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

Percentage Accurate: 94.9% → 97.7%

Time: 11.9s

Alternatives: 19

Speedup: 0.5×

• 36.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* (- (+ y t) 2.0) b))))
   (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))) + (((y + t) - 2.0) * b);
	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))) + (((y + t) - 2.0) * b);
	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))) + (((y + t) - 2.0) * b)
	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(Float64(Float64(y + t) - 2.0) * b))
	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))) + (((y + t) - 2.0) * b);
	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[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 83.9%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 83.9%

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

4. Final simplification 99.2%

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

Alternative 2: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+99}:\\ \;\;\;\;x + t\_2\\ \mathbf{elif}\;b \leq 20:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \left(x + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -3.1e+99)
     (+ x t_2)
     (if (<= b 20.0) (+ x (+ (* z (- 1.0 y)) t_1)) (+ t_2 (+ x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -3.1e+99) {
		tmp = x + t_2;
	} else if (b <= 20.0) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = t_2 + (x + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-3.1d+99)) then
        tmp = x + t_2
    else if (b <= 20.0d0) then
        tmp = x + ((z * (1.0d0 - y)) + t_1)
    else
        tmp = t_2 + (x + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -3.1e+99) {
		tmp = x + t_2;
	} else if (b <= 20.0) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = t_2 + (x + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -3.1e+99:
		tmp = x + t_2
	elif b <= 20.0:
		tmp = x + ((z * (1.0 - y)) + t_1)
	else:
		tmp = t_2 + (x + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -3.1e+99)
		tmp = Float64(x + t_2);
	elseif (b <= 20.0)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	else
		tmp = Float64(t_2 + Float64(x + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -3.1e+99)
		tmp = x + t_2;
	elseif (b <= 20.0)
		tmp = x + ((z * (1.0 - y)) + t_1);
	else
		tmp = t_2 + (x + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -3.1e+99], N[(x + t$95$2), $MachinePrecision], If[LessEqual[b, 20.0], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(x + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1000000000000001e99

   1. Initial program 85.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 85.5%

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

   if -3.1000000000000001e99 < b < 20

   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 b around 0

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 90.5%

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

   if 20 < b

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, 1\right), a\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 93.2%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+99}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 20:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3 \cdot 10^{+98}:\\ \;\;\;\;x + t\_2\\ \mathbf{elif}\;b \leq 0.0056:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -3e+98)
     (+ x t_2)
     (if (<= b 0.0056) (+ x (+ (* z (- 1.0 y)) t_1)) (+ t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -3e+98) {
		tmp = x + t_2;
	} else if (b <= 0.0056) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-3d+98)) then
        tmp = x + t_2
    else if (b <= 0.0056d0) then
        tmp = x + ((z * (1.0d0 - y)) + t_1)
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -3e+98) {
		tmp = x + t_2;
	} else if (b <= 0.0056) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -3e+98:
		tmp = x + t_2
	elif b <= 0.0056:
		tmp = x + ((z * (1.0 - y)) + t_1)
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -3e+98)
		tmp = Float64(x + t_2);
	elseif (b <= 0.0056)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -3e+98)
		tmp = x + t_2;
	elseif (b <= 0.0056)
		tmp = x + ((z * (1.0 - y)) + t_1);
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -3e+98], N[(x + t$95$2), $MachinePrecision], If[LessEqual[b, 0.0056], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.0000000000000001e98

   1. Initial program 85.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 85.5%

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

   if -3.0000000000000001e98 < b < 0.00559999999999999994

   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 b around 0

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 90.5%

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

   if 0.00559999999999999994 < b

   1. Initial program 94.4%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot \left(1 - t\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot -1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot -1 + -1 \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(-1 + t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(t + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot t + -1 \cdot -1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 - t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      16. --lowering--.f64 88.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 88.9%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+98}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 0.0056:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1300:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -2.7e+99)
     t_1
     (if (<= b 1300.0) (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.7e+99) {
		tmp = t_1;
	} else if (b <= 1300.0) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-2.7d+99)) then
        tmp = t_1
    else if (b <= 1300.0d0) then
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.7e+99) {
		tmp = t_1;
	} else if (b <= 1300.0) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -2.7e+99:
		tmp = t_1
	elif b <= 1300.0:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -2.7e+99)
		tmp = t_1;
	elseif (b <= 1300.0)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -2.7e+99)
		tmp = t_1;
	elseif (b <= 1300.0)
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.7e+99], t$95$1, If[LessEqual[b, 1300.0], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.69999999999999989e99 or 1300 < b

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 85.0%

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

   if -2.69999999999999989e99 < b < 1300

   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 b around 0

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 90.6%

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

Alternative 5: 71.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 160:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.15e+88)
     t_1
     (if (<= b 160.0) (+ x (+ a (* z (- 1.0 y)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.15e+88) {
		tmp = t_1;
	} else if (b <= 160.0) {
		tmp = x + (a + (z * (1.0 - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-1.15d+88)) then
        tmp = t_1
    else if (b <= 160.0d0) then
        tmp = x + (a + (z * (1.0d0 - y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.15e+88) {
		tmp = t_1;
	} else if (b <= 160.0) {
		tmp = x + (a + (z * (1.0 - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -1.15e+88:
		tmp = t_1
	elif b <= 160.0:
		tmp = x + (a + (z * (1.0 - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.15e+88)
		tmp = t_1;
	elseif (b <= 160.0)
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -1.15e+88)
		tmp = t_1;
	elseif (b <= 160.0)
		tmp = x + (a + (z * (1.0 - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+88], t$95$1, If[LessEqual[b, 160.0], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1500000000000001e88 or 160 < b

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 85.0%

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

   if -1.1500000000000001e88 < b < 160

   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 b around 0

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 90.6%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \color{blue}{a}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 73.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+88}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 160:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.08 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{-6}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.08e+88) t_1 (if (<= b 1e-6) (+ x (* z (- 1.0 y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.08e+88) {
		tmp = t_1;
	} else if (b <= 1e-6) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-1.08d+88)) then
        tmp = t_1
    else if (b <= 1d-6) then
        tmp = x + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.08e+88) {
		tmp = t_1;
	} else if (b <= 1e-6) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -1.08e+88:
		tmp = t_1
	elif b <= 1e-6:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.08e+88)
		tmp = t_1;
	elseif (b <= 1e-6)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -1.08e+88)
		tmp = t_1;
	elseif (b <= 1e-6)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.08e+88], t$95$1, If[LessEqual[b, 1e-6], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.08000000000000003e88 or 9.99999999999999955e-7 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 84.3%

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

   if -1.08000000000000003e88 < b < 9.99999999999999955e-7

   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 b around 0

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 90.5%

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

   6. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      3. --lowering--.f64 62.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 62.7%

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

Alternative 7: 26.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+42}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-16}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.55e+42)
   (* y b)
   (if (<= y -3.1e-21) x (if (<= y 6.2e-16) z (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.55e+42) {
		tmp = y * b;
	} else if (y <= -3.1e-21) {
		tmp = x;
	} else if (y <= 6.2e-16) {
		tmp = z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.55d+42)) then
        tmp = y * b
    else if (y <= (-3.1d-21)) then
        tmp = x
    else if (y <= 6.2d-16) then
        tmp = z
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.55e+42) {
		tmp = y * b;
	} else if (y <= -3.1e-21) {
		tmp = x;
	} else if (y <= 6.2e-16) {
		tmp = z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.55e+42:
		tmp = y * b
	elif y <= -3.1e-21:
		tmp = x
	elif y <= 6.2e-16:
		tmp = z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.55e+42)
		tmp = Float64(y * b);
	elseif (y <= -3.1e-21)
		tmp = x;
	elseif (y <= 6.2e-16)
		tmp = z;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.55e+42)
		tmp = y * b;
	elseif (y <= -3.1e-21)
		tmp = x;
	elseif (y <= 6.2e-16)
		tmp = z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.55e+42], N[(y * b), $MachinePrecision], If[LessEqual[y, -3.1e-21], x, If[LessEqual[y, 6.2e-16], z, N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.55e42 or 6.2000000000000002e-16 < y

   1. Initial program 91.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 57.1%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 37.7%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{y}\right) \]

   8. Simplified 37.7%

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

   if -2.55e42 < y < -3.0999999999999998e-21

   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

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 45.4%

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

   if -3.0999999999999998e-21 < y < 6.2000000000000002e-16

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

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

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 24.9%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 24.9%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 24.9%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+42}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-16}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1300:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -7.2e+90) t_1 (if (<= b 1300.0) (+ x (* z (- 1.0 y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -7.2e+90) {
		tmp = t_1;
	} else if (b <= 1300.0) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t + (y + (-2.0d0)))
    if (b <= (-7.2d+90)) then
        tmp = t_1
    else if (b <= 1300.0d0) then
        tmp = x + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -7.2e+90) {
		tmp = t_1;
	} else if (b <= 1300.0) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -7.2e+90:
		tmp = t_1
	elif b <= 1300.0:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -7.2e+90)
		tmp = t_1;
	elseif (b <= 1300.0)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -7.2e+90)
		tmp = t_1;
	elseif (b <= 1300.0)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+90], t$95$1, If[LessEqual[b, 1300.0], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2e90 or 1300 < b

   1. Initial program 91.0%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 80.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 80.7%

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

   if -7.2e90 < b < 1300

   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 b around 0

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 90.6%

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

   6. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      3. --lowering--.f64 62.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 62.3%

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

Alternative 9: 61.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+14}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -2.8e+58) t_1 (if (<= b 3e+14) (+ x (* a (- 1.0 t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -2.8e+58) {
		tmp = t_1;
	} else if (b <= 3e+14) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t + (y + (-2.0d0)))
    if (b <= (-2.8d+58)) then
        tmp = t_1
    else if (b <= 3d+14) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -2.8e+58) {
		tmp = t_1;
	} else if (b <= 3e+14) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -2.8e+58:
		tmp = t_1
	elif b <= 3e+14:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -2.8e+58)
		tmp = t_1;
	elseif (b <= 3e+14)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -2.8e+58)
		tmp = t_1;
	elseif (b <= 3e+14)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+58], t$95$1, If[LessEqual[b, 3e+14], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.7999999999999998e58 or 3e14 < b

   1. Initial program 91.2%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 79.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 79.5%

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

   if -2.7999999999999998e58 < b < 3e14

   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 x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, 1\right), a\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 60.0%

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

   6. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. sub-neg N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. mul-1-neg N/A

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

      13. cancel-sign-sub N/A

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

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(a \cdot \left(1 - t\right)\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(1 - t\right)}\right)\right) \]

      16. --lowering--.f64 52.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 52.2%

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

Alternative 10: 50.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -6.8e+89) t_1 (if (<= b 2.7e-5) (* z (- 1.0 y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -6.8e+89) {
		tmp = t_1;
	} else if (b <= 2.7e-5) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t + (y + (-2.0d0)))
    if (b <= (-6.8d+89)) then
        tmp = t_1
    else if (b <= 2.7d-5) then
        tmp = z * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -6.8e+89) {
		tmp = t_1;
	} else if (b <= 2.7e-5) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -6.8e+89:
		tmp = t_1
	elif b <= 2.7e-5:
		tmp = z * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -6.8e+89)
		tmp = t_1;
	elseif (b <= 2.7e-5)
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -6.8e+89)
		tmp = t_1;
	elseif (b <= 2.7e-5)
		tmp = z * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+89], t$95$1, If[LessEqual[b, 2.7e-5], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.8000000000000004e89 or 2.6999999999999999e-5 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 80.0%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 80.0%

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

   if -6.8000000000000004e89 < b < 2.6999999999999999e-5

   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 z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

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

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 42.6%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 42.6%

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

Alternative 11: 50.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1050000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1050000000.0) t_1 (if (<= t 1.5e+75) (* y (- b z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1050000000.0) {
		tmp = t_1;
	} else if (t <= 1.5e+75) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1050000000.0d0)) then
        tmp = t_1
    else if (t <= 1.5d+75) then
        tmp = y * (b - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1050000000.0) {
		tmp = t_1;
	} else if (t <= 1.5e+75) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1050000000.0:
		tmp = t_1
	elif t <= 1.5e+75:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1050000000.0)
		tmp = t_1;
	elseif (t <= 1.5e+75)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1050000000.0)
		tmp = t_1;
	elseif (t <= 1.5e+75)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1050000000.0], t$95$1, If[LessEqual[t, 1.5e+75], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e9 or 1.5e75 < t

   1. Initial program 90.7%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 73.9%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 73.9%

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

   if -1.05e9 < t < 1.5e75

   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 y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 44.7%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 44.7%

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

Alternative 12: 47.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2800:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2800.0) t_1 (if (<= t 7.5e+77) (* b (+ y -2.0)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2800.0) {
		tmp = t_1;
	} else if (t <= 7.5e+77) {
		tmp = b * (y + -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-2800.0d0)) then
        tmp = t_1
    else if (t <= 7.5d+77) then
        tmp = b * (y + (-2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2800.0) {
		tmp = t_1;
	} else if (t <= 7.5e+77) {
		tmp = b * (y + -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2800.0:
		tmp = t_1
	elif t <= 7.5e+77:
		tmp = b * (y + -2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2800.0)
		tmp = t_1;
	elseif (t <= 7.5e+77)
		tmp = Float64(b * Float64(y + -2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -2800.0)
		tmp = t_1;
	elseif (t <= 7.5e+77)
		tmp = b * (y + -2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2800.0], t$95$1, If[LessEqual[t, 7.5e+77], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2800 or 7.49999999999999955e77 < t

   1. Initial program 90.7%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 73.9%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 73.9%

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

   if -2800 < t < 7.49999999999999955e77

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 32.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 32.8%

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

   6. Taylor expanded in t around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y - 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      4. metadata-eval 32.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right) \]

   8. Simplified 32.8%

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

Alternative 13: 39.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.6e+60)
   (* b (+ y -2.0))
   (if (<= b 4.3e+80) (* a (- 1.0 t)) (* b (+ t -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+60) {
		tmp = b * (y + -2.0);
	} else if (b <= 4.3e+80) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.6d+60)) then
        tmp = b * (y + (-2.0d0))
    else if (b <= 4.3d+80) then
        tmp = a * (1.0d0 - t)
    else
        tmp = b * (t + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+60) {
		tmp = b * (y + -2.0);
	} else if (b <= 4.3e+80) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.6e+60:
		tmp = b * (y + -2.0)
	elif b <= 4.3e+80:
		tmp = a * (1.0 - t)
	else:
		tmp = b * (t + -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.6e+60)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (b <= 4.3e+80)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(b * Float64(t + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.6e+60)
		tmp = b * (y + -2.0);
	elseif (b <= 4.3e+80)
		tmp = a * (1.0 - t);
	else
		tmp = b * (t + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.6e+60], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e+80], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.59999999999999968e60

   1. Initial program 87.0%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 76.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 76.9%

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

   6. Taylor expanded in t around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y - 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      4. metadata-eval 45.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right) \]

   8. Simplified 45.2%

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

   if -3.59999999999999968e60 < b < 4.30000000000000004e80

   1. Initial program 98.7%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 33.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 33.7%

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

   if 4.30000000000000004e80 < b

   1. Initial program 92.9%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 86.0%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 86.0%

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

   6. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(t - 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      4. metadata-eval 55.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right) \]

   8. Simplified 55.5%

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

Alternative 14: 39.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + -2\right)\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t -2.0))))
   (if (<= b -4.6e+59) t_1 (if (<= b 2.3e+80) (* a (- 1.0 t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + -2.0);
	double tmp;
	if (b <= -4.6e+59) {
		tmp = t_1;
	} else if (b <= 2.3e+80) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t + (-2.0d0))
    if (b <= (-4.6d+59)) then
        tmp = t_1
    else if (b <= 2.3d+80) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + -2.0);
	double tmp;
	if (b <= -4.6e+59) {
		tmp = t_1;
	} else if (b <= 2.3e+80) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + -2.0)
	tmp = 0
	if b <= -4.6e+59:
		tmp = t_1
	elif b <= 2.3e+80:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + -2.0))
	tmp = 0.0
	if (b <= -4.6e+59)
		tmp = t_1;
	elseif (b <= 2.3e+80)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + -2.0);
	tmp = 0.0;
	if (b <= -4.6e+59)
		tmp = t_1;
	elseif (b <= 2.3e+80)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.6e+59], t$95$1, If[LessEqual[b, 2.3e+80], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.60000000000000016e59 or 2.30000000000000004e80 < b

   1. Initial program 90.2%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 81.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 81.9%

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

   6. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(t - 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      4. metadata-eval 50.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right) \]

   8. Simplified 50.7%

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

   if -4.60000000000000016e59 < b < 2.30000000000000004e80

   1. Initial program 98.7%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 33.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 33.7%

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

Alternative 15: 34.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+59}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+78}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.2e+59) (* y b) (if (<= b 1.15e+78) (* a (- 1.0 t)) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.2e+59) {
		tmp = y * b;
	} else if (b <= 1.15e+78) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.2d+59)) then
        tmp = y * b
    else if (b <= 1.15d+78) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.2e+59) {
		tmp = y * b;
	} else if (b <= 1.15e+78) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.2e+59:
		tmp = y * b
	elif b <= 1.15e+78:
		tmp = a * (1.0 - t)
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.2e+59)
		tmp = Float64(y * b);
	elseif (b <= 1.15e+78)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.2e+59)
		tmp = y * b;
	elseif (b <= 1.15e+78)
		tmp = a * (1.0 - t);
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.2e+59], N[(y * b), $MachinePrecision], If[LessEqual[b, 1.15e+78], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.19999999999999982e59

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 82.8%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 41.0%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{y}\right) \]

   8. Simplified 41.0%

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

   if -3.19999999999999982e59 < b < 1.1500000000000001e78

   1. Initial program 98.7%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 33.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 33.7%

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

   if 1.1500000000000001e78 < b

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 44.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 44.5%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{b}\right) \]

   8. Simplified 42.4%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+59}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+78}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+82}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+105}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6e+82) (* t b) (if (<= t 2.7e+105) (* y b) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6e+82) {
		tmp = t * b;
	} else if (t <= 2.7e+105) {
		tmp = y * b;
	} 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+82)) then
        tmp = t * b
    else if (t <= 2.7d+105) then
        tmp = y * b
    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+82) {
		tmp = t * b;
	} else if (t <= 2.7e+105) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6e+82:
		tmp = t * b
	elif t <= 2.7e+105:
		tmp = y * b
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6e+82)
		tmp = Float64(t * b);
	elseif (t <= 2.7e+105)
		tmp = Float64(y * b);
	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+82)
		tmp = t * b;
	elseif (t <= 2.7e+105)
		tmp = y * b;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6e+82], N[(t * b), $MachinePrecision], If[LessEqual[t, 2.7e+105], N[(y * b), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.99999999999999978e82 or 2.70000000000000016e105 < t

   1. Initial program 89.3%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 78.7%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 78.7%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 52.9%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{b}\right) \]

   8. Simplified 52.9%

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

   if -5.99999999999999978e82 < t < 2.70000000000000016e105

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 49.4%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 24.8%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{y}\right) \]

   8. Simplified 24.8%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+82}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+105}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 21.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+18}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.7e+122) x (if (<= x 9.2e+18) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.7e+122) {
		tmp = x;
	} else if (x <= 9.2e+18) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.7d+122)) then
        tmp = x
    else if (x <= 9.2d+18) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.7e+122) {
		tmp = x;
	} else if (x <= 9.2e+18) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.7e+122:
		tmp = x
	elif x <= 9.2e+18:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.7e+122)
		tmp = x;
	elseif (x <= 9.2e+18)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.7e+122)
		tmp = x;
	elseif (x <= 9.2e+18)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.7e+122], x, If[LessEqual[x, 9.2e+18], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e122 or 9.2e18 < x

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 35.0%

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

   if -1.7e122 < x < 9.2e18

   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 z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

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

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 34.6%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 34.6%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 16.3%

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

Alternative 18: 21.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+188}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+143}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.2e+188) a (if (<= a 2.1e+143) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.2e+188) {
		tmp = a;
	} else if (a <= 2.1e+143) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.2d+188)) then
        tmp = a
    else if (a <= 2.1d+143) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.2e+188) {
		tmp = a;
	} else if (a <= 2.1e+143) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.2e+188:
		tmp = a
	elif a <= 2.1e+143:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.2e+188)
		tmp = a;
	elseif (a <= 2.1e+143)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.2e+188)
		tmp = a;
	elseif (a <= 2.1e+143)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.2e+188], a, If[LessEqual[a, 2.1e+143], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.19999999999999999e188 or 2.09999999999999988e143 < a

   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 inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 58.3%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 58.3%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a} \]
   7. Step-by-step derivation

   8. Simplified 28.0%

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

   if -2.19999999999999999e188 < a < 2.09999999999999988e143

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 18.4%

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

Alternative 19: 11.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

3. Taylor expanded in a around inf

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

   1. sub-neg N/A

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

   2. metadata-eval N/A

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

   3. neg-mul-1 N/A

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

   4. distribute-lft-in N/A

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

   5. +-commutative N/A

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

   6. metadata-eval N/A

      \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

   7. sub-neg N/A

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

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

   9. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

   11. distribute-lft-in N/A

       \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right) \]

   13. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right) \]

   14. neg-mul-1 N/A

       \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

   15. sub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

   16. --lowering--.f64 26.3%

       \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

5. Simplified 26.3%

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

6. Taylor expanded in t around 0

   \[\leadsto \color{blue}{a} \]
7. Step-by-step derivation

8. Simplified 10.3%

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

Reproduce

herbie shell --seed 2024138 
(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)))