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

Percentage Accurate: 95.1% → 98.1%

Time: 19.5s

Alternatives: 22

Speedup: 0.5×

• 35.7% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = -4.6271208579359695e+150
  2. y = -3.2756088174104586e-179
  3. z = -1.7514928648887628e-65
  4. t = 6.355771710690433e-73
  5. a = 8.662249039568471e-11
  6. b = -1.7197983326744749e+151

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 78.0%

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

4. Final simplification 99.2%

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

Alternative 2: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 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. Step-by-step derivation

   1. +-commutative 96.5%

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

   2. fma-def 97.6%

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

   3. associate--l+ 97.6%

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

   4. sub-neg 97.6%

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

   5. metadata-eval 97.6%

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

   6. sub-neg 97.6%

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

   7. associate-+l- 97.6%

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

   8. fma-neg 98.0%

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

   9. sub-neg 98.0%

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

   10. metadata-eval 98.0%

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

   11. remove-double-neg 98.0%

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

   12. sub-neg 98.0%

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

   13. metadata-eval 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 3: 36.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+182}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -190000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 13:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+38}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{+209}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- y 2.0))))
   (if (<= b -7.5e+182)
     (* t b)
     (if (<= b -190000000000.0)
       t_2
       (if (<= b 3.3e-271)
         t_1
         (if (<= b 6.5e-238)
           x
           (if (<= b 13.0)
             t_1
             (if (<= b 2e+38)
               (* t b)
               (if (<= b 3.2e+150) t_1 (if (<= b 1e+209) (* t b) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -7.5e+182) {
		tmp = t * b;
	} else if (b <= -190000000000.0) {
		tmp = t_2;
	} else if (b <= 3.3e-271) {
		tmp = t_1;
	} else if (b <= 6.5e-238) {
		tmp = x;
	} else if (b <= 13.0) {
		tmp = t_1;
	} else if (b <= 2e+38) {
		tmp = t * b;
	} else if (b <= 3.2e+150) {
		tmp = t_1;
	} else if (b <= 1e+209) {
		tmp = t * b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * (y - 2.0d0)
    if (b <= (-7.5d+182)) then
        tmp = t * b
    else if (b <= (-190000000000.0d0)) then
        tmp = t_2
    else if (b <= 3.3d-271) then
        tmp = t_1
    else if (b <= 6.5d-238) then
        tmp = x
    else if (b <= 13.0d0) then
        tmp = t_1
    else if (b <= 2d+38) then
        tmp = t * b
    else if (b <= 3.2d+150) then
        tmp = t_1
    else if (b <= 1d+209) then
        tmp = t * b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -7.5e+182) {
		tmp = t * b;
	} else if (b <= -190000000000.0) {
		tmp = t_2;
	} else if (b <= 3.3e-271) {
		tmp = t_1;
	} else if (b <= 6.5e-238) {
		tmp = x;
	} else if (b <= 13.0) {
		tmp = t_1;
	} else if (b <= 2e+38) {
		tmp = t * b;
	} else if (b <= 3.2e+150) {
		tmp = t_1;
	} else if (b <= 1e+209) {
		tmp = t * b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * (y - 2.0)
	tmp = 0
	if b <= -7.5e+182:
		tmp = t * b
	elif b <= -190000000000.0:
		tmp = t_2
	elif b <= 3.3e-271:
		tmp = t_1
	elif b <= 6.5e-238:
		tmp = x
	elif b <= 13.0:
		tmp = t_1
	elif b <= 2e+38:
		tmp = t * b
	elif b <= 3.2e+150:
		tmp = t_1
	elif b <= 1e+209:
		tmp = t * b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -7.5e+182)
		tmp = Float64(t * b);
	elseif (b <= -190000000000.0)
		tmp = t_2;
	elseif (b <= 3.3e-271)
		tmp = t_1;
	elseif (b <= 6.5e-238)
		tmp = x;
	elseif (b <= 13.0)
		tmp = t_1;
	elseif (b <= 2e+38)
		tmp = Float64(t * b);
	elseif (b <= 3.2e+150)
		tmp = t_1;
	elseif (b <= 1e+209)
		tmp = Float64(t * b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -7.5e+182)
		tmp = t * b;
	elseif (b <= -190000000000.0)
		tmp = t_2;
	elseif (b <= 3.3e-271)
		tmp = t_1;
	elseif (b <= 6.5e-238)
		tmp = x;
	elseif (b <= 13.0)
		tmp = t_1;
	elseif (b <= 2e+38)
		tmp = t * b;
	elseif (b <= 3.2e+150)
		tmp = t_1;
	elseif (b <= 1e+209)
		tmp = t * b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+182], N[(t * b), $MachinePrecision], If[LessEqual[b, -190000000000.0], t$95$2, If[LessEqual[b, 3.3e-271], t$95$1, If[LessEqual[b, 6.5e-238], x, If[LessEqual[b, 13.0], t$95$1, If[LessEqual[b, 2e+38], N[(t * b), $MachinePrecision], If[LessEqual[b, 3.2e+150], t$95$1, If[LessEqual[b, 1e+209], N[(t * b), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.49999999999999989e182 or 13 < b < 1.99999999999999995e38 or 3.20000000000000016e150 < b < 1.0000000000000001e209

   1. Initial program 94.2%

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

   3. Taylor expanded in a around 0 96.2%

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

   4. Taylor expanded in t around inf 62.5%

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

   if -7.49999999999999989e182 < b < -1.9e11 or 1.0000000000000001e209 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in t around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-in 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in t around 0 50.1%

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

   if -1.9e11 < b < 3.3000000000000002e-271 or 6.5000000000000006e-238 < b < 13 or 1.99999999999999995e38 < b < 3.20000000000000016e150

   1. Initial program 98.5%

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

   3. Taylor expanded in a around inf 47.1%

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

   if 3.3000000000000002e-271 < b < 6.5000000000000006e-238

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 63.4%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+182}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -190000000000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 13:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+38}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 10^{+209}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := a \cdot \left(1 - t\right)\\ t_3 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -115000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (* a (- 1.0 t)))
        (t_3 (* b (- (+ y t) 2.0))))
   (if (<= b -115000000000.0)
     t_3
     (if (<= b 3.4e-271)
       t_2
       (if (<= b 2.1e-237)
         x
         (if (<= b 1.75e-140)
           t_2
           (if (<= b 8.5e-77)
             t_1
             (if (<= b 7.5e+62)
               (+ x (* t b))
               (if (<= b 4.8e+115) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = a * (1.0 - t);
	double t_3 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -115000000000.0) {
		tmp = t_3;
	} else if (b <= 3.4e-271) {
		tmp = t_2;
	} else if (b <= 2.1e-237) {
		tmp = x;
	} else if (b <= 1.75e-140) {
		tmp = t_2;
	} else if (b <= 8.5e-77) {
		tmp = t_1;
	} else if (b <= 7.5e+62) {
		tmp = x + (t * b);
	} else if (b <= 4.8e+115) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = a * (1.0d0 - t)
    t_3 = b * ((y + t) - 2.0d0)
    if (b <= (-115000000000.0d0)) then
        tmp = t_3
    else if (b <= 3.4d-271) then
        tmp = t_2
    else if (b <= 2.1d-237) then
        tmp = x
    else if (b <= 1.75d-140) then
        tmp = t_2
    else if (b <= 8.5d-77) then
        tmp = t_1
    else if (b <= 7.5d+62) then
        tmp = x + (t * b)
    else if (b <= 4.8d+115) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = a * (1.0 - t);
	double t_3 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -115000000000.0) {
		tmp = t_3;
	} else if (b <= 3.4e-271) {
		tmp = t_2;
	} else if (b <= 2.1e-237) {
		tmp = x;
	} else if (b <= 1.75e-140) {
		tmp = t_2;
	} else if (b <= 8.5e-77) {
		tmp = t_1;
	} else if (b <= 7.5e+62) {
		tmp = x + (t * b);
	} else if (b <= 4.8e+115) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = a * (1.0 - t)
	t_3 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -115000000000.0:
		tmp = t_3
	elif b <= 3.4e-271:
		tmp = t_2
	elif b <= 2.1e-237:
		tmp = x
	elif b <= 1.75e-140:
		tmp = t_2
	elif b <= 8.5e-77:
		tmp = t_1
	elif b <= 7.5e+62:
		tmp = x + (t * b)
	elif b <= 4.8e+115:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(a * Float64(1.0 - t))
	t_3 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -115000000000.0)
		tmp = t_3;
	elseif (b <= 3.4e-271)
		tmp = t_2;
	elseif (b <= 2.1e-237)
		tmp = x;
	elseif (b <= 1.75e-140)
		tmp = t_2;
	elseif (b <= 8.5e-77)
		tmp = t_1;
	elseif (b <= 7.5e+62)
		tmp = Float64(x + Float64(t * b));
	elseif (b <= 4.8e+115)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = a * (1.0 - t);
	t_3 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -115000000000.0)
		tmp = t_3;
	elseif (b <= 3.4e-271)
		tmp = t_2;
	elseif (b <= 2.1e-237)
		tmp = x;
	elseif (b <= 1.75e-140)
		tmp = t_2;
	elseif (b <= 8.5e-77)
		tmp = t_1;
	elseif (b <= 7.5e+62)
		tmp = x + (t * b);
	elseif (b <= 4.8e+115)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -115000000000.0], t$95$3, If[LessEqual[b, 3.4e-271], t$95$2, If[LessEqual[b, 2.1e-237], x, If[LessEqual[b, 1.75e-140], t$95$2, If[LessEqual[b, 8.5e-77], t$95$1, If[LessEqual[b, 7.5e+62], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e+115], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.15e11 or 4.8000000000000001e115 < b

   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 b around inf 75.2%

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

   if -1.15e11 < b < 3.4000000000000001e-271 or 2.1000000000000001e-237 < b < 1.7499999999999999e-140

   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 55.1%

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

   if 3.4000000000000001e-271 < b < 2.1000000000000001e-237

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 63.4%

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

   if 1.7499999999999999e-140 < b < 8.4999999999999998e-77 or 7.49999999999999998e62 < b < 4.8000000000000001e115

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf 64.6%

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

   if 8.4999999999999998e-77 < b < 7.49999999999999998e62

   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 85.3%

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

   4. Taylor expanded in a around 0 67.8%

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

   5. Taylor expanded in t around inf 58.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -115000000000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-77}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 76:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.3 \cdot 10^{+56} \lor \neg \left(b \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -1.05e+14)
     t_2
     (if (<= b 3e-140)
       t_1
       (if (<= b 4e-77)
         t_3
         (if (<= b 76.0)
           t_1
           (if (or (<= b 7.3e+56) (not (<= b 4.6e+115))) t_2 (+ x t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.05e+14) {
		tmp = t_2;
	} else if (b <= 3e-140) {
		tmp = t_1;
	} else if (b <= 4e-77) {
		tmp = t_3;
	} else if (b <= 76.0) {
		tmp = t_1;
	} else if ((b <= 7.3e+56) || !(b <= 4.6e+115)) {
		tmp = t_2;
	} else {
		tmp = x + t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = z * (1.0d0 - y)
    if (b <= (-1.05d+14)) then
        tmp = t_2
    else if (b <= 3d-140) then
        tmp = t_1
    else if (b <= 4d-77) then
        tmp = t_3
    else if (b <= 76.0d0) then
        tmp = t_1
    else if ((b <= 7.3d+56) .or. (.not. (b <= 4.6d+115))) then
        tmp = t_2
    else
        tmp = x + t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.05e+14) {
		tmp = t_2;
	} else if (b <= 3e-140) {
		tmp = t_1;
	} else if (b <= 4e-77) {
		tmp = t_3;
	} else if (b <= 76.0) {
		tmp = t_1;
	} else if ((b <= 7.3e+56) || !(b <= 4.6e+115)) {
		tmp = t_2;
	} else {
		tmp = x + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -1.05e+14:
		tmp = t_2
	elif b <= 3e-140:
		tmp = t_1
	elif b <= 4e-77:
		tmp = t_3
	elif b <= 76.0:
		tmp = t_1
	elif (b <= 7.3e+56) or not (b <= 4.6e+115):
		tmp = t_2
	else:
		tmp = x + t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -1.05e+14)
		tmp = t_2;
	elseif (b <= 3e-140)
		tmp = t_1;
	elseif (b <= 4e-77)
		tmp = t_3;
	elseif (b <= 76.0)
		tmp = t_1;
	elseif ((b <= 7.3e+56) || !(b <= 4.6e+115))
		tmp = t_2;
	else
		tmp = Float64(x + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -1.05e+14)
		tmp = t_2;
	elseif (b <= 3e-140)
		tmp = t_1;
	elseif (b <= 4e-77)
		tmp = t_3;
	elseif (b <= 76.0)
		tmp = t_1;
	elseif ((b <= 7.3e+56) || ~((b <= 4.6e+115)))
		tmp = t_2;
	else
		tmp = x + t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+14], t$95$2, If[LessEqual[b, 3e-140], t$95$1, If[LessEqual[b, 4e-77], t$95$3, If[LessEqual[b, 76.0], t$95$1, If[Or[LessEqual[b, 7.3e+56], N[Not[LessEqual[b, 4.6e+115]], $MachinePrecision]], t$95$2, N[(x + t$95$3), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.05e14 or 76 < b < 7.3e56 or 4.60000000000000007e115 < b

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 87.8%

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

   4. Taylor expanded in a around 0 83.6%

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

   if -1.05e14 < b < 3.00000000000000018e-140 or 3.9999999999999997e-77 < b < 76

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 72.9%

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

   4. Taylor expanded in b around 0 69.3%

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

   if 3.00000000000000018e-140 < b < 3.9999999999999997e-77

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 65.0%

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

   if 7.3e56 < b < 4.60000000000000007e115

   1. Initial program 92.3%

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

   3. Taylor expanded in a around 0 77.5%

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

   4. Taylor expanded in b around 0 69.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-140}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 76:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.3 \cdot 10^{+56} \lor \neg \left(b \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-76}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 35:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+50} \lor \neg \left(b \leq 3.8 \cdot 10^{+80}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -7.6e+15)
     t_2
     (if (<= b 4.5e-140)
       t_1
       (if (<= b 1.2e-76)
         t_3
         (if (<= b 35.0)
           t_1
           (if (or (<= b 7.2e+50) (not (<= b 3.8e+80))) t_2 (+ x t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -7.6e+15) {
		tmp = t_2;
	} else if (b <= 4.5e-140) {
		tmp = t_1;
	} else if (b <= 1.2e-76) {
		tmp = t_3;
	} else if (b <= 35.0) {
		tmp = t_1;
	} else if ((b <= 7.2e+50) || !(b <= 3.8e+80)) {
		tmp = t_2;
	} else {
		tmp = x + t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = z * (1.0d0 - y)
    if (b <= (-7.6d+15)) then
        tmp = t_2
    else if (b <= 4.5d-140) then
        tmp = t_1
    else if (b <= 1.2d-76) then
        tmp = t_3
    else if (b <= 35.0d0) then
        tmp = t_1
    else if ((b <= 7.2d+50) .or. (.not. (b <= 3.8d+80))) then
        tmp = t_2
    else
        tmp = x + t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -7.6e+15) {
		tmp = t_2;
	} else if (b <= 4.5e-140) {
		tmp = t_1;
	} else if (b <= 1.2e-76) {
		tmp = t_3;
	} else if (b <= 35.0) {
		tmp = t_1;
	} else if ((b <= 7.2e+50) || !(b <= 3.8e+80)) {
		tmp = t_2;
	} else {
		tmp = x + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = b * ((y + t) - 2.0)
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -7.6e+15:
		tmp = t_2
	elif b <= 4.5e-140:
		tmp = t_1
	elif b <= 1.2e-76:
		tmp = t_3
	elif b <= 35.0:
		tmp = t_1
	elif (b <= 7.2e+50) or not (b <= 3.8e+80):
		tmp = t_2
	else:
		tmp = x + t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -7.6e+15)
		tmp = t_2;
	elseif (b <= 4.5e-140)
		tmp = t_1;
	elseif (b <= 1.2e-76)
		tmp = t_3;
	elseif (b <= 35.0)
		tmp = t_1;
	elseif ((b <= 7.2e+50) || !(b <= 3.8e+80))
		tmp = t_2;
	else
		tmp = Float64(x + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -7.6e+15)
		tmp = t_2;
	elseif (b <= 4.5e-140)
		tmp = t_1;
	elseif (b <= 1.2e-76)
		tmp = t_3;
	elseif (b <= 35.0)
		tmp = t_1;
	elseif ((b <= 7.2e+50) || ~((b <= 3.8e+80)))
		tmp = t_2;
	else
		tmp = x + t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.6e+15], t$95$2, If[LessEqual[b, 4.5e-140], t$95$1, If[LessEqual[b, 1.2e-76], t$95$3, If[LessEqual[b, 35.0], t$95$1, If[Or[LessEqual[b, 7.2e+50], N[Not[LessEqual[b, 3.8e+80]], $MachinePrecision]], t$95$2, N[(x + t$95$3), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.6e15 or 35 < b < 7.19999999999999972e50 or 3.79999999999999997e80 < b

   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 b around inf 74.5%

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

   if -7.6e15 < b < 4.50000000000000004e-140 or 1.20000000000000007e-76 < b < 35

   1. Initial program 99.1%

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

   3. Taylor expanded in 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 69.6%

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

   if 4.50000000000000004e-140 < b < 1.20000000000000007e-76

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 65.0%

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

   if 7.19999999999999972e50 < b < 3.79999999999999997e80

   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 0 70.8%

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

   4. Taylor expanded in b around 0 69.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-140}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-76}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 35:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+50} \lor \neg \left(b \leq 3.8 \cdot 10^{+80}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(t - 2\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- t 2.0)))) (t_2 (* y (- b z))))
   (if (<= y -2.7e+37)
     t_2
     (if (<= y 8e-282)
       t_1
       (if (<= y 1.66e-168)
         (* t (- b a))
         (if (<= y 2.9e-162)
           t_1
           (if (<= y 4e-125) (* a (- 1.0 t)) (if (<= y 6.7e+36) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (t - 2.0));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.7e+37) {
		tmp = t_2;
	} else if (y <= 8e-282) {
		tmp = t_1;
	} else if (y <= 1.66e-168) {
		tmp = t * (b - a);
	} else if (y <= 2.9e-162) {
		tmp = t_1;
	} else if (y <= 4e-125) {
		tmp = a * (1.0 - t);
	} else if (y <= 6.7e+36) {
		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 + (b * (t - 2.0d0))
    t_2 = y * (b - z)
    if (y <= (-2.7d+37)) then
        tmp = t_2
    else if (y <= 8d-282) then
        tmp = t_1
    else if (y <= 1.66d-168) then
        tmp = t * (b - a)
    else if (y <= 2.9d-162) then
        tmp = t_1
    else if (y <= 4d-125) then
        tmp = a * (1.0d0 - t)
    else if (y <= 6.7d+36) 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 + (b * (t - 2.0));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.7e+37) {
		tmp = t_2;
	} else if (y <= 8e-282) {
		tmp = t_1;
	} else if (y <= 1.66e-168) {
		tmp = t * (b - a);
	} else if (y <= 2.9e-162) {
		tmp = t_1;
	} else if (y <= 4e-125) {
		tmp = a * (1.0 - t);
	} else if (y <= 6.7e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * (t - 2.0))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -2.7e+37:
		tmp = t_2
	elif y <= 8e-282:
		tmp = t_1
	elif y <= 1.66e-168:
		tmp = t * (b - a)
	elif y <= 2.9e-162:
		tmp = t_1
	elif y <= 4e-125:
		tmp = a * (1.0 - t)
	elif y <= 6.7e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(t - 2.0)))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.7e+37)
		tmp = t_2;
	elseif (y <= 8e-282)
		tmp = t_1;
	elseif (y <= 1.66e-168)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 2.9e-162)
		tmp = t_1;
	elseif (y <= 4e-125)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 6.7e+36)
		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 + (b * (t - 2.0));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.7e+37)
		tmp = t_2;
	elseif (y <= 8e-282)
		tmp = t_1;
	elseif (y <= 1.66e-168)
		tmp = t * (b - a);
	elseif (y <= 2.9e-162)
		tmp = t_1;
	elseif (y <= 4e-125)
		tmp = a * (1.0 - t);
	elseif (y <= 6.7e+36)
		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[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+37], t$95$2, If[LessEqual[y, 8e-282], t$95$1, If[LessEqual[y, 1.66e-168], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-162], t$95$1, If[LessEqual[y, 4e-125], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.7e+36], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.69999999999999986e37 or 6.6999999999999997e36 < y

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf 64.0%

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

   if -2.69999999999999986e37 < y < 8.0000000000000001e-282 or 1.65999999999999998e-168 < y < 2.9000000000000001e-162 or 4.00000000000000005e-125 < y < 6.6999999999999997e36

   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 83.7%

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

   4. Taylor expanded in a around 0 62.9%

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

   5. Taylor expanded in y around 0 62.3%

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

   if 8.0000000000000001e-282 < y < 1.65999999999999998e-168

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 65.9%

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

   if 2.9000000000000001e-162 < y < 4.00000000000000005e-125

   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 69.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-282}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-162}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+36}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.95 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-77}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 80:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+57}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 1.62 \cdot 10^{+118}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -2.95e+16)
     t_2
     (if (<= b 8.5e-142)
       t_1
       (if (<= b 4.4e-77)
         t_3
         (if (<= b 80.0)
           t_1
           (if (<= b 1.25e+57)
             (+ x (* b (- t 2.0)))
             (if (<= b 1.62e+118) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -2.95e+16) {
		tmp = t_2;
	} else if (b <= 8.5e-142) {
		tmp = t_1;
	} else if (b <= 4.4e-77) {
		tmp = t_3;
	} else if (b <= 80.0) {
		tmp = t_1;
	} else if (b <= 1.25e+57) {
		tmp = x + (b * (t - 2.0));
	} else if (b <= 1.62e+118) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = z * (1.0d0 - y)
    if (b <= (-2.95d+16)) then
        tmp = t_2
    else if (b <= 8.5d-142) then
        tmp = t_1
    else if (b <= 4.4d-77) then
        tmp = t_3
    else if (b <= 80.0d0) then
        tmp = t_1
    else if (b <= 1.25d+57) then
        tmp = x + (b * (t - 2.0d0))
    else if (b <= 1.62d+118) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -2.95e+16) {
		tmp = t_2;
	} else if (b <= 8.5e-142) {
		tmp = t_1;
	} else if (b <= 4.4e-77) {
		tmp = t_3;
	} else if (b <= 80.0) {
		tmp = t_1;
	} else if (b <= 1.25e+57) {
		tmp = x + (b * (t - 2.0));
	} else if (b <= 1.62e+118) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = b * ((y + t) - 2.0)
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -2.95e+16:
		tmp = t_2
	elif b <= 8.5e-142:
		tmp = t_1
	elif b <= 4.4e-77:
		tmp = t_3
	elif b <= 80.0:
		tmp = t_1
	elif b <= 1.25e+57:
		tmp = x + (b * (t - 2.0))
	elif b <= 1.62e+118:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -2.95e+16)
		tmp = t_2;
	elseif (b <= 8.5e-142)
		tmp = t_1;
	elseif (b <= 4.4e-77)
		tmp = t_3;
	elseif (b <= 80.0)
		tmp = t_1;
	elseif (b <= 1.25e+57)
		tmp = Float64(x + Float64(b * Float64(t - 2.0)));
	elseif (b <= 1.62e+118)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -2.95e+16)
		tmp = t_2;
	elseif (b <= 8.5e-142)
		tmp = t_1;
	elseif (b <= 4.4e-77)
		tmp = t_3;
	elseif (b <= 80.0)
		tmp = t_1;
	elseif (b <= 1.25e+57)
		tmp = x + (b * (t - 2.0));
	elseif (b <= 1.62e+118)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.95e+16], t$95$2, If[LessEqual[b, 8.5e-142], t$95$1, If[LessEqual[b, 4.4e-77], t$95$3, If[LessEqual[b, 80.0], t$95$1, If[LessEqual[b, 1.25e+57], N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.62e+118], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.95e16 or 1.6199999999999999e118 < b

   1. Initial program 93.4%

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

   3. Taylor expanded in b around inf 76.4%

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

   if -2.95e16 < b < 8.4999999999999996e-142 or 4.40000000000000014e-77 < b < 80

   1. Initial program 99.1%

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

   3. Taylor expanded in 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 69.6%

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

   if 8.4999999999999996e-142 < b < 4.40000000000000014e-77 or 1.24999999999999993e57 < b < 1.6199999999999999e118

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf 63.4%

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

   if 80 < b < 1.24999999999999993e57

   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 91.2%

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

   4. Taylor expanded in a around 0 78.2%

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

   5. Taylor expanded in y around 0 65.3%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-142}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 80:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+57}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 1.62 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 33.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.18 \cdot 10^{+175}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 100 \lor \neg \left(b \leq 5 \cdot 10^{+38}\right) \land b \leq 8.5 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -2.18e+175)
     (* t b)
     (if (<= b 3.4e-271)
       t_1
       (if (<= b 6.5e-238)
         x
         (if (or (<= b 100.0) (and (not (<= b 5e+38)) (<= b 8.5e+148)))
           t_1
           (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -2.18e+175) {
		tmp = t * b;
	} else if (b <= 3.4e-271) {
		tmp = t_1;
	} else if (b <= 6.5e-238) {
		tmp = x;
	} else if ((b <= 100.0) || (!(b <= 5e+38) && (b <= 8.5e+148))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-2.18d+175)) then
        tmp = t * b
    else if (b <= 3.4d-271) then
        tmp = t_1
    else if (b <= 6.5d-238) then
        tmp = x
    else if ((b <= 100.0d0) .or. (.not. (b <= 5d+38)) .and. (b <= 8.5d+148)) then
        tmp = t_1
    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 t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -2.18e+175) {
		tmp = t * b;
	} else if (b <= 3.4e-271) {
		tmp = t_1;
	} else if (b <= 6.5e-238) {
		tmp = x;
	} else if ((b <= 100.0) || (!(b <= 5e+38) && (b <= 8.5e+148))) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -2.18e+175:
		tmp = t * b
	elif b <= 3.4e-271:
		tmp = t_1
	elif b <= 6.5e-238:
		tmp = x
	elif (b <= 100.0) or (not (b <= 5e+38) and (b <= 8.5e+148)):
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -2.18e+175)
		tmp = Float64(t * b);
	elseif (b <= 3.4e-271)
		tmp = t_1;
	elseif (b <= 6.5e-238)
		tmp = x;
	elseif ((b <= 100.0) || (!(b <= 5e+38) && (b <= 8.5e+148)))
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -2.18e+175)
		tmp = t * b;
	elseif (b <= 3.4e-271)
		tmp = t_1;
	elseif (b <= 6.5e-238)
		tmp = x;
	elseif ((b <= 100.0) || (~((b <= 5e+38)) && (b <= 8.5e+148)))
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.18e+175], N[(t * b), $MachinePrecision], If[LessEqual[b, 3.4e-271], t$95$1, If[LessEqual[b, 6.5e-238], x, If[Or[LessEqual[b, 100.0], And[N[Not[LessEqual[b, 5e+38]], $MachinePrecision], LessEqual[b, 8.5e+148]]], t$95$1, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1799999999999999e175 or 100 < b < 4.9999999999999997e38 or 8.4999999999999996e148 < b

   1. Initial program 93.7%

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

   3. Taylor expanded in a around 0 96.8%

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

   4. Taylor expanded in t around inf 55.6%

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

   if -2.1799999999999999e175 < b < 3.4000000000000001e-271 or 6.5000000000000006e-238 < b < 100 or 4.9999999999999997e38 < b < 8.4999999999999996e148

   1. Initial program 98.2%

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

   3. Taylor expanded in a around inf 42.4%

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

   if 3.4000000000000001e-271 < b < 6.5000000000000006e-238

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 63.4%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.18 \cdot 10^{+175}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 100 \lor \neg \left(b \leq 5 \cdot 10^{+38}\right) \land b \leq 8.5 \cdot 10^{+148}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-290}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.65 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 135000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -8.6e+57)
     t_2
     (if (<= t -3.3e-84)
       t_1
       (if (<= t -1.25e-290)
         a
         (if (<= t 1.25e-92)
           t_1
           (if (<= t 5.65e-36) x (if (<= t 135000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8.6e+57) {
		tmp = t_2;
	} else if (t <= -3.3e-84) {
		tmp = t_1;
	} else if (t <= -1.25e-290) {
		tmp = a;
	} else if (t <= 1.25e-92) {
		tmp = t_1;
	} else if (t <= 5.65e-36) {
		tmp = x;
	} else if (t <= 135000000.0) {
		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 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-8.6d+57)) then
        tmp = t_2
    else if (t <= (-3.3d-84)) then
        tmp = t_1
    else if (t <= (-1.25d-290)) then
        tmp = a
    else if (t <= 1.25d-92) then
        tmp = t_1
    else if (t <= 5.65d-36) then
        tmp = x
    else if (t <= 135000000.0d0) 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 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8.6e+57) {
		tmp = t_2;
	} else if (t <= -3.3e-84) {
		tmp = t_1;
	} else if (t <= -1.25e-290) {
		tmp = a;
	} else if (t <= 1.25e-92) {
		tmp = t_1;
	} else if (t <= 5.65e-36) {
		tmp = x;
	} else if (t <= 135000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -8.6e+57:
		tmp = t_2
	elif t <= -3.3e-84:
		tmp = t_1
	elif t <= -1.25e-290:
		tmp = a
	elif t <= 1.25e-92:
		tmp = t_1
	elif t <= 5.65e-36:
		tmp = x
	elif t <= 135000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.6e+57)
		tmp = t_2;
	elseif (t <= -3.3e-84)
		tmp = t_1;
	elseif (t <= -1.25e-290)
		tmp = a;
	elseif (t <= 1.25e-92)
		tmp = t_1;
	elseif (t <= 5.65e-36)
		tmp = x;
	elseif (t <= 135000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -8.6e+57)
		tmp = t_2;
	elseif (t <= -3.3e-84)
		tmp = t_1;
	elseif (t <= -1.25e-290)
		tmp = a;
	elseif (t <= 1.25e-92)
		tmp = t_1;
	elseif (t <= 5.65e-36)
		tmp = x;
	elseif (t <= 135000000.0)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+57], t$95$2, If[LessEqual[t, -3.3e-84], t$95$1, If[LessEqual[t, -1.25e-290], a, If[LessEqual[t, 1.25e-92], t$95$1, If[LessEqual[t, 5.65e-36], x, If[LessEqual[t, 135000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.60000000000000066e57 or 1.35e8 < 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 74.7%

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

   if -8.60000000000000066e57 < t < -3.29999999999999984e-84 or -1.25e-290 < t < 1.25000000000000003e-92 or 5.6500000000000001e-36 < t < 1.35e8

   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 45.2%

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

   if -3.29999999999999984e-84 < t < -1.25e-290

   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 a around inf 35.0%

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

   4. Taylor expanded in t around 0 35.0%

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

   if 1.25000000000000003e-92 < t < 5.6500000000000001e-36

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 41.7%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-290}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 5.65 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 135000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot b\\ t_2 := a \cdot \left(1 - t\right)\\ t_3 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-263}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-162}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t b))) (t_2 (* a (- 1.0 t))) (t_3 (* y (- b z))))
   (if (<= y -5e+34)
     t_3
     (if (<= y -6e-265)
       t_1
       (if (<= y 1.9e-263)
         t_2
         (if (<= y 4e-162)
           (* t (- b a))
           (if (<= y 1.15e-125) t_2 (if (<= y 2.35e+37) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * b);
	double t_2 = a * (1.0 - t);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -5e+34) {
		tmp = t_3;
	} else if (y <= -6e-265) {
		tmp = t_1;
	} else if (y <= 1.9e-263) {
		tmp = t_2;
	} else if (y <= 4e-162) {
		tmp = t * (b - a);
	} else if (y <= 1.15e-125) {
		tmp = t_2;
	} else if (y <= 2.35e+37) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (t * b)
    t_2 = a * (1.0d0 - t)
    t_3 = y * (b - z)
    if (y <= (-5d+34)) then
        tmp = t_3
    else if (y <= (-6d-265)) then
        tmp = t_1
    else if (y <= 1.9d-263) then
        tmp = t_2
    else if (y <= 4d-162) then
        tmp = t * (b - a)
    else if (y <= 1.15d-125) then
        tmp = t_2
    else if (y <= 2.35d+37) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * b);
	double t_2 = a * (1.0 - t);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -5e+34) {
		tmp = t_3;
	} else if (y <= -6e-265) {
		tmp = t_1;
	} else if (y <= 1.9e-263) {
		tmp = t_2;
	} else if (y <= 4e-162) {
		tmp = t * (b - a);
	} else if (y <= 1.15e-125) {
		tmp = t_2;
	} else if (y <= 2.35e+37) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * b)
	t_2 = a * (1.0 - t)
	t_3 = y * (b - z)
	tmp = 0
	if y <= -5e+34:
		tmp = t_3
	elif y <= -6e-265:
		tmp = t_1
	elif y <= 1.9e-263:
		tmp = t_2
	elif y <= 4e-162:
		tmp = t * (b - a)
	elif y <= 1.15e-125:
		tmp = t_2
	elif y <= 2.35e+37:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * b))
	t_2 = Float64(a * Float64(1.0 - t))
	t_3 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -5e+34)
		tmp = t_3;
	elseif (y <= -6e-265)
		tmp = t_1;
	elseif (y <= 1.9e-263)
		tmp = t_2;
	elseif (y <= 4e-162)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 1.15e-125)
		tmp = t_2;
	elseif (y <= 2.35e+37)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * b);
	t_2 = a * (1.0 - t);
	t_3 = y * (b - z);
	tmp = 0.0;
	if (y <= -5e+34)
		tmp = t_3;
	elseif (y <= -6e-265)
		tmp = t_1;
	elseif (y <= 1.9e-263)
		tmp = t_2;
	elseif (y <= 4e-162)
		tmp = t * (b - a);
	elseif (y <= 1.15e-125)
		tmp = t_2;
	elseif (y <= 2.35e+37)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+34], t$95$3, If[LessEqual[y, -6e-265], t$95$1, If[LessEqual[y, 1.9e-263], t$95$2, If[LessEqual[y, 4e-162], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-125], t$95$2, If[LessEqual[y, 2.35e+37], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.9999999999999998e34 or 2.3499999999999998e37 < y

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf 64.0%

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

   if -4.9999999999999998e34 < y < -5.9999999999999996e-265 or 1.15e-125 < y < 2.3499999999999998e37

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 82.8%

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

   4. Taylor expanded in a around 0 63.9%

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

   5. Taylor expanded in t around inf 52.1%

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

   if -5.9999999999999996e-265 < y < 1.90000000000000002e-263 or 3.99999999999999982e-162 < y < 1.15e-125

   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 57.8%

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

   if 1.90000000000000002e-263 < y < 3.99999999999999982e-162

   1. Initial program 95.9%

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

   3. Taylor expanded in t around inf 67.3%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-265}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-263}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-162}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+44} \lor \neg \left(b \leq 100 \lor \neg \left(b \leq 6.6 \cdot 10^{+37}\right) \land b \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.2e+44)
         (not (or (<= b 100.0) (and (not (<= b 6.6e+37)) (<= b 4.6e+115)))))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.2e+44) || !((b <= 100.0) || (!(b <= 6.6e+37) && (b <= 4.6e+115)))) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-9.2d+44)) .or. (.not. (b <= 100.0d0) .or. (.not. (b <= 6.6d+37)) .and. (b <= 4.6d+115))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.2e+44) || !((b <= 100.0) || (!(b <= 6.6e+37) && (b <= 4.6e+115)))) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -9.2e+44) or not ((b <= 100.0) or (not (b <= 6.6e+37) and (b <= 4.6e+115))):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9.2e+44) || !((b <= 100.0) || (!(b <= 6.6e+37) && (b <= 4.6e+115))))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -9.2e+44) || ~(((b <= 100.0) || (~((b <= 6.6e+37)) && (b <= 4.6e+115)))))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9.2e+44], N[Not[Or[LessEqual[b, 100.0], And[N[Not[LessEqual[b, 6.6e+37]], $MachinePrecision], LessEqual[b, 4.6e+115]]]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.20000000000000018e44 or 100 < b < 6.6000000000000002e37 or 4.60000000000000007e115 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 90.0%

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

   4. Taylor expanded in a around 0 87.2%

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

   if -9.20000000000000018e44 < b < 100 or 6.6000000000000002e37 < b < 4.60000000000000007e115

   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 b around 0 93.5%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+44} \lor \neg \left(b \leq 100 \lor \neg \left(b \leq 6.6 \cdot 10^{+37}\right) \land b \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := t\_2 + t\_1\\ t_4 := x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-77}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+57}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+116}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (+ t_2 t_1))
        (t_4 (+ x (+ t_1 (* z (- 1.0 y))))))
   (if (<= b -7.2e+43)
     t_3
     (if (<= b 3.2e-77)
       t_4
       (if (<= b 1.28e+57) t_3 (if (<= b 8.8e+116) t_4 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = t_2 + t_1;
	double t_4 = x + (t_1 + (z * (1.0 - y)));
	double tmp;
	if (b <= -7.2e+43) {
		tmp = t_3;
	} else if (b <= 3.2e-77) {
		tmp = t_4;
	} else if (b <= 1.28e+57) {
		tmp = t_3;
	} else if (b <= 8.8e+116) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = t_2 + t_1
    t_4 = x + (t_1 + (z * (1.0d0 - y)))
    if (b <= (-7.2d+43)) then
        tmp = t_3
    else if (b <= 3.2d-77) then
        tmp = t_4
    else if (b <= 1.28d+57) then
        tmp = t_3
    else if (b <= 8.8d+116) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = t_2 + t_1;
	double t_4 = x + (t_1 + (z * (1.0 - y)));
	double tmp;
	if (b <= -7.2e+43) {
		tmp = t_3;
	} else if (b <= 3.2e-77) {
		tmp = t_4;
	} else if (b <= 1.28e+57) {
		tmp = t_3;
	} else if (b <= 8.8e+116) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = t_2 + t_1
	t_4 = x + (t_1 + (z * (1.0 - y)))
	tmp = 0
	if b <= -7.2e+43:
		tmp = t_3
	elif b <= 3.2e-77:
		tmp = t_4
	elif b <= 1.28e+57:
		tmp = t_3
	elif b <= 8.8e+116:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(t_2 + t_1)
	t_4 = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))))
	tmp = 0.0
	if (b <= -7.2e+43)
		tmp = t_3;
	elseif (b <= 3.2e-77)
		tmp = t_4;
	elseif (b <= 1.28e+57)
		tmp = t_3;
	elseif (b <= 8.8e+116)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = t_2 + t_1;
	t_4 = x + (t_1 + (z * (1.0 - y)));
	tmp = 0.0;
	if (b <= -7.2e+43)
		tmp = t_3;
	elseif (b <= 3.2e-77)
		tmp = t_4;
	elseif (b <= 1.28e+57)
		tmp = t_3;
	elseif (b <= 8.8e+116)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+43], t$95$3, If[LessEqual[b, 3.2e-77], t$95$4, If[LessEqual[b, 1.28e+57], t$95$3, If[LessEqual[b, 8.8e+116], t$95$4, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.2000000000000002e43 or 3.2e-77 < b < 1.28000000000000001e57

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 90.1%

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

   if -7.2000000000000002e43 < b < 3.2e-77 or 1.28000000000000001e57 < b < 8.799999999999999e116

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0 94.5%

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

   if 8.799999999999999e116 < b

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 88.2%

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

   4. Taylor expanded in a around 0 89.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+43}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-77}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+57}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+116}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;b \leq -2.18 \cdot 10^{+175}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -2.95 \cdot 10^{+16}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= b -2.18e+175)
     (* t b)
     (if (<= b -2.95e+16)
       (* y b)
       (if (<= b 3.4e-271)
         t_1
         (if (<= b 8.5e-219) x (if (<= b 4.2e-5) t_1 (* t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (b <= -2.18e+175) {
		tmp = t * b;
	} else if (b <= -2.95e+16) {
		tmp = y * b;
	} else if (b <= 3.4e-271) {
		tmp = t_1;
	} else if (b <= 8.5e-219) {
		tmp = x;
	} else if (b <= 4.2e-5) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (b <= (-2.18d+175)) then
        tmp = t * b
    else if (b <= (-2.95d+16)) then
        tmp = y * b
    else if (b <= 3.4d-271) then
        tmp = t_1
    else if (b <= 8.5d-219) then
        tmp = x
    else if (b <= 4.2d-5) then
        tmp = t_1
    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 t_1 = t * -a;
	double tmp;
	if (b <= -2.18e+175) {
		tmp = t * b;
	} else if (b <= -2.95e+16) {
		tmp = y * b;
	} else if (b <= 3.4e-271) {
		tmp = t_1;
	} else if (b <= 8.5e-219) {
		tmp = x;
	} else if (b <= 4.2e-5) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if b <= -2.18e+175:
		tmp = t * b
	elif b <= -2.95e+16:
		tmp = y * b
	elif b <= 3.4e-271:
		tmp = t_1
	elif b <= 8.5e-219:
		tmp = x
	elif b <= 4.2e-5:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (b <= -2.18e+175)
		tmp = Float64(t * b);
	elseif (b <= -2.95e+16)
		tmp = Float64(y * b);
	elseif (b <= 3.4e-271)
		tmp = t_1;
	elseif (b <= 8.5e-219)
		tmp = x;
	elseif (b <= 4.2e-5)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (b <= -2.18e+175)
		tmp = t * b;
	elseif (b <= -2.95e+16)
		tmp = y * b;
	elseif (b <= 3.4e-271)
		tmp = t_1;
	elseif (b <= 8.5e-219)
		tmp = x;
	elseif (b <= 4.2e-5)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[b, -2.18e+175], N[(t * b), $MachinePrecision], If[LessEqual[b, -2.95e+16], N[(y * b), $MachinePrecision], If[LessEqual[b, 3.4e-271], t$95$1, If[LessEqual[b, 8.5e-219], x, If[LessEqual[b, 4.2e-5], t$95$1, N[(t * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.1799999999999999e175 or 4.19999999999999977e-5 < b

   1. Initial program 93.4%

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

   3. Taylor expanded in a around 0 91.3%

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

   4. Taylor expanded in t around inf 45.4%

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

   if -2.1799999999999999e175 < b < -2.95e16

   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 z around 0 82.4%

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

   4. Taylor expanded in y around inf 34.9%

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

   if -2.95e16 < b < 3.4000000000000001e-271 or 8.49999999999999964e-219 < b < 4.19999999999999977e-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 t around inf 38.4%

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

   4. Taylor expanded in b around 0 35.7%

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

      1. associate-*r* 35.7%

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

      2. mul-1-neg 35.7%

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

   6. Simplified 35.7%

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

   if 3.4000000000000001e-271 < b < 8.49999999999999964e-219

   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 x around inf 51.0%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.18 \cdot 10^{+175}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -2.95 \cdot 10^{+16}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.3 \cdot 10^{+31}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-267}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.3e+31)
   (* t b)
   (if (<= t -2.5e-88)
     (* y b)
     (if (<= t -3.5e-135)
       x
       (if (<= t 4.8e-267) a (if (<= t 2.9e+19) x (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.3e+31) {
		tmp = t * b;
	} else if (t <= -2.5e-88) {
		tmp = y * b;
	} else if (t <= -3.5e-135) {
		tmp = x;
	} else if (t <= 4.8e-267) {
		tmp = a;
	} else if (t <= 2.9e+19) {
		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 <= (-7.3d+31)) then
        tmp = t * b
    else if (t <= (-2.5d-88)) then
        tmp = y * b
    else if (t <= (-3.5d-135)) then
        tmp = x
    else if (t <= 4.8d-267) then
        tmp = a
    else if (t <= 2.9d+19) 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 <= -7.3e+31) {
		tmp = t * b;
	} else if (t <= -2.5e-88) {
		tmp = y * b;
	} else if (t <= -3.5e-135) {
		tmp = x;
	} else if (t <= 4.8e-267) {
		tmp = a;
	} else if (t <= 2.9e+19) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.3e+31:
		tmp = t * b
	elif t <= -2.5e-88:
		tmp = y * b
	elif t <= -3.5e-135:
		tmp = x
	elif t <= 4.8e-267:
		tmp = a
	elif t <= 2.9e+19:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.3e+31)
		tmp = Float64(t * b);
	elseif (t <= -2.5e-88)
		tmp = Float64(y * b);
	elseif (t <= -3.5e-135)
		tmp = x;
	elseif (t <= 4.8e-267)
		tmp = a;
	elseif (t <= 2.9e+19)
		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 <= -7.3e+31)
		tmp = t * b;
	elseif (t <= -2.5e-88)
		tmp = y * b;
	elseif (t <= -3.5e-135)
		tmp = x;
	elseif (t <= 4.8e-267)
		tmp = a;
	elseif (t <= 2.9e+19)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.3e+31], N[(t * b), $MachinePrecision], If[LessEqual[t, -2.5e-88], N[(y * b), $MachinePrecision], If[LessEqual[t, -3.5e-135], x, If[LessEqual[t, 4.8e-267], a, If[LessEqual[t, 2.9e+19], x, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.30000000000000023e31 or 2.9e19 < 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 a around 0 70.3%

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

   4. Taylor expanded in t around inf 45.3%

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

   if -7.30000000000000023e31 < t < -2.50000000000000004e-88

   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 72.3%

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

   4. Taylor expanded in y around inf 28.2%

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

   if -2.50000000000000004e-88 < t < -3.4999999999999998e-135 or 4.7999999999999996e-267 < t < 2.9e19

   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 31.5%

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

   if -3.4999999999999998e-135 < t < 4.7999999999999996e-267

   1. Initial program 97.1%

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

   3. Taylor expanded in a around inf 38.9%

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

   4. Taylor expanded in t around 0 38.9%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.3 \cdot 10^{+31}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-267}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 16000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -6000.0)
     t_2
     (if (<= t -2.6e-84)
       t_1
       (if (<= t -1.65e-113) x (if (<= t 16000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6000.0) {
		tmp = t_2;
	} else if (t <= -2.6e-84) {
		tmp = t_1;
	} else if (t <= -1.65e-113) {
		tmp = x;
	} else if (t <= 16000000.0) {
		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 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-6000.0d0)) then
        tmp = t_2
    else if (t <= (-2.6d-84)) then
        tmp = t_1
    else if (t <= (-1.65d-113)) then
        tmp = x
    else if (t <= 16000000.0d0) 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 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6000.0) {
		tmp = t_2;
	} else if (t <= -2.6e-84) {
		tmp = t_1;
	} else if (t <= -1.65e-113) {
		tmp = x;
	} else if (t <= 16000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -6000.0:
		tmp = t_2
	elif t <= -2.6e-84:
		tmp = t_1
	elif t <= -1.65e-113:
		tmp = x
	elif t <= 16000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6000.0)
		tmp = t_2;
	elseif (t <= -2.6e-84)
		tmp = t_1;
	elseif (t <= -1.65e-113)
		tmp = x;
	elseif (t <= 16000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -6000.0)
		tmp = t_2;
	elseif (t <= -2.6e-84)
		tmp = t_1;
	elseif (t <= -1.65e-113)
		tmp = x;
	elseif (t <= 16000000.0)
		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[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6000.0], t$95$2, If[LessEqual[t, -2.6e-84], t$95$1, If[LessEqual[t, -1.65e-113], x, If[LessEqual[t, 16000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6e3 or 1.6e7 < 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 72.0%

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

   if -6e3 < t < -2.6e-84 or -1.6500000000000001e-113 < t < 1.6e7

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf 33.8%

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

      1. mul-1-neg 33.8%

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

      2. distribute-rgt-neg-in 33.8%

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

   5. Simplified 33.8%

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

   6. Taylor expanded in t around 0 33.4%

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

   if -2.6e-84 < t < -1.6500000000000001e-113

   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 52.5%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 16000000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{+47} \lor \neg \left(b \leq 35\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -2.1e+47) (not (<= b 35.0)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (+ (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -2.1e+47) || !(b <= 35.0)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + ((a * (1.0 - 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 = z * (1.0d0 - y)
    if ((b <= (-2.1d+47)) .or. (.not. (b <= 35.0d0))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + ((a * (1.0d0 - 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 = z * (1.0 - y);
	double tmp;
	if ((b <= -2.1e+47) || !(b <= 35.0)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -2.1e+47) or not (b <= 35.0):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + ((a * (1.0 - t)) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((b <= -2.1e+47) || !(b <= 35.0))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + t_1));
	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 <= -2.1e+47) || ~((b <= 35.0)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + ((a * (1.0 - t)) + t_1);
	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, -2.1e+47], N[Not[LessEqual[b, 35.0]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1e47 or 35 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in a around 0 89.2%

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

   if -2.1e47 < b < 35

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0 94.1%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+47} \lor \neg \left(b \leq 35\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+14}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.7e+14)
   (* t (- b a))
   (if (<= t 2.2e+14)
     (+ x (+ a (* b (+ y -2.0))))
     (- (* b (- (+ y t) 2.0)) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.7e+14) {
		tmp = t * (b - a);
	} else if (t <= 2.2e+14) {
		tmp = x + (a + (b * (y + -2.0)));
	} else {
		tmp = (b * ((y + t) - 2.0)) - (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 (t <= (-2.7d+14)) then
        tmp = t * (b - a)
    else if (t <= 2.2d+14) then
        tmp = x + (a + (b * (y + (-2.0d0))))
    else
        tmp = (b * ((y + t) - 2.0d0)) - (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 (t <= -2.7e+14) {
		tmp = t * (b - a);
	} else if (t <= 2.2e+14) {
		tmp = x + (a + (b * (y + -2.0)));
	} else {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.7e+14:
		tmp = t * (b - a)
	elif t <= 2.2e+14:
		tmp = x + (a + (b * (y + -2.0)))
	else:
		tmp = (b * ((y + t) - 2.0)) - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.7e+14)
		tmp = Float64(t * Float64(b - a));
	elseif (t <= 2.2e+14)
		tmp = Float64(x + Float64(a + Float64(b * Float64(y + -2.0))));
	else
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.7e+14)
		tmp = t * (b - a);
	elseif (t <= 2.2e+14)
		tmp = x + (a + (b * (y + -2.0)));
	else
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.7e+14], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+14], N[(x + N[(a + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e14

   1. Initial program 91.4%

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

   3. Taylor expanded in t around inf 72.7%

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

   if -2.7e14 < t < 2.2e14

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 74.6%

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

   4. Taylor expanded in t around 0 73.7%

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

      1. associate--l+ 73.7%

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

      2. sub-neg 73.7%

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

      3. metadata-eval 73.7%

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

      4. neg-mul-1 73.7%

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

   6. Simplified 73.7%

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

   if 2.2e14 < t

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. distribute-rgt-neg-in 77.0%

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

   5. Simplified 77.0%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+14}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 66.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4200000000000 \lor \neg \left(t \leq 2.75 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4200000000000.0) (not (<= t 2.75e+14)))
   (* t (- b a))
   (+ x (+ a (* b (+ y -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4200000000000.0) || !(t <= 2.75e+14)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (a + (b * (y + -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4200000000000.0d0)) .or. (.not. (t <= 2.75d+14))) then
        tmp = t * (b - a)
    else
        tmp = x + (a + (b * (y + (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4200000000000.0) || !(t <= 2.75e+14)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (a + (b * (y + -2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4200000000000.0) or not (t <= 2.75e+14):
		tmp = t * (b - a)
	else:
		tmp = x + (a + (b * (y + -2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4200000000000.0) || !(t <= 2.75e+14))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + Float64(a + Float64(b * Float64(y + -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4200000000000.0) || ~((t <= 2.75e+14)))
		tmp = t * (b - a);
	else
		tmp = x + (a + (b * (y + -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4200000000000.0], N[Not[LessEqual[t, 2.75e+14]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(a + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.2e12 or 2.75e14 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf 73.1%

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

   if -4.2e12 < t < 2.75e14

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 74.6%

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

   4. Taylor expanded in t around 0 73.7%

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

      1. associate--l+ 73.7%

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

      2. sub-neg 73.7%

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

      3. metadata-eval 73.7%

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

      4. neg-mul-1 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4200000000000 \lor \neg \left(t \leq 2.75 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 26.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+25}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-267}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6e+25)
   (* t b)
   (if (<= t 6.2e-267) a (if (<= t 3.8e+18) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6e+25) {
		tmp = t * b;
	} else if (t <= 6.2e-267) {
		tmp = a;
	} else if (t <= 3.8e+18) {
		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 <= (-6d+25)) then
        tmp = t * b
    else if (t <= 6.2d-267) then
        tmp = a
    else if (t <= 3.8d+18) 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 <= -6e+25) {
		tmp = t * b;
	} else if (t <= 6.2e-267) {
		tmp = a;
	} else if (t <= 3.8e+18) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6e+25:
		tmp = t * b
	elif t <= 6.2e-267:
		tmp = a
	elif t <= 3.8e+18:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6e+25)
		tmp = Float64(t * b);
	elseif (t <= 6.2e-267)
		tmp = a;
	elseif (t <= 3.8e+18)
		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 <= -6e+25)
		tmp = t * b;
	elseif (t <= 6.2e-267)
		tmp = a;
	elseif (t <= 3.8e+18)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6e+25], N[(t * b), $MachinePrecision], If[LessEqual[t, 6.2e-267], a, If[LessEqual[t, 3.8e+18], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.00000000000000011e25 or 3.8e18 < 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 a around 0 70.3%

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

   4. Taylor expanded in t around inf 45.3%

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

   if -6.00000000000000011e25 < t < 6.2000000000000002e-267

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf 31.8%

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

   4. Taylor expanded in t around 0 27.9%

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

   if 6.2000000000000002e-267 < t < 3.8e18

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 27.6%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+25}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-267}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+44}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.5e+43) x (if (<= x 7.2e+44) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.5e+43) {
		tmp = x;
	} else if (x <= 7.2e+44) {
		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 <= (-8.5d+43)) then
        tmp = x
    else if (x <= 7.2d+44) 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 <= -8.5e+43) {
		tmp = x;
	} else if (x <= 7.2e+44) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.5e+43:
		tmp = x
	elif x <= 7.2e+44:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.5e+43)
		tmp = x;
	elseif (x <= 7.2e+44)
		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 <= -8.5e+43)
		tmp = x;
	elseif (x <= 7.2e+44)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.5e+43], x, If[LessEqual[x, 7.2e+44], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5e43 or 7.2e44 < x

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf 30.6%

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

   if -8.5e43 < x < 7.2e44

   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 a around inf 37.3%

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

   4. Taylor expanded in t around 0 14.9%

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

4. Final simplification 21.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+44}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 11.4% 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 96.5%

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

3. Taylor expanded in a around inf 32.5%

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

4. Taylor expanded in t around 0 12.1%

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

5. Final simplification 12.1%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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)))