e-307) {
		tmp = t_1;
	} else if (t <= 5.5e-248) {
		tmp = x;
	} else if (t <= 1.52e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-3.25d+35)) then
        tmp = t_2
    else if (t <= (-2.2d-307)) then
        tmp = t_1
    else if (t <= 5.5d-248) then
        tmp = x
    else if (t <= 1.52d+16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3.25e+35) {
		tmp = t_2;
	} else if (t <= -2.2e-307) {
		tmp = t_1;
	} else if (t <= 5.5e-248) {
		tmp = x;
	} else if (t <= 1.52e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -3.25e+35:
		tmp = t_2
	elif t <= -2.2e-307:
		tmp = t_1
	elif t <= 5.5e-248:
		tmp = x
	elif t <= 1.52e+16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.25e+35)
		tmp = t_2;
	elseif (t <= -2.2e-307)
		tmp = t_1;
	elseif (t <= 5.5e-248)
		tmp = x;
	elseif (t <= 1.52e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.25e+35)
		tmp = t_2;
	elseif (t <= -2.2e-307)
		tmp = t_1;
	elseif (t <= 5.5e-248)
		tmp = x;
	elseif (t <= 1.52e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.25e+35], t$95$2, If[LessEqual[t, -2.2e-307], t$95$1, If[LessEqual[t, 5.5e-248], x, If[LessEqual[t, 1.52e+16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2500000000000002e35 or 1.52e16 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf 71.2%

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

   if -3.2500000000000002e35 < t < -2.2e-307 or 5.49999999999999979e-248 < t < 1.52e16

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf 44.9%

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

   if -2.2e-307 < t < 5.49999999999999979e-248

   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 x around inf 38.2%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.25 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -9000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* t (- b a))))
   (if (<= t -9000.0)
     t_2
     (if (<= t 4.5e-229)
       t_1
       (if (<= t 3.05e-130) (* y (- b z)) (if (<= t 3.7e+18) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -9000.0) {
		tmp = t_2;
	} else if (t <= 4.5e-229) {
		tmp = t_1;
	} else if (t <= 3.05e-130) {
		tmp = y * (b - z);
	} else if (t <= 3.7e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = t * (b - a)
    if (t <= (-9000.0d0)) then
        tmp = t_2
    else if (t <= 4.5d-229) then
        tmp = t_1
    else if (t <= 3.05d-130) then
        tmp = y * (b - z)
    else if (t <= 3.7d+18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -9000.0) {
		tmp = t_2;
	} else if (t <= 4.5e-229) {
		tmp = t_1;
	} else if (t <= 3.05e-130) {
		tmp = y * (b - z);
	} else if (t <= 3.7e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -9000.0:
		tmp = t_2
	elif t <= 4.5e-229:
		tmp = t_1
	elif t <= 3.05e-130:
		tmp = y * (b - z)
	elif t <= 3.7e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -9000.0)
		tmp = t_2;
	elseif (t <= 4.5e-229)
		tmp = t_1;
	elseif (t <= 3.05e-130)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 3.7e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -9000.0)
		tmp = t_2;
	elseif (t <= 4.5e-229)
		tmp = t_1;
	elseif (t <= 3.05e-130)
		tmp = y * (b - z);
	elseif (t <= 3.7e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9000.0], t$95$2, If[LessEqual[t, 4.5e-229], t$95$1, If[LessEqual[t, 3.05e-130], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e+18], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9e3 or 3.7e18 < t

   1. Initial program 91.9%

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

   3. Taylor expanded in t around inf 69.3%

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

   if -9e3 < t < 4.5000000000000002e-229 or 3.04999999999999998e-130 < t < 3.7e18

   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 b around 0 74.0%

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

   4. Taylor expanded in y around inf 50.9%

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

   if 4.5000000000000002e-229 < t < 3.04999999999999998e-130

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf 64.4%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-229}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-15} \lor \neg \left(b \leq 1.05 \cdot 10^{-51}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -6.8e-15) (not (<= b 1.05e-51)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (+ t_1 (* z (- 1.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -6.8e-15) || !(b <= 1.05e-51)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-6.8d-15)) .or. (.not. (b <= 1.05d-51))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -6.8e-15) || !(b <= 1.05e-51)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -6.8e-15) or not (b <= 1.05e-51):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + (t_1 + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -6.8e-15) || !(b <= 1.05e-51))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((b <= -6.8e-15) || ~((b <= 1.05e-51)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + (t_1 + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -6.8e-15], N[Not[LessEqual[b, 1.05e-51]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.8000000000000001e-15 or 1.05000000000000001e-51 < b

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 86.2%

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

   if -6.8000000000000001e-15 < b < 1.05000000000000001e-51

   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 93.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-15} \lor \neg \left(b \leq 1.05 \cdot 10^{-51}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 82.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+145}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -9e-15)
     (+ x t_1)
     (if (<= b 4e+145) (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y)))) 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 <= -9e-15) {
		tmp = x + t_1;
	} else if (b <= 4e+145) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} 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 <= (-9d-15)) then
        tmp = x + t_1
    else if (b <= 4d+145) then
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    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 <= -9e-15) {
		tmp = x + t_1;
	} else if (b <= 4e+145) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} 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 <= -9e-15:
		tmp = x + t_1
	elif b <= 4e+145:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	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 <= -9e-15)
		tmp = Float64(x + t_1);
	elseif (b <= 4e+145)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	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 <= -9e-15)
		tmp = x + t_1;
	elseif (b <= 4e+145)
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	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, -9e-15], N[(x + t$95$1), $MachinePrecision], If[LessEqual[b, 4e+145], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.9999999999999995e-15

   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 0 88.0%

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

   4. Taylor expanded in a around 0 76.1%

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

   if -8.9999999999999995e-15 < b < 4e145

   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 88.2%

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

   if 4e145 < b

   1. Initial program 82.1%

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

   3. Taylor expanded in b around inf 88.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+145}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -370000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-232}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+41}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -370000000000.0)
     t_1
     (if (<= b 1.9e-232)
       (- x (* y z))
       (if (<= b 1.55e+41) (- x (* t a)) 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 <= -370000000000.0) {
		tmp = t_1;
	} else if (b <= 1.9e-232) {
		tmp = x - (y * z);
	} else if (b <= 1.55e+41) {
		tmp = x - (t * 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 * ((y + t) - 2.0d0)
    if (b <= (-370000000000.0d0)) then
        tmp = t_1
    else if (b <= 1.9d-232) then
        tmp = x - (y * z)
    else if (b <= 1.55d+41) then
        tmp = x - (t * 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 * ((y + t) - 2.0);
	double tmp;
	if (b <= -370000000000.0) {
		tmp = t_1;
	} else if (b <= 1.9e-232) {
		tmp = x - (y * z);
	} else if (b <= 1.55e+41) {
		tmp = x - (t * a);
	} 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 <= -370000000000.0:
		tmp = t_1
	elif b <= 1.9e-232:
		tmp = x - (y * z)
	elif b <= 1.55e+41:
		tmp = x - (t * a)
	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 <= -370000000000.0)
		tmp = t_1;
	elseif (b <= 1.9e-232)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= 1.55e+41)
		tmp = Float64(x - Float64(t * a));
	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 <= -370000000000.0)
		tmp = t_1;
	elseif (b <= 1.9e-232)
		tmp = x - (y * z);
	elseif (b <= 1.55e+41)
		tmp = x - (t * 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[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -370000000000.0], t$95$1, If[LessEqual[b, 1.9e-232], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e+41], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.7e11 or 1.55e41 < b

   1. Initial program 86.5%

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

   3. Taylor expanded in b around inf 72.3%

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

   if -3.7e11 < b < 1.9000000000000001e-232

   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 90.6%

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

   4. Taylor expanded in y around inf 57.6%

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

   if 1.9000000000000001e-232 < b < 1.55e41

   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 b around 0 87.2%

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

   4. Taylor expanded in t around inf 80.2%

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

      1. *-commutative 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in t around inf 62.1%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -370000000000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-232}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+41}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+136}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -9e-15)
     (+ x t_1)
     (if (<= b 4.3e+136) (+ x (- (* z (- 1.0 y)) (* t a))) 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 <= -9e-15) {
		tmp = x + t_1;
	} else if (b <= 4.3e+136) {
		tmp = x + ((z * (1.0 - y)) - (t * 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 * ((y + t) - 2.0d0)
    if (b <= (-9d-15)) then
        tmp = x + t_1
    else if (b <= 4.3d+136) then
        tmp = x + ((z * (1.0d0 - y)) - (t * 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 * ((y + t) - 2.0);
	double tmp;
	if (b <= -9e-15) {
		tmp = x + t_1;
	} else if (b <= 4.3e+136) {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	} 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 <= -9e-15:
		tmp = x + t_1
	elif b <= 4.3e+136:
		tmp = x + ((z * (1.0 - y)) - (t * a))
	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 <= -9e-15)
		tmp = Float64(x + t_1);
	elseif (b <= 4.3e+136)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(t * a)));
	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 <= -9e-15)
		tmp = x + t_1;
	elseif (b <= 4.3e+136)
		tmp = x + ((z * (1.0 - y)) - (t * 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[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e-15], N[(x + t$95$1), $MachinePrecision], If[LessEqual[b, 4.3e+136], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.9999999999999995e-15

   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 0 88.0%

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

   4. Taylor expanded in a around 0 76.1%

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

   if -8.9999999999999995e-15 < b < 4.2999999999999999e136

   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 88.2%

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

   4. Taylor expanded in t around inf 78.5%

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

      1. *-commutative 78.5%

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

   6. Simplified 78.5%

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

   if 4.2999999999999999e136 < b

   1. Initial program 82.1%

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

   3. Taylor expanded in b around inf 88.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+136}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 62.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+128} \lor \neg \left(a \leq 1.85 \cdot 10^{+146}\right):\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.4e+128) (not (<= a 1.85e+146)))
   (+ x (* a (- 1.0 t)))
   (+ x (* b (- (+ y t) 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.4e+128) || !(a <= 1.85e+146)) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = x + (b * ((y + t) - 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-6.4d+128)) .or. (.not. (a <= 1.85d+146))) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = x + (b * ((y + t) - 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.4e+128) || !(a <= 1.85e+146)) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = x + (b * ((y + t) - 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6.4e+128) or not (a <= 1.85e+146):
		tmp = x + (a * (1.0 - t))
	else:
		tmp = x + (b * ((y + t) - 2.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6.4e+128) || !(a <= 1.85e+146))
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -6.4e+128) || ~((a <= 1.85e+146)))
		tmp = x + (a * (1.0 - t));
	else
		tmp = x + (b * ((y + t) - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6.4e+128], N[Not[LessEqual[a, 1.85e+146]], $MachinePrecision]], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.39999999999999971e128 or 1.85000000000000002e146 < a

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 77.4%

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

   4. Taylor expanded in b around 0 70.1%

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

   if -6.39999999999999971e128 < a < 1.85000000000000002e146

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 74.8%

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

   4. Taylor expanded in a around 0 66.6%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+128} \lor \neg \left(a \leq 1.85 \cdot 10^{+146}\right):\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+38} \lor \neg \left(y \leq 3.1 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.2e+38) (not (<= y 3.1e+31))) (* y (- b z)) (+ x (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+38) || !(y <= 3.1e+31)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (b * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.2d+38)) .or. (.not. (y <= 3.1d+31))) then
        tmp = y * (b - z)
    else
        tmp = x + (b * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+38) || !(y <= 3.1e+31)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (b * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.2e+38) or not (y <= 3.1e+31):
		tmp = y * (b - z)
	else:
		tmp = x + (b * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.2e+38) || !(y <= 3.1e+31))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x + Float64(b * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.2e+38) || ~((y <= 3.1e+31)))
		tmp = y * (b - z);
	else
		tmp = x + (b * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.2e+38], N[Not[LessEqual[y, 3.1e+31]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000035e38 or 3.1000000000000002e31 < y

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 68.4%

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

   if -6.20000000000000035e38 < y < 3.1000000000000002e31

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 85.6%

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

   4. Taylor expanded in a around 0 61.5%

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

   5. Taylor expanded in t around inf 48.7%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+38} \lor \neg \left(y \leq 3.1 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 24.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+191} \lor \neg \left(y \leq 2.4 \cdot 10^{+58}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.5e+191) (not (<= y 2.4e+58))) (* b y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.5e+191) || !(y <= 2.4e+58)) {
		tmp = b * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.5d+191)) .or. (.not. (y <= 2.4d+58))) then
        tmp = b * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.5e+191) || !(y <= 2.4e+58)) {
		tmp = b * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.5e+191) or not (y <= 2.4e+58):
		tmp = b * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.5e+191) || !(y <= 2.4e+58))
		tmp = Float64(b * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.5e+191) || ~((y <= 2.4e+58)))
		tmp = b * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.5e+191], N[Not[LessEqual[y, 2.4e+58]], $MachinePrecision]], N[(b * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.5000000000000001e191 or 2.4e58 < y

   1. Initial program 85.1%

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

   3. Taylor expanded in z around 0 60.6%

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

   4. Taylor expanded in y around inf 39.4%

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

   if -2.5000000000000001e191 < y < 2.4e58

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 23.1%

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

4. Final simplification 27.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+191} \lor \neg \left(y \leq 2.4 \cdot 10^{+58}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 20.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+139}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7e-15) x (if (<= x 1.9e+139) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7e-15) {
		tmp = x;
	} else if (x <= 1.9e+139) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-7d-15)) then
        tmp = x
    else if (x <= 1.9d+139) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7e-15) {
		tmp = x;
	} else if (x <= 1.9e+139) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7e-15:
		tmp = x
	elif x <= 1.9e+139:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7e-15)
		tmp = x;
	elseif (x <= 1.9e+139)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7e-15)
		tmp = x;
	elseif (x <= 1.9e+139)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7e-15], x, If[LessEqual[x, 1.9e+139], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.0000000000000001e-15 or 1.9e139 < x

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 41.6%

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

   if -7.0000000000000001e-15 < x < 1.9e139

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf 36.0%

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

   4. Taylor expanded in t around 0 12.8%

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

4. Final simplification 24.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+139}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 11.1% 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 93.7%

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

3. Taylor expanded in a around inf 28.4%

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

4. Taylor expanded in t around 0 9.9%

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

5. Final simplification 9.9%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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)))