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

Percentage Accurate: 94.8% → 97.3%

Time: 11.8s

Alternatives: 25

Speedup: 0.5×

• 35.1% 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: 97.3% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (- (+ (- x (* (+ y -1.0) z)) (* a (- 1.0 t))) (* b (- 2.0 (+ y t))))
      INFINITY)
   (fma (+ y (+ t -2.0)) b (- x (fma (+ 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) {
	double tmp;
	if ((((x - ((y + -1.0) * z)) + (a * (1.0 - t))) - (b * (2.0 - (y + t)))) <= ((double) INFINITY)) {
		tmp = fma((y + (t + -2.0)), b, (x - fma((y + -1.0), z, ((t + -1.0) * a))));
	} else {
		tmp = ((y + t) - 2.0) * b;
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around inf 80.0%

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

4. Final simplification 99.2%

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

Alternative 2: 97.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around inf 80.0%

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

4. Final simplification 99.2%

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

Alternative 3: 56.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-48}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-124}:\\ \;\;\;\;a + t\_2\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-27}:\\ \;\;\;\;x + t\_2\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* b (- y 2.0))))
   (if (<= t -1.26e+57)
     t_1
     (if (<= t -1.02e-48)
       (- x (* y z))
       (if (<= t 4.8e-124)
         (+ a t_2)
         (if (<= t 1.25e-27)
           (+ x t_2)
           (if (<= t 3.7e+19) (* z (- 1.0 y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (t <= -1.26e+57) {
		tmp = t_1;
	} else if (t <= -1.02e-48) {
		tmp = x - (y * z);
	} else if (t <= 4.8e-124) {
		tmp = a + t_2;
	} else if (t <= 1.25e-27) {
		tmp = x + t_2;
	} else if (t <= 3.7e+19) {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = b * (y - 2.0d0)
    if (t <= (-1.26d+57)) then
        tmp = t_1
    else if (t <= (-1.02d-48)) then
        tmp = x - (y * z)
    else if (t <= 4.8d-124) then
        tmp = a + t_2
    else if (t <= 1.25d-27) then
        tmp = x + t_2
    else if (t <= 3.7d+19) then
        tmp = 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 = t * (b - a);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (t <= -1.26e+57) {
		tmp = t_1;
	} else if (t <= -1.02e-48) {
		tmp = x - (y * z);
	} else if (t <= 4.8e-124) {
		tmp = a + t_2;
	} else if (t <= 1.25e-27) {
		tmp = x + t_2;
	} else if (t <= 3.7e+19) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = b * (y - 2.0)
	tmp = 0
	if t <= -1.26e+57:
		tmp = t_1
	elif t <= -1.02e-48:
		tmp = x - (y * z)
	elif t <= 4.8e-124:
		tmp = a + t_2
	elif t <= 1.25e-27:
		tmp = x + t_2
	elif t <= 3.7e+19:
		tmp = z * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (t <= -1.26e+57)
		tmp = t_1;
	elseif (t <= -1.02e-48)
		tmp = Float64(x - Float64(y * z));
	elseif (t <= 4.8e-124)
		tmp = Float64(a + t_2);
	elseif (t <= 1.25e-27)
		tmp = Float64(x + t_2);
	elseif (t <= 3.7e+19)
		tmp = 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 = t * (b - a);
	t_2 = b * (y - 2.0);
	tmp = 0.0;
	if (t <= -1.26e+57)
		tmp = t_1;
	elseif (t <= -1.02e-48)
		tmp = x - (y * z);
	elseif (t <= 4.8e-124)
		tmp = a + t_2;
	elseif (t <= 1.25e-27)
		tmp = x + t_2;
	elseif (t <= 3.7e+19)
		tmp = 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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+57], t$95$1, If[LessEqual[t, -1.02e-48], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-124], N[(a + t$95$2), $MachinePrecision], If[LessEqual[t, 1.25e-27], N[(x + t$95$2), $MachinePrecision], If[LessEqual[t, 3.7e+19], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.26e57 or 3.7e19 < t

   1. Initial program 93.5%

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

   3. Taylor expanded in t around inf 75.6%

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

   if -1.26e57 < t < -1.02000000000000005e-48

   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 91.3%

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

   4. Taylor expanded in a around 0 66.3%

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

   5. Taylor expanded in y around inf 62.0%

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

   if -1.02000000000000005e-48 < t < 4.79999999999999985e-124

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 70.9%

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

   4. Taylor expanded in t around 0 70.9%

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

      1. sub-neg 70.9%

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

      2. +-commutative 70.9%

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

      3. sub-neg 70.9%

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

      4. metadata-eval 70.9%

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

      5. neg-mul-1 70.9%

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

      6. remove-double-neg 70.9%

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

   6. Simplified 70.9%

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

   7. Taylor expanded in x around 0 59.6%

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

   if 4.79999999999999985e-124 < t < 1.25e-27

   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 0 75.5%

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

   4. Taylor expanded in t around 0 75.5%

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

      1. sub-neg 75.5%

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

      2. +-commutative 75.5%

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

      3. sub-neg 75.5%

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

      4. metadata-eval 75.5%

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

      5. neg-mul-1 75.5%

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

      6. remove-double-neg 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in a around 0 70.4%

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

   if 1.25e-27 < t < 3.7e19

   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 81.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-48}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-124}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-27}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-71}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-186}:\\ \;\;\;\;a + b \cdot -2\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+15}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3e+56)
     t_1
     (if (<= t -2.75e-71)
       (- x (* y z))
       (if (<= t 4.5e-186)
         (+ a (* b -2.0))
         (if (<= t 2.45e-142)
           (* y (- b z))
           (if (<= t 6.5e+15) (+ x 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 <= -3e+56) {
		tmp = t_1;
	} else if (t <= -2.75e-71) {
		tmp = x - (y * z);
	} else if (t <= 4.5e-186) {
		tmp = a + (b * -2.0);
	} else if (t <= 2.45e-142) {
		tmp = y * (b - z);
	} else if (t <= 6.5e+15) {
		tmp = x + 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 <= (-3d+56)) then
        tmp = t_1
    else if (t <= (-2.75d-71)) then
        tmp = x - (y * z)
    else if (t <= 4.5d-186) then
        tmp = a + (b * (-2.0d0))
    else if (t <= 2.45d-142) then
        tmp = y * (b - z)
    else if (t <= 6.5d+15) then
        tmp = x + 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 <= -3e+56) {
		tmp = t_1;
	} else if (t <= -2.75e-71) {
		tmp = x - (y * z);
	} else if (t <= 4.5e-186) {
		tmp = a + (b * -2.0);
	} else if (t <= 2.45e-142) {
		tmp = y * (b - z);
	} else if (t <= 6.5e+15) {
		tmp = x + 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 <= -3e+56:
		tmp = t_1
	elif t <= -2.75e-71:
		tmp = x - (y * z)
	elif t <= 4.5e-186:
		tmp = a + (b * -2.0)
	elif t <= 2.45e-142:
		tmp = y * (b - z)
	elif t <= 6.5e+15:
		tmp = x + 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 <= -3e+56)
		tmp = t_1;
	elseif (t <= -2.75e-71)
		tmp = Float64(x - Float64(y * z));
	elseif (t <= 4.5e-186)
		tmp = Float64(a + Float64(b * -2.0));
	elseif (t <= 2.45e-142)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 6.5e+15)
		tmp = Float64(x + 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 <= -3e+56)
		tmp = t_1;
	elseif (t <= -2.75e-71)
		tmp = x - (y * z);
	elseif (t <= 4.5e-186)
		tmp = a + (b * -2.0);
	elseif (t <= 2.45e-142)
		tmp = y * (b - z);
	elseif (t <= 6.5e+15)
		tmp = x + 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, -3e+56], t$95$1, If[LessEqual[t, -2.75e-71], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-186], N[(a + N[(b * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e-142], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+15], N[(x + z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.00000000000000006e56 or 6.5e15 < t

   1. Initial program 93.6%

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

   3. Taylor expanded in t around inf 74.9%

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

   if -3.00000000000000006e56 < t < -2.7499999999999999e-71

   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 81.9%

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

   4. Taylor expanded in a around 0 60.5%

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

   5. Taylor expanded in y around inf 56.9%

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

   if -2.7499999999999999e-71 < t < 4.4999999999999998e-186

   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 z around 0 70.9%

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

   4. Taylor expanded in t around 0 70.9%

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

      1. sub-neg 70.9%

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

      2. +-commutative 70.9%

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

      3. sub-neg 70.9%

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

      4. metadata-eval 70.9%

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

      5. neg-mul-1 70.9%

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

      6. remove-double-neg 70.9%

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

   6. Simplified 70.9%

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

   7. Taylor expanded in y around 0 55.1%

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

      1. *-commutative 55.1%

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

   9. Simplified 55.1%

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

   10. Taylor expanded in x around 0 43.4%

       \[\leadsto \color{blue}{a + -2 \cdot b} \]

   if 4.4999999999999998e-186 < t < 2.4500000000000002e-142

   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 67.7%

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

   if 2.4500000000000002e-142 < t < 6.5e15

   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 73.1%

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

   4. Taylor expanded in a around 0 61.8%

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

   5. Taylor expanded in y around 0 49.7%

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

      1. cancel-sign-sub-inv 49.7%

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

      2. metadata-eval 49.7%

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

      3. *-lft-identity 49.7%

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

   7. Simplified 49.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-71}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-186}:\\ \;\;\;\;a + b \cdot -2\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+15}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y + -1\right) \cdot z\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-293}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 920000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ y -1.0) z))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.05e+74)
     t_2
     (if (<= b -2.15e-61)
       t_1
       (if (<= b 3.2e-293)
         (+ x (* a (- 1.0 t)))
         (if (<= b 920000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.05e+74) {
		tmp = t_2;
	} else if (b <= -2.15e-61) {
		tmp = t_1;
	} else if (b <= 3.2e-293) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 920000000.0) {
		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 + (-1.0d0)) * z)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-2.05d+74)) then
        tmp = t_2
    else if (b <= (-2.15d-61)) then
        tmp = t_1
    else if (b <= 3.2d-293) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 920000000.0d0) 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 + -1.0) * z);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.05e+74) {
		tmp = t_2;
	} else if (b <= -2.15e-61) {
		tmp = t_1;
	} else if (b <= 3.2e-293) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 920000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((y + -1.0) * z)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -2.05e+74:
		tmp = t_2
	elif b <= -2.15e-61:
		tmp = t_1
	elif b <= 3.2e-293:
		tmp = x + (a * (1.0 - t))
	elif b <= 920000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y + -1.0) * z))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.05e+74)
		tmp = t_2;
	elseif (b <= -2.15e-61)
		tmp = t_1;
	elseif (b <= 3.2e-293)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 920000000.0)
		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 + -1.0) * z);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.05e+74)
		tmp = t_2;
	elseif (b <= -2.15e-61)
		tmp = t_1;
	elseif (b <= 3.2e-293)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 920000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.05e+74], t$95$2, If[LessEqual[b, -2.15e-61], t$95$1, If[LessEqual[b, 3.2e-293], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 920000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.05e74 or 9.2e8 < b

   1. Initial program 91.3%

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

   3. Taylor expanded in b around inf 70.6%

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

   if -2.05e74 < b < -2.1500000000000002e-61 or 3.20000000000000005e-293 < b < 9.2e8

   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 88.6%

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

   4. Taylor expanded in a around 0 61.7%

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

   if -2.1500000000000002e-61 < b < 3.20000000000000005e-293

   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 0 78.3%

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

   4. Taylor expanded in b around 0 74.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+74}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-61}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-293}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 920000000:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-50}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-49}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -7.5e+66)
     t_1
     (if (<= t -8e-50)
       (- x (* y z))
       (if (<= t 1.4e-49)
         (+ a (* b (- y 2.0)))
         (if (<= t 5.2e+18) (* z (- 1.0 y)) 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 <= -7.5e+66) {
		tmp = t_1;
	} else if (t <= -8e-50) {
		tmp = x - (y * z);
	} else if (t <= 1.4e-49) {
		tmp = a + (b * (y - 2.0));
	} else if (t <= 5.2e+18) {
		tmp = 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 = t * (b - a)
    if (t <= (-7.5d+66)) then
        tmp = t_1
    else if (t <= (-8d-50)) then
        tmp = x - (y * z)
    else if (t <= 1.4d-49) then
        tmp = a + (b * (y - 2.0d0))
    else if (t <= 5.2d+18) then
        tmp = 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 = t * (b - a);
	double tmp;
	if (t <= -7.5e+66) {
		tmp = t_1;
	} else if (t <= -8e-50) {
		tmp = x - (y * z);
	} else if (t <= 1.4e-49) {
		tmp = a + (b * (y - 2.0));
	} else if (t <= 5.2e+18) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -7.5e+66:
		tmp = t_1
	elif t <= -8e-50:
		tmp = x - (y * z)
	elif t <= 1.4e-49:
		tmp = a + (b * (y - 2.0))
	elif t <= 5.2e+18:
		tmp = z * (1.0 - y)
	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 <= -7.5e+66)
		tmp = t_1;
	elseif (t <= -8e-50)
		tmp = Float64(x - Float64(y * z));
	elseif (t <= 1.4e-49)
		tmp = Float64(a + Float64(b * Float64(y - 2.0)));
	elseif (t <= 5.2e+18)
		tmp = 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 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.5e+66)
		tmp = t_1;
	elseif (t <= -8e-50)
		tmp = x - (y * z);
	elseif (t <= 1.4e-49)
		tmp = a + (b * (y - 2.0));
	elseif (t <= 5.2e+18)
		tmp = 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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+66], t$95$1, If[LessEqual[t, -8e-50], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-49], N[(a + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+18], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.50000000000000024e66 or 5.2e18 < t

   1. Initial program 93.5%

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

   3. Taylor expanded in t around inf 75.6%

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

   if -7.50000000000000024e66 < t < -8.00000000000000006e-50

   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 91.3%

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

   4. Taylor expanded in a around 0 66.3%

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

   5. Taylor expanded in y around inf 62.0%

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

   if -8.00000000000000006e-50 < t < 1.39999999999999999e-49

   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 z around 0 72.7%

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

   4. Taylor expanded in t around 0 72.7%

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

      1. sub-neg 72.7%

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

      2. +-commutative 72.7%

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

      3. sub-neg 72.7%

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

      4. metadata-eval 72.7%

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

      5. neg-mul-1 72.7%

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

      6. remove-double-neg 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in x around 0 59.0%

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

   if 1.39999999999999999e-49 < t < 5.2e18

   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 60.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-50}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-49}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -25000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-223}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+14}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -25000000.0)
     t_1
     (if (<= t 2.35e-223)
       (+ x a)
       (if (<= t 9.5e-139) (* y (- b z)) (if (<= t 6.6e+14) (+ x 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 <= -25000000.0) {
		tmp = t_1;
	} else if (t <= 2.35e-223) {
		tmp = x + a;
	} else if (t <= 9.5e-139) {
		tmp = y * (b - z);
	} else if (t <= 6.6e+14) {
		tmp = x + 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 <= (-25000000.0d0)) then
        tmp = t_1
    else if (t <= 2.35d-223) then
        tmp = x + a
    else if (t <= 9.5d-139) then
        tmp = y * (b - z)
    else if (t <= 6.6d+14) then
        tmp = x + 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 <= -25000000.0) {
		tmp = t_1;
	} else if (t <= 2.35e-223) {
		tmp = x + a;
	} else if (t <= 9.5e-139) {
		tmp = y * (b - z);
	} else if (t <= 6.6e+14) {
		tmp = x + 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 <= -25000000.0:
		tmp = t_1
	elif t <= 2.35e-223:
		tmp = x + a
	elif t <= 9.5e-139:
		tmp = y * (b - z)
	elif t <= 6.6e+14:
		tmp = x + 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 <= -25000000.0)
		tmp = t_1;
	elseif (t <= 2.35e-223)
		tmp = Float64(x + a);
	elseif (t <= 9.5e-139)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 6.6e+14)
		tmp = Float64(x + 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 <= -25000000.0)
		tmp = t_1;
	elseif (t <= 2.35e-223)
		tmp = x + a;
	elseif (t <= 9.5e-139)
		tmp = y * (b - z);
	elseif (t <= 6.6e+14)
		tmp = x + 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, -25000000.0], t$95$1, If[LessEqual[t, 2.35e-223], N[(x + a), $MachinePrecision], If[LessEqual[t, 9.5e-139], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+14], N[(x + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.5e7 or 6.6e14 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf 71.3%

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

   if -2.5e7 < t < 2.3500000000000001e-223

   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 z around 0 72.5%

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

   4. Taylor expanded in t around 0 71.8%

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

      1. sub-neg 71.8%

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

      2. +-commutative 71.8%

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

      3. sub-neg 71.8%

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

      4. metadata-eval 71.8%

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

      5. neg-mul-1 71.8%

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

      6. remove-double-neg 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in b around 0 45.0%

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

   if 2.3500000000000001e-223 < t < 9.5000000000000006e-139

   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. Add Preprocessing

   3. Taylor expanded in y around inf 53.7%

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

   if 9.5000000000000006e-139 < t < 6.6e14

   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 73.1%

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

   4. Taylor expanded in a around 0 61.8%

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

   5. Taylor expanded in y around 0 49.7%

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

      1. cancel-sign-sub-inv 49.7%

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

      2. metadata-eval 49.7%

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

      3. *-lft-identity 49.7%

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

   7. Simplified 49.7%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -25000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-223}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+14}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+25} \lor \neg \left(y \leq 5.5 \cdot 10^{+59}\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.2e+25) (not (<= y 5.5e+59)))
   (+ (- x (* b (- 2.0 (+ y t)))) (* z (- 1.0 y)))
   (+ (+ x (+ z (* b (- t 2.0)))) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+25) || !(y <= 5.5e+59)) {
		tmp = (x - (b * (2.0 - (y + t)))) + (z * (1.0 - y));
	} else {
		tmp = (x + (z + (b * (t - 2.0)))) + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.2d+25)) .or. (.not. (y <= 5.5d+59))) then
        tmp = (x - (b * (2.0d0 - (y + t)))) + (z * (1.0d0 - y))
    else
        tmp = (x + (z + (b * (t - 2.0d0)))) + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+25) || !(y <= 5.5e+59)) {
		tmp = (x - (b * (2.0 - (y + t)))) + (z * (1.0 - y));
	} else {
		tmp = (x + (z + (b * (t - 2.0)))) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.2e+25) or not (y <= 5.5e+59):
		tmp = (x - (b * (2.0 - (y + t)))) + (z * (1.0 - y))
	else:
		tmp = (x + (z + (b * (t - 2.0)))) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.2e+25) || !(y <= 5.5e+59))
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(Float64(x + Float64(z + Float64(b * Float64(t - 2.0)))) + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.2e+25) || ~((y <= 5.5e+59)))
		tmp = (x - (b * (2.0 - (y + t)))) + (z * (1.0 - y));
	else
		tmp = (x + (z + (b * (t - 2.0)))) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.2e+25], N[Not[LessEqual[y, 5.5e+59]], $MachinePrecision]], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999996e25 or 5.4999999999999999e59 < y

   1. Initial program 95.6%

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

   3. Taylor expanded in a around 0 81.8%

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

   if -6.1999999999999996e25 < y < 5.4999999999999999e59

   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 y around 0 94.6%

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

   4. Taylor expanded in z around 0 94.6%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+25} \lor \neg \left(y \leq 5.5 \cdot 10^{+59}\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{-19} \lor \neg \left(b \leq 5.1 \cdot 10^{-34}\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -2.4e-19) (not (<= b 5.1e-34)))
     (+ (- x (* b (- 2.0 (+ y t)))) t_1)
     (+ x (+ t_1 (* a (- 1.0 t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -2.4e-19) || !(b <= 5.1e-34)) {
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	} else {
		tmp = x + (t_1 + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((b <= (-2.4d-19)) .or. (.not. (b <= 5.1d-34))) then
        tmp = (x - (b * (2.0d0 - (y + t)))) + t_1
    else
        tmp = x + (t_1 + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -2.4e-19) || !(b <= 5.1e-34)) {
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	} else {
		tmp = x + (t_1 + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -2.4e-19) or not (b <= 5.1e-34):
		tmp = (x - (b * (2.0 - (y + t)))) + t_1
	else:
		tmp = x + (t_1 + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((b <= -2.4e-19) || !(b <= 5.1e-34))
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + t_1);
	else
		tmp = Float64(x + Float64(t_1 + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((b <= -2.4e-19) || ~((b <= 5.1e-34)))
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	else
		tmp = x + (t_1 + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2.4e-19], N[Not[LessEqual[b, 5.1e-34]], $MachinePrecision]], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.40000000000000023e-19 or 5.1000000000000001e-34 < b

   1. Initial program 93.1%

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

   3. Taylor expanded in a around 0 84.7%

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

   if -2.40000000000000023e-19 < b < 5.1000000000000001e-34

   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 96.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-19} \lor \neg \left(b \leq 5.1 \cdot 10^{-34}\right):\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+37} \lor \neg \left(z \leq 9 \cdot 10^{+152}\right):\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= z -4.9e+37) (not (<= z 9e+152)))
     (+ x (+ (* z (- 1.0 y)) t_1))
     (+ (- x (* b (- 2.0 (+ y t)))) 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 ((z <= -4.9e+37) || !(z <= 9e+152)) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = (x - (b * (2.0 - (y + t)))) + 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 ((z <= (-4.9d+37)) .or. (.not. (z <= 9d+152))) then
        tmp = x + ((z * (1.0d0 - y)) + t_1)
    else
        tmp = (x - (b * (2.0d0 - (y + t)))) + 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 ((z <= -4.9e+37) || !(z <= 9e+152)) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (z <= -4.9e+37) or not (z <= 9e+152):
		tmp = x + ((z * (1.0 - y)) + t_1)
	else:
		tmp = (x - (b * (2.0 - (y + t)))) + 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 ((z <= -4.9e+37) || !(z <= 9e+152))
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	else
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + 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 ((z <= -4.9e+37) || ~((z <= 9e+152)))
		tmp = x + ((z * (1.0 - y)) + t_1);
	else
		tmp = (x - (b * (2.0 - (y + t)))) + 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[Or[LessEqual[z, -4.9e+37], N[Not[LessEqual[z, 9e+152]], $MachinePrecision]], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9000000000000004e37 or 9.0000000000000002e152 < z

   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. Add Preprocessing

   3. Taylor expanded in b around 0 83.7%

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

   if -4.9000000000000004e37 < z < 9.0000000000000002e152

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 89.2%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+37} \lor \neg \left(z \leq 9 \cdot 10^{+152}\right):\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.24 \cdot 10^{-293}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-23}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -3.7e+93)
     t_1
     (if (<= b 1.24e-293)
       (+ (+ x z) (* a (- 1.0 t)))
       (if (<= b 1.15e-23) (+ x (+ a (* z (- 1.0 y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -3.7e+93) {
		tmp = t_1;
	} else if (b <= 1.24e-293) {
		tmp = (x + z) + (a * (1.0 - t));
	} else if (b <= 1.15e-23) {
		tmp = x + (a + (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 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-3.7d+93)) then
        tmp = t_1
    else if (b <= 1.24d-293) then
        tmp = (x + z) + (a * (1.0d0 - t))
    else if (b <= 1.15d-23) then
        tmp = x + (a + (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 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -3.7e+93) {
		tmp = t_1;
	} else if (b <= 1.24e-293) {
		tmp = (x + z) + (a * (1.0 - t));
	} else if (b <= 1.15e-23) {
		tmp = x + (a + (z * (1.0 - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -3.7e+93:
		tmp = t_1
	elif b <= 1.24e-293:
		tmp = (x + z) + (a * (1.0 - t))
	elif b <= 1.15e-23:
		tmp = x + (a + (z * (1.0 - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -3.7e+93)
		tmp = t_1;
	elseif (b <= 1.24e-293)
		tmp = Float64(Float64(x + z) + Float64(a * Float64(1.0 - t)));
	elseif (b <= 1.15e-23)
		tmp = Float64(x + Float64(a + 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 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -3.7e+93)
		tmp = t_1;
	elseif (b <= 1.24e-293)
		tmp = (x + z) + (a * (1.0 - t));
	elseif (b <= 1.15e-23)
		tmp = x + (a + (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[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e+93], t$95$1, If[LessEqual[b, 1.24e-293], N[(N[(x + z), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-23], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.69999999999999987e93 or 1.15000000000000005e-23 < b

   1. Initial program 91.3%

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

   3. Taylor expanded in z around 0 81.3%

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

   4. Taylor expanded in a around 0 76.5%

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

   if -3.69999999999999987e93 < b < 1.24000000000000001e-293

   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 88.9%

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

   4. Taylor expanded in y around 0 73.6%

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

      1. associate--r+ 73.6%

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

      2. sub-neg 73.6%

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

      3. metadata-eval 73.6%

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

      4. *-commutative 73.6%

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

      5. cancel-sign-sub-inv 73.6%

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

      6. sub-neg 73.6%

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

      7. neg-mul-1 73.6%

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

      8. remove-double-neg 73.6%

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

      9. +-commutative 73.6%

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

      10. distribute-neg-in 73.6%

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

      11. metadata-eval 73.6%

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

      12. sub-neg 73.6%

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

      13. *-commutative 73.6%

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

   6. Simplified 73.6%

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

   if 1.24000000000000001e-293 < b < 1.15000000000000005e-23

   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 95.9%

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

   4. Taylor expanded in t around 0 76.6%

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

      1. neg-mul-1 76.6%

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

      2. +-commutative 76.6%

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

      3. sub-neg 76.6%

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

      4. metadata-eval 76.6%

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

      5. unsub-neg 76.6%

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

   6. Simplified 76.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+93}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq 1.24 \cdot 10^{-293}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-23}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -40000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-288}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-26}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -40000000.0)
     t_1
     (if (<= b 4.4e-288)
       (+ x (* a (- 1.0 t)))
       (if (<= b 2.45e-26) (- x (* (+ y -1.0) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -40000000.0) {
		tmp = t_1;
	} else if (b <= 4.4e-288) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.45e-26) {
		tmp = x - ((y + -1.0) * 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 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-40000000.0d0)) then
        tmp = t_1
    else if (b <= 4.4d-288) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 2.45d-26) then
        tmp = x - ((y + (-1.0d0)) * 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 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -40000000.0) {
		tmp = t_1;
	} else if (b <= 4.4e-288) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.45e-26) {
		tmp = x - ((y + -1.0) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -40000000.0:
		tmp = t_1
	elif b <= 4.4e-288:
		tmp = x + (a * (1.0 - t))
	elif b <= 2.45e-26:
		tmp = x - ((y + -1.0) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -40000000.0)
		tmp = t_1;
	elseif (b <= 4.4e-288)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 2.45e-26)
		tmp = Float64(x - Float64(Float64(y + -1.0) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -40000000.0)
		tmp = t_1;
	elseif (b <= 4.4e-288)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 2.45e-26)
		tmp = x - ((y + -1.0) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -40000000.0], t$95$1, If[LessEqual[b, 4.4e-288], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.45e-26], N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4e7 or 2.45e-26 < b

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 78.8%

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

   4. Taylor expanded in a around 0 70.9%

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

   if -4e7 < b < 4.4000000000000003e-288

   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 0 73.1%

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

   4. Taylor expanded in b around 0 67.4%

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

   if 4.4000000000000003e-288 < b < 2.45e-26

   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 95.9%

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

   4. Taylor expanded in a around 0 66.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -40000000:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-288}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-26}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+284}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.24 \cdot 10^{-132}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+16}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.7e+284)
   (* t (- a))
   (if (<= t -1.55e+65)
     (* t b)
     (if (<= t 1.24e-132) (+ x a) (if (<= t 7e+16) (+ x z) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.7e+284) {
		tmp = t * -a;
	} else if (t <= -1.55e+65) {
		tmp = t * b;
	} else if (t <= 1.24e-132) {
		tmp = x + a;
	} else if (t <= 7e+16) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.7d+284)) then
        tmp = t * -a
    else if (t <= (-1.55d+65)) then
        tmp = t * b
    else if (t <= 1.24d-132) then
        tmp = x + a
    else if (t <= 7d+16) then
        tmp = x + z
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.7e+284) {
		tmp = t * -a;
	} else if (t <= -1.55e+65) {
		tmp = t * b;
	} else if (t <= 1.24e-132) {
		tmp = x + a;
	} else if (t <= 7e+16) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.7e+284:
		tmp = t * -a
	elif t <= -1.55e+65:
		tmp = t * b
	elif t <= 1.24e-132:
		tmp = x + a
	elif t <= 7e+16:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.7e+284)
		tmp = Float64(t * Float64(-a));
	elseif (t <= -1.55e+65)
		tmp = Float64(t * b);
	elseif (t <= 1.24e-132)
		tmp = Float64(x + a);
	elseif (t <= 7e+16)
		tmp = Float64(x + z);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.7e+284)
		tmp = t * -a;
	elseif (t <= -1.55e+65)
		tmp = t * b;
	elseif (t <= 1.24e-132)
		tmp = x + a;
	elseif (t <= 7e+16)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.7e+284], N[(t * (-a)), $MachinePrecision], If[LessEqual[t, -1.55e+65], N[(t * b), $MachinePrecision], If[LessEqual[t, 1.24e-132], N[(x + a), $MachinePrecision], If[LessEqual[t, 7e+16], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.69999999999999998e284

   1. Initial program 87.5%

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

   3. Taylor expanded in t around inf 87.6%

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

   4. Taylor expanded in b around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. distribute-lft-neg-out 75.1%

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

      3. *-commutative 75.1%

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

   6. Simplified 75.1%

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

   if -3.69999999999999998e284 < t < -1.54999999999999995e65 or 7e16 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf 73.9%

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

   4. Taylor expanded in b around inf 45.6%

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

   if -1.54999999999999995e65 < t < 1.24000000000000006e-132

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 71.8%

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

   4. Taylor expanded in t around 0 68.9%

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

      1. sub-neg 68.9%

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

      2. +-commutative 68.9%

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

      3. sub-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. neg-mul-1 68.9%

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

      6. remove-double-neg 68.9%

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

   6. Simplified 68.9%

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

   7. Taylor expanded in b around 0 38.6%

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

   if 1.24000000000000006e-132 < t < 7e16

   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 72.2%

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

   4. Taylor expanded in a around 0 63.8%

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

   5. Taylor expanded in y around 0 51.4%

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

      1. cancel-sign-sub-inv 51.4%

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

      2. metadata-eval 51.4%

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

      3. *-lft-identity 51.4%

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

   7. Simplified 51.4%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+284}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.24 \cdot 10^{-132}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+16}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+66}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-123}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.5e+66)
   (* t b)
   (if (<= t -2.4e-48)
     x
     (if (<= t 1.25e-123) a (if (<= t 3.6e-5) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+66) {
		tmp = t * b;
	} else if (t <= -2.4e-48) {
		tmp = x;
	} else if (t <= 1.25e-123) {
		tmp = a;
	} else if (t <= 3.6e-5) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9.5d+66)) then
        tmp = t * b
    else if (t <= (-2.4d-48)) then
        tmp = x
    else if (t <= 1.25d-123) then
        tmp = a
    else if (t <= 3.6d-5) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+66) {
		tmp = t * b;
	} else if (t <= -2.4e-48) {
		tmp = x;
	} else if (t <= 1.25e-123) {
		tmp = a;
	} else if (t <= 3.6e-5) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.5e+66:
		tmp = t * b
	elif t <= -2.4e-48:
		tmp = x
	elif t <= 1.25e-123:
		tmp = a
	elif t <= 3.6e-5:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.5e+66)
		tmp = Float64(t * b);
	elseif (t <= -2.4e-48)
		tmp = x;
	elseif (t <= 1.25e-123)
		tmp = a;
	elseif (t <= 3.6e-5)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.5e+66)
		tmp = t * b;
	elseif (t <= -2.4e-48)
		tmp = x;
	elseif (t <= 1.25e-123)
		tmp = a;
	elseif (t <= 3.6e-5)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.5e+66], N[(t * b), $MachinePrecision], If[LessEqual[t, -2.4e-48], x, If[LessEqual[t, 1.25e-123], a, If[LessEqual[t, 3.6e-5], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.50000000000000051e66 or 3.60000000000000009e-5 < t

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf 73.1%

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

   4. Taylor expanded in b around inf 42.4%

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

   if -9.50000000000000051e66 < t < -2.4e-48 or 1.25000000000000007e-123 < t < 3.60000000000000009e-5

   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 35.0%

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

   if -2.4e-48 < t < 1.25000000000000007e-123

   1. Initial program 96.9%

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

   3. Taylor expanded in a around inf 25.5%

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

   4. Taylor expanded in t around 0 25.5%

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

Alternative 15: 83.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+94} \lor \neg \left(b \leq 2.45 \cdot 10^{+135}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.35e+94) (not (<= b 2.45e+135)))
   (- x (* b (- 2.0 (+ y t))))
   (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.35e+94) || !(b <= 2.45e+135)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.35d+94)) .or. (.not. (b <= 2.45d+135))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.35e+94) || !(b <= 2.45e+135)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.35e+94) or not (b <= 2.45e+135):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.35e+94) || !(b <= 2.45e+135))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.35e+94) || ~((b <= 2.45e+135)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.35e+94], N[Not[LessEqual[b, 2.45e+135]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3500000000000001e94 or 2.4500000000000001e135 < b

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 83.1%

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

   4. Taylor expanded in a around 0 85.6%

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

   if -1.3500000000000001e94 < b < 2.4500000000000001e135

   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 84.9%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+94} \lor \neg \left(b \leq 2.45 \cdot 10^{+135}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -32500000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 31000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -32500000.0)
     t_1
     (if (<= b 3e-288)
       (* a (- 1.0 t))
       (if (<= b 31000000.0) (- x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -32500000.0) {
		tmp = t_1;
	} else if (b <= 3e-288) {
		tmp = a * (1.0 - t);
	} else if (b <= 31000000.0) {
		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 = ((y + t) - 2.0d0) * b
    if (b <= (-32500000.0d0)) then
        tmp = t_1
    else if (b <= 3d-288) then
        tmp = a * (1.0d0 - t)
    else if (b <= 31000000.0d0) 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 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -32500000.0) {
		tmp = t_1;
	} else if (b <= 3e-288) {
		tmp = a * (1.0 - t);
	} else if (b <= 31000000.0) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -32500000.0:
		tmp = t_1
	elif b <= 3e-288:
		tmp = a * (1.0 - t)
	elif b <= 31000000.0:
		tmp = x - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -32500000.0)
		tmp = t_1;
	elseif (b <= 3e-288)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 31000000.0)
		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 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -32500000.0)
		tmp = t_1;
	elseif (b <= 3e-288)
		tmp = a * (1.0 - t);
	elseif (b <= 31000000.0)
		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[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -32500000.0], t$95$1, If[LessEqual[b, 3e-288], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 31000000.0], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.25e7 or 3.1e7 < b

   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 b around inf 66.1%

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

   if -3.25e7 < b < 2.99999999999999999e-288

   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 48.8%

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

   if 2.99999999999999999e-288 < b < 3.1e7

   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 93.0%

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

   4. Taylor expanded in a around 0 66.4%

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

   5. Taylor expanded in y around inf 56.2%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -32500000:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 31000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 75.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.35 \cdot 10^{+72} \lor \neg \left(b \leq 1.15 \cdot 10^{-23}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.35e+72) (not (<= b 1.15e-23)))
   (- x (* b (- 2.0 (+ y t))))
   (- x (+ (* (+ y -1.0) z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.35e+72) || !(b <= 1.15e-23)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x - (((y + -1.0) * z) + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.35d+72)) .or. (.not. (b <= 1.15d-23))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x - (((y + (-1.0d0)) * z) + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.35e+72) || !(b <= 1.15e-23)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x - (((y + -1.0) * z) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.35e+72) or not (b <= 1.15e-23):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x - (((y + -1.0) * z) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.35e+72) || !(b <= 1.15e-23))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x - Float64(Float64(Float64(y + -1.0) * z) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.35e+72) || ~((b <= 1.15e-23)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x - (((y + -1.0) * z) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.35e+72], N[Not[LessEqual[b, 1.15e-23]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.3499999999999999e72 or 1.15000000000000005e-23 < b

   1. Initial program 91.7%

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

   3. Taylor expanded in z around 0 81.3%

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

   4. Taylor expanded in a around 0 75.1%

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

   if -3.3499999999999999e72 < b < 1.15000000000000005e-23

   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 92.6%

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

   4. Taylor expanded in t around inf 78.0%

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

      1. *-commutative 78.0%

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

   6. Simplified 78.0%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.35 \cdot 10^{+72} \lor \neg \left(b \leq 1.15 \cdot 10^{-23}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-134}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+15}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.15e+15)
     t_1
     (if (<= t 3.3e-134) (+ x a) (if (<= t 6.2e+15) (+ x 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 <= -1.15e+15) {
		tmp = t_1;
	} else if (t <= 3.3e-134) {
		tmp = x + a;
	} else if (t <= 6.2e+15) {
		tmp = x + 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 <= (-1.15d+15)) then
        tmp = t_1
    else if (t <= 3.3d-134) then
        tmp = x + a
    else if (t <= 6.2d+15) then
        tmp = x + 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 <= -1.15e+15) {
		tmp = t_1;
	} else if (t <= 3.3e-134) {
		tmp = x + a;
	} else if (t <= 6.2e+15) {
		tmp = x + 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 <= -1.15e+15:
		tmp = t_1
	elif t <= 3.3e-134:
		tmp = x + a
	elif t <= 6.2e+15:
		tmp = x + 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 <= -1.15e+15)
		tmp = t_1;
	elseif (t <= 3.3e-134)
		tmp = Float64(x + a);
	elseif (t <= 6.2e+15)
		tmp = Float64(x + 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 <= -1.15e+15)
		tmp = t_1;
	elseif (t <= 3.3e-134)
		tmp = x + a;
	elseif (t <= 6.2e+15)
		tmp = x + 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, -1.15e+15], t$95$1, If[LessEqual[t, 3.3e-134], N[(x + a), $MachinePrecision], If[LessEqual[t, 6.2e+15], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e15 or 6.2e15 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf 71.3%

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

   if -1.15e15 < t < 3.30000000000000019e-134

   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 73.7%

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

   4. Taylor expanded in t around 0 73.1%

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

      1. sub-neg 73.1%

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

      2. +-commutative 73.1%

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

      3. sub-neg 73.1%

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

      4. metadata-eval 73.1%

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

      5. neg-mul-1 73.1%

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

      6. remove-double-neg 73.1%

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

   6. Simplified 73.1%

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

   7. Taylor expanded in b around 0 40.9%

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

   if 3.30000000000000019e-134 < t < 6.2e15

   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 72.2%

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

   4. Taylor expanded in a around 0 63.8%

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

   5. Taylor expanded in y around 0 51.4%

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

      1. cancel-sign-sub-inv 51.4%

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

      2. metadata-eval 51.4%

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

      3. *-lft-identity 51.4%

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

   7. Simplified 51.4%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-134}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+15}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+93} \lor \neg \left(b \leq 2.5 \cdot 10^{-32}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.8e+93) (not (<= b 2.5e-32)))
   (- x (* b (- 2.0 (+ y t))))
   (+ (+ x z) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.8e+93) || !(b <= 2.5e-32)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = (x + z) + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.8d+93)) .or. (.not. (b <= 2.5d-32))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = (x + z) + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.8e+93) || !(b <= 2.5e-32)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = (x + z) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.8e+93) or not (b <= 2.5e-32):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = (x + z) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.8e+93) || !(b <= 2.5e-32))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(Float64(x + z) + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.8e+93) || ~((b <= 2.5e-32)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = (x + z) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.8e+93], N[Not[LessEqual[b, 2.5e-32]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.7999999999999998e93 or 2.5e-32 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 80.9%

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

   4. Taylor expanded in a around 0 76.3%

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

   if -3.7999999999999998e93 < b < 2.5e-32

   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 92.0%

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

   4. Taylor expanded in y around 0 71.4%

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

      1. associate--r+ 71.4%

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

      2. sub-neg 71.4%

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

      3. metadata-eval 71.4%

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

      4. *-commutative 71.4%

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

      5. cancel-sign-sub-inv 71.4%

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

      6. sub-neg 71.4%

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

      7. neg-mul-1 71.4%

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

      8. remove-double-neg 71.4%

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

      9. +-commutative 71.4%

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

      10. distribute-neg-in 71.4%

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

      11. metadata-eval 71.4%

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

      12. sub-neg 71.4%

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

      13. *-commutative 71.4%

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

   6. Simplified 71.4%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+93} \lor \neg \left(b \leq 2.5 \cdot 10^{-32}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+67}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-132}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+18}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1e+67)
   (* t b)
   (if (<= t 6.6e-132) (+ x a) (if (<= t 3e+18) (+ x z) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e+67) {
		tmp = t * b;
	} else if (t <= 6.6e-132) {
		tmp = x + a;
	} else if (t <= 3e+18) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1d+67)) then
        tmp = t * b
    else if (t <= 6.6d-132) then
        tmp = x + a
    else if (t <= 3d+18) then
        tmp = x + z
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e+67) {
		tmp = t * b;
	} else if (t <= 6.6e-132) {
		tmp = x + a;
	} else if (t <= 3e+18) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1e+67:
		tmp = t * b
	elif t <= 6.6e-132:
		tmp = x + a
	elif t <= 3e+18:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1e+67)
		tmp = Float64(t * b);
	elseif (t <= 6.6e-132)
		tmp = Float64(x + a);
	elseif (t <= 3e+18)
		tmp = Float64(x + z);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1e+67)
		tmp = t * b;
	elseif (t <= 6.6e-132)
		tmp = x + a;
	elseif (t <= 3e+18)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1e+67], N[(t * b), $MachinePrecision], If[LessEqual[t, 6.6e-132], N[(x + a), $MachinePrecision], If[LessEqual[t, 3e+18], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999983e66 or 3e18 < t

   1. Initial program 93.6%

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

   3. Taylor expanded in t around inf 74.9%

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

   4. Taylor expanded in b around inf 43.4%

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

   if -9.99999999999999983e66 < t < 6.5999999999999994e-132

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 71.8%

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

   4. Taylor expanded in t around 0 68.9%

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

      1. sub-neg 68.9%

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

      2. +-commutative 68.9%

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

      3. sub-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. neg-mul-1 68.9%

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

      6. remove-double-neg 68.9%

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

   6. Simplified 68.9%

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

   7. Taylor expanded in b around 0 38.6%

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

   if 6.5999999999999994e-132 < t < 3e18

   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 72.2%

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

   4. Taylor expanded in a around 0 63.8%

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

   5. Taylor expanded in y around 0 51.4%

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

      1. cancel-sign-sub-inv 51.4%

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

      2. metadata-eval 51.4%

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

      3. *-lft-identity 51.4%

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

   7. Simplified 51.4%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+67}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-132}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+18}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 61.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+72} \lor \neg \left(b \leq 1.3 \cdot 10^{-29}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.1e+72) (not (<= b 1.3e-29)))
   (* (- (+ y t) 2.0) b)
   (+ x (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.1e+72) || !(b <= 1.3e-29)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.1d+72)) .or. (.not. (b <= 1.3d-29))) then
        tmp = ((y + t) - 2.0d0) * b
    else
        tmp = x + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.1e+72) || !(b <= 1.3e-29)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.1e+72) or not (b <= 1.3e-29):
		tmp = ((y + t) - 2.0) * b
	else:
		tmp = x + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.1e+72) || !(b <= 1.3e-29))
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	else
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.1e+72) || ~((b <= 1.3e-29)))
		tmp = ((y + t) - 2.0) * b;
	else
		tmp = x + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.1e+72], N[Not[LessEqual[b, 1.3e-29]], $MachinePrecision]], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.09999999999999988e72 or 1.3000000000000001e-29 < b

   1. Initial program 91.8%

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

   3. Taylor expanded in b around inf 69.2%

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

   if -3.09999999999999988e72 < b < 1.3000000000000001e-29

   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 0 65.9%

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

   4. Taylor expanded in b around 0 59.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+72} \lor \neg \left(b \leq 1.3 \cdot 10^{-29}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 42.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+46} \lor \neg \left(a \leq 1.45 \cdot 10^{+45}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.15e+46) (not (<= a 1.45e+45))) (* a (- 1.0 t)) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.15e+46) || !(a <= 1.45e+45)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.15d+46)) .or. (.not. (a <= 1.45d+45))) then
        tmp = a * (1.0d0 - t)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.15e+46) || !(a <= 1.45e+45)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.15e+46) or not (a <= 1.45e+45):
		tmp = a * (1.0 - t)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.15e+46) || !(a <= 1.45e+45))
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.15e+46) || ~((a <= 1.45e+45)))
		tmp = a * (1.0 - t);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.15e+46], N[Not[LessEqual[a, 1.45e+45]], $MachinePrecision]], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.15000000000000002e46 or 1.4499999999999999e45 < a

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 57.4%

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

   if -2.15000000000000002e46 < a < 1.4499999999999999e45

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0 57.4%

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

   4. Taylor expanded in a around 0 51.1%

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

   5. Taylor expanded in y around 0 32.0%

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

      1. cancel-sign-sub-inv 32.0%

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

      2. metadata-eval 32.0%

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

      3. *-lft-identity 32.0%

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

   7. Simplified 32.0%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+46} \lor \neg \left(a \leq 1.45 \cdot 10^{+45}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 35.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+61} \lor \neg \left(t \leq 330000000\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.3e+61) (not (<= t 330000000.0))) (* t b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.3e+61) || !(t <= 330000000.0)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.3d+61)) .or. (.not. (t <= 330000000.0d0))) then
        tmp = t * b
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.3e+61) || !(t <= 330000000.0)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.3e+61) or not (t <= 330000000.0):
		tmp = t * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.3e+61) || !(t <= 330000000.0))
		tmp = Float64(t * b);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.3e+61) || ~((t <= 330000000.0)))
		tmp = t * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.3e+61], N[Not[LessEqual[t, 330000000.0]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2999999999999998e61 or 3.3e8 < t

   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 t around inf 74.4%

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

   4. Taylor expanded in b around inf 43.2%

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

   if -3.2999999999999998e61 < t < 3.3e8

   1. Initial program 97.9%

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

   3. Taylor expanded in z around 0 69.4%

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

   4. Taylor expanded in t around 0 67.1%

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

      1. sub-neg 67.1%

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

      2. +-commutative 67.1%

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

      3. sub-neg 67.1%

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

      4. metadata-eval 67.1%

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

      5. neg-mul-1 67.1%

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

      6. remove-double-neg 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in b around 0 37.8%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+61} \lor \neg \left(t \leq 330000000\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+162}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7e+106) x (if (<= x 1.45e+162) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7e+106) {
		tmp = x;
	} else if (x <= 1.45e+162) {
		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+106)) then
        tmp = x
    else if (x <= 1.45d+162) 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+106) {
		tmp = x;
	} else if (x <= 1.45e+162) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7e+106:
		tmp = x
	elif x <= 1.45e+162:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7e+106)
		tmp = x;
	elseif (x <= 1.45e+162)
		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+106)
		tmp = x;
	elseif (x <= 1.45e+162)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7e+106], x, If[LessEqual[x, 1.45e+162], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.99999999999999962e106 or 1.45000000000000003e162 < x

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 38.1%

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

   if -6.99999999999999962e106 < x < 1.45000000000000003e162

   1. Initial program 95.5%

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

   3. Taylor expanded in a around inf 31.2%

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

   4. Taylor expanded in t around 0 16.5%

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

Alternative 25: 11.8% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 a around inf 28.2%

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

4. Taylor expanded in t around 0 12.5%

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

Reproduce

herbie shell --seed 2024139 
(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)))