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

Percentage Accurate: 95.4% → 97.8%

Time: 10.9s

Alternatives: 17

Speedup: 1.0×

• 35.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.4% 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: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	t_2 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + t_1
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = x + t_1
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(x + t$95$1), $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 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 75.1%

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

4. Final simplification 98.8%

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

Alternative 2: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ t_2 := \left(t + -1\right) \cdot a\\ t_3 := z \cdot \left(1 - y\right) - t\_2\\ \mathbf{if}\;b \leq -2 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{+36}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-273}:\\ \;\;\;\;x + \left(z - t\_2\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+63}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b)))
        (t_2 (* (+ t -1.0) a))
        (t_3 (- (* z (- 1.0 y)) t_2)))
   (if (<= b -2e+78)
     t_1
     (if (<= b -1.02e+36)
       t_3
       (if (<= b 8e-273) (+ x (- z t_2)) (if (<= b 7.2e+63) t_3 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 t_2 = (t + -1.0) * a;
	double t_3 = (z * (1.0 - y)) - t_2;
	double tmp;
	if (b <= -2e+78) {
		tmp = t_1;
	} else if (b <= -1.02e+36) {
		tmp = t_3;
	} else if (b <= 8e-273) {
		tmp = x + (z - t_2);
	} else if (b <= 7.2e+63) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    t_2 = (t + (-1.0d0)) * a
    t_3 = (z * (1.0d0 - y)) - t_2
    if (b <= (-2d+78)) then
        tmp = t_1
    else if (b <= (-1.02d+36)) then
        tmp = t_3
    else if (b <= 8d-273) then
        tmp = x + (z - t_2)
    else if (b <= 7.2d+63) then
        tmp = t_3
    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 t_2 = (t + -1.0) * a;
	double t_3 = (z * (1.0 - y)) - t_2;
	double tmp;
	if (b <= -2e+78) {
		tmp = t_1;
	} else if (b <= -1.02e+36) {
		tmp = t_3;
	} else if (b <= 8e-273) {
		tmp = x + (z - t_2);
	} else if (b <= 7.2e+63) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	t_2 = (t + -1.0) * a
	t_3 = (z * (1.0 - y)) - t_2
	tmp = 0
	if b <= -2e+78:
		tmp = t_1
	elif b <= -1.02e+36:
		tmp = t_3
	elif b <= 8e-273:
		tmp = x + (z - t_2)
	elif b <= 7.2e+63:
		tmp = t_3
	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))
	t_2 = Float64(Float64(t + -1.0) * a)
	t_3 = Float64(Float64(z * Float64(1.0 - y)) - t_2)
	tmp = 0.0
	if (b <= -2e+78)
		tmp = t_1;
	elseif (b <= -1.02e+36)
		tmp = t_3;
	elseif (b <= 8e-273)
		tmp = Float64(x + Float64(z - t_2));
	elseif (b <= 7.2e+63)
		tmp = t_3;
	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);
	t_2 = (t + -1.0) * a;
	t_3 = (z * (1.0 - y)) - t_2;
	tmp = 0.0;
	if (b <= -2e+78)
		tmp = t_1;
	elseif (b <= -1.02e+36)
		tmp = t_3;
	elseif (b <= 8e-273)
		tmp = x + (z - t_2);
	elseif (b <= 7.2e+63)
		tmp = t_3;
	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]}, Block[{t$95$2 = N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[b, -2e+78], t$95$1, If[LessEqual[b, -1.02e+36], t$95$3, If[LessEqual[b, 8e-273], N[(x + N[(z - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e+63], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.00000000000000002e78 or 7.19999999999999998e63 < b

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 83.1%

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

   if -2.00000000000000002e78 < b < -1.02000000000000003e36 or 8.000000000000001e-273 < b < 7.19999999999999998e63

   1. Initial program 97.3%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      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

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

      26. sub-neg N/A

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

   5. Simplified 78.5%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

      5. --lowering--.f64 67.5%

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

   8. Simplified 67.5%

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

   if -1.02000000000000003e36 < b < 8.000000000000001e-273

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      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

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

      26. sub-neg N/A

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

   5. Simplified 88.8%

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

   6. Taylor expanded in y around 0

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

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

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

      2. remove-double-neg N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-out N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. --lowering--.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, \left(0 - \color{blue}{\left(1 - t\right)}\right)\right)\right)\right) \]

      12. associate--r- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, \left(\left(0 - 1\right) + \color{blue}{t}\right)\right)\right)\right) \]

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. +-lowering-+.f64 71.1%

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

   8. Simplified 71.1%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+78}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-273}:\\ \;\;\;\;x + \left(z - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(t + -2\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (+ t -2.0))))
   (if (<= b -6.5e+72)
     t_2
     (if (<= b -2.6e-97)
       t_1
       (if (<= b 1.7e-269) x (if (<= b 1.5e+127) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (t + -2.0);
	double tmp;
	if (b <= -6.5e+72) {
		tmp = t_2;
	} else if (b <= -2.6e-97) {
		tmp = t_1;
	} else if (b <= 1.7e-269) {
		tmp = x;
	} else if (b <= 1.5e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * (t + (-2.0d0))
    if (b <= (-6.5d+72)) then
        tmp = t_2
    else if (b <= (-2.6d-97)) then
        tmp = t_1
    else if (b <= 1.7d-269) then
        tmp = x
    else if (b <= 1.5d+127) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (t + -2.0);
	double tmp;
	if (b <= -6.5e+72) {
		tmp = t_2;
	} else if (b <= -2.6e-97) {
		tmp = t_1;
	} else if (b <= 1.7e-269) {
		tmp = x;
	} else if (b <= 1.5e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * (t + -2.0)
	tmp = 0
	if b <= -6.5e+72:
		tmp = t_2
	elif b <= -2.6e-97:
		tmp = t_1
	elif b <= 1.7e-269:
		tmp = x
	elif b <= 1.5e+127:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(t + -2.0))
	tmp = 0.0
	if (b <= -6.5e+72)
		tmp = t_2;
	elseif (b <= -2.6e-97)
		tmp = t_1;
	elseif (b <= 1.7e-269)
		tmp = x;
	elseif (b <= 1.5e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * (t + -2.0);
	tmp = 0.0;
	if (b <= -6.5e+72)
		tmp = t_2;
	elseif (b <= -2.6e-97)
		tmp = t_1;
	elseif (b <= 1.7e-269)
		tmp = x;
	elseif (b <= 1.5e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+72], t$95$2, If[LessEqual[b, -2.6e-97], t$95$1, If[LessEqual[b, 1.7e-269], x, If[LessEqual[b, 1.5e+127], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.5000000000000001e72 or 1.5000000000000001e127 < b

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

      12. --lowering--.f64 N/A

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. sub-neg N/A

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

   5. Simplified 90.5%

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

   6. Taylor expanded in z around inf

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

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

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. --lowering--.f64 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
   10. 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. metadata-eval N/A

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

       4. +-lowering-+.f64 54.6%

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

   11. Simplified 54.6%

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

   if -6.5000000000000001e72 < b < -2.60000000000000007e-97 or 1.6999999999999999e-269 < b < 1.5000000000000001e127

   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 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. neg-mul-1 N/A

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

      3. metadata-eval N/A

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

      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 34.1%

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

   5. Simplified 34.1%

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

   if -2.60000000000000007e-97 < b < 1.6999999999999999e-269

   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 44.9%

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

Alternative 4: 83.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+56}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + t\_1\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+110}:\\ \;\;\;\;x + \left(t\_1 - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= b -4.2e+56)
     (+ (* (- (+ y t) 2.0) b) t_1)
     (if (<= b 7.8e+110)
       (+ x (- t_1 (* (+ t -1.0) a)))
       (* b (+ y (+ t -2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (b <= -4.2e+56) {
		tmp = (((y + t) - 2.0) * b) + t_1;
	} else if (b <= 7.8e+110) {
		tmp = x + (t_1 - ((t + -1.0) * a));
	} else {
		tmp = b * (y + (t + -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (b <= (-4.2d+56)) then
        tmp = (((y + t) - 2.0d0) * b) + t_1
    else if (b <= 7.8d+110) then
        tmp = x + (t_1 - ((t + (-1.0d0)) * a))
    else
        tmp = b * (y + (t + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (b <= -4.2e+56) {
		tmp = (((y + t) - 2.0) * b) + t_1;
	} else if (b <= 7.8e+110) {
		tmp = x + (t_1 - ((t + -1.0) * a));
	} else {
		tmp = b * (y + (t + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if b <= -4.2e+56:
		tmp = (((y + t) - 2.0) * b) + t_1
	elif b <= 7.8e+110:
		tmp = x + (t_1 - ((t + -1.0) * a))
	else:
		tmp = b * (y + (t + -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -4.2e+56)
		tmp = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) + t_1);
	elseif (b <= 7.8e+110)
		tmp = Float64(x + Float64(t_1 - Float64(Float64(t + -1.0) * a)));
	else
		tmp = Float64(b * Float64(y + Float64(t + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -4.2e+56)
		tmp = (((y + t) - 2.0) * b) + t_1;
	elseif (b <= 7.8e+110)
		tmp = x + (t_1 - ((t + -1.0) * a));
	else
		tmp = b * (y + (t + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+56], N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 7.8e+110], N[(x + N[(t$95$1 - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.20000000000000034e56

   1. Initial program 90.9%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 81.1%

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

   5. Simplified 81.1%

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

   if -4.20000000000000034e56 < b < 7.8000000000000007e110

   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 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. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      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

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

      26. sub-neg N/A

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

   5. Simplified 83.0%

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

   if 7.8000000000000007e110 < b

   1. Initial program 89.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. +-commutative N/A

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

      3. associate-+r- N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval 92.0%

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

   5. Simplified 92.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+56}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+110}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+81}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+111}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.75e+81)
   (+ x (* (- (+ y t) 2.0) b))
   (if (<= b 3.5e+111)
     (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))
     (* b (+ y (+ t -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+81) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= 3.5e+111) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else {
		tmp = b * (y + (t + -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.75d+81)) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else if (b <= 3.5d+111) then
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    else
        tmp = b * (y + (t + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+81) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= 3.5e+111) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else {
		tmp = b * (y + (t + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.75e+81:
		tmp = x + (((y + t) - 2.0) * b)
	elif b <= 3.5e+111:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	else:
		tmp = b * (y + (t + -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.75e+81)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (b <= 3.5e+111)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	else
		tmp = Float64(b * Float64(y + Float64(t + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.75e+81)
		tmp = x + (((y + t) - 2.0) * b);
	elseif (b <= 3.5e+111)
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	else
		tmp = b * (y + (t + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.75e+81], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+111], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.75e81

   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 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 79.5%

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

   if -1.75e81 < b < 3.5000000000000002e111

   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 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. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      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

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

      26. sub-neg N/A

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

   5. Simplified 82.8%

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

   if 3.5000000000000002e111 < b

   1. Initial program 89.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. +-commutative N/A

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

      3. associate-+r- N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval 92.0%

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

   5. Simplified 92.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+81}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+111}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + (b * (t + -2.0))) + ((y * (b - z)) + (z - ((t + -1.0) * 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 = (x + (b * (t + (-2.0d0)))) + ((y * (b - z)) + (z - ((t + (-1.0d0)) * a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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 y around 0

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

   1. associate-+r+ N/A

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

   2. associate--l+ N/A

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

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

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

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

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

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

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

   6. sub-neg N/A

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

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

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

   8. metadata-eval N/A

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

   9. sub-neg N/A

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

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

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

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

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

   12. --lowering--.f64 N/A

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

   13. distribute-neg-in N/A

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

   14. mul-1-neg N/A

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

   15. remove-double-neg N/A

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

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

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

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

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

   18. mul-1-neg N/A

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

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

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

   20. sub-neg N/A

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

5. Simplified 95.7%

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

6. Final simplification 95.7%

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

Alternative 7: 70.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-93}:\\ \;\;\;\;x + \left(z - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -7.5e+34)
     t_1
     (if (<= b 7.5e-93) (+ x (- z (* (+ t -1.0) a))) 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 <= -7.5e+34) {
		tmp = t_1;
	} else if (b <= 7.5e-93) {
		tmp = x + (z - ((t + -1.0) * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-7.5d+34)) then
        tmp = t_1
    else if (b <= 7.5d-93) then
        tmp = x + (z - ((t + (-1.0d0)) * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -7.5e+34) {
		tmp = t_1;
	} else if (b <= 7.5e-93) {
		tmp = x + (z - ((t + -1.0) * a));
	} 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 <= -7.5e+34:
		tmp = t_1
	elif b <= 7.5e-93:
		tmp = x + (z - ((t + -1.0) * a))
	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 <= -7.5e+34)
		tmp = t_1;
	elseif (b <= 7.5e-93)
		tmp = Float64(x + Float64(z - Float64(Float64(t + -1.0) * a)));
	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 <= -7.5e+34)
		tmp = t_1;
	elseif (b <= 7.5e-93)
		tmp = x + (z - ((t + -1.0) * a));
	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, -7.5e+34], t$95$1, If[LessEqual[b, 7.5e-93], N[(x + N[(z - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.49999999999999976e34 or 7.50000000000000034e-93 < b

   1. Initial program 93.1%

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

   3. Taylor expanded in 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 73.1%

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

   if -7.49999999999999976e34 < b < 7.50000000000000034e-93

   1. Initial program 98.2%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      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

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

      26. sub-neg N/A

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

   5. Simplified 88.2%

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

   6. Taylor expanded in y around 0

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

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

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

      2. remove-double-neg N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-out N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. --lowering--.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, \left(0 - \color{blue}{\left(1 - t\right)}\right)\right)\right)\right) \]

      12. associate--r- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, \left(\left(0 - 1\right) + \color{blue}{t}\right)\right)\right)\right) \]

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. +-lowering-+.f64 68.6%

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

   8. Simplified 68.6%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+34}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-93}:\\ \;\;\;\;x + \left(z - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-93}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -3.2e+34) t_1 (if (<= b 6.4e-93) (- x (* (+ t -1.0) a)) 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 <= -3.2e+34) {
		tmp = t_1;
	} else if (b <= 6.4e-93) {
		tmp = x - ((t + -1.0) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-3.2d+34)) then
        tmp = t_1
    else if (b <= 6.4d-93) then
        tmp = x - ((t + (-1.0d0)) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.2e+34) {
		tmp = t_1;
	} else if (b <= 6.4e-93) {
		tmp = x - ((t + -1.0) * a);
	} 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 <= -3.2e+34:
		tmp = t_1
	elif b <= 6.4e-93:
		tmp = x - ((t + -1.0) * a)
	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 <= -3.2e+34)
		tmp = t_1;
	elseif (b <= 6.4e-93)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	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 <= -3.2e+34)
		tmp = t_1;
	elseif (b <= 6.4e-93)
		tmp = x - ((t + -1.0) * a);
	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, -3.2e+34], t$95$1, If[LessEqual[b, 6.4e-93], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.1999999999999998e34 or 6.3999999999999997e-93 < b

   1. Initial program 93.1%

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

   3. Taylor expanded in 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 73.1%

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

   if -3.1999999999999998e34 < b < 6.3999999999999997e-93

   1. Initial program 98.2%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      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

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

      26. sub-neg N/A

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

   5. Simplified 88.2%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. --lowering--.f64 60.3%

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

   8. Simplified 60.3%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-93}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -1.28 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+110}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (+ t -2.0)))))
   (if (<= b -1.28e+36) t_1 (if (<= b 9.5e+110) (- x (* (+ t -1.0) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -1.28e+36) {
		tmp = t_1;
	} else if (b <= 9.5e+110) {
		tmp = x - ((t + -1.0) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y + (t + (-2.0d0)))
    if (b <= (-1.28d+36)) then
        tmp = t_1
    else if (b <= 9.5d+110) then
        tmp = x - ((t + (-1.0d0)) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -1.28e+36) {
		tmp = t_1;
	} else if (b <= 9.5e+110) {
		tmp = x - ((t + -1.0) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y + (t + -2.0))
	tmp = 0
	if b <= -1.28e+36:
		tmp = t_1
	elif b <= 9.5e+110:
		tmp = x - ((t + -1.0) * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -1.28e+36)
		tmp = t_1;
	elseif (b <= 9.5e+110)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y + (t + -2.0));
	tmp = 0.0;
	if (b <= -1.28e+36)
		tmp = t_1;
	elseif (b <= 9.5e+110)
		tmp = x - ((t + -1.0) * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.28e+36], t$95$1, If[LessEqual[b, 9.5e+110], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.27999999999999993e36 or 9.49999999999999939e110 < b

   1. Initial program 90.4%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. associate-+r- N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval 78.4%

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

   5. Simplified 78.4%

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

   if -1.27999999999999993e36 < b < 9.49999999999999939e110

   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 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. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      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

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

      26. sub-neg N/A

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

   5. Simplified 82.6%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. --lowering--.f64 55.8%

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

   8. Simplified 55.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.28 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+110}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.8e+32) t_1 (if (<= y 7.6e+16) (+ x (* t b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.8e+32) {
		tmp = t_1;
	} else if (y <= 7.6e+16) {
		tmp = x + (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1.8d+32)) then
        tmp = t_1
    else if (y <= 7.6d+16) then
        tmp = x + (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.8e+32) {
		tmp = t_1;
	} else if (y <= 7.6e+16) {
		tmp = x + (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.8e+32:
		tmp = t_1
	elif y <= 7.6e+16:
		tmp = x + (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.8e+32)
		tmp = t_1;
	elseif (y <= 7.6e+16)
		tmp = Float64(x + Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.8e+32)
		tmp = t_1;
	elseif (y <= 7.6e+16)
		tmp = x + (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+32], t$95$1, If[LessEqual[y, 7.6e+16], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999998e32 or 7.6e16 < y

   1. Initial program 93.0%

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

   3. Taylor expanded in 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 67.1%

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

   5. Simplified 67.1%

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

   if -1.7999999999999998e32 < y < 7.6e16

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 59.7%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot t\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 45.7%

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

   8. Simplified 45.7%

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

Alternative 11: 49.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.9e+32) t_1 (if (<= t 9.2e+60) (* 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 <= -1.9e+32) {
		tmp = t_1;
	} else if (t <= 9.2e+60) {
		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 <= (-1.9d+32)) then
        tmp = t_1
    else if (t <= 9.2d+60) 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 <= -1.9e+32) {
		tmp = t_1;
	} else if (t <= 9.2e+60) {
		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 <= -1.9e+32:
		tmp = t_1
	elif t <= 9.2e+60:
		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 <= -1.9e+32)
		tmp = t_1;
	elseif (t <= 9.2e+60)
		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 <= -1.9e+32)
		tmp = t_1;
	elseif (t <= 9.2e+60)
		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, -1.9e+32], t$95$1, If[LessEqual[t, 9.2e+60], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9000000000000002e32 or 9.20000000000000068e60 < t

   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 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 68.0%

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

   5. Simplified 68.0%

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

   if -1.9000000000000002e32 < t < 9.20000000000000068e60

   1. Initial program 97.9%

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

   3. Taylor expanded in 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 46.1%

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

   5. Simplified 46.1%

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

Alternative 12: 40.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+60}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.25e+27) t_1 (if (<= t 8.6e+60) (* y b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.25e+27) {
		tmp = t_1;
	} else if (t <= 8.6e+60) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1.25d+27)) then
        tmp = t_1
    else if (t <= 8.6d+60) then
        tmp = y * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.25e+27) {
		tmp = t_1;
	} else if (t <= 8.6e+60) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.25e+27:
		tmp = t_1
	elif t <= 8.6e+60:
		tmp = y * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.25e+27)
		tmp = t_1;
	elseif (t <= 8.6e+60)
		tmp = Float64(y * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.25e+27)
		tmp = t_1;
	elseif (t <= 8.6e+60)
		tmp = y * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+27], t$95$1, If[LessEqual[t, 8.6e+60], N[(y * b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999995e27 or 8.59999999999999942e60 < t

   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 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 68.0%

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

   5. Simplified 68.0%

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

   if -1.24999999999999995e27 < t < 8.59999999999999942e60

   1. Initial program 97.9%

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

   3. Taylor expanded in 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 61.0%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 30.4%

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

   8. Simplified 30.4%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+60}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+31}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+68}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.4e+31) (* t b) (if (<= t 3.7e+68) (* y b) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.4e+31) {
		tmp = t * b;
	} else if (t <= 3.7e+68) {
		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 <= (-3.4d+31)) then
        tmp = t * b
    else if (t <= 3.7d+68) 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 <= -3.4e+31) {
		tmp = t * b;
	} else if (t <= 3.7e+68) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.4e+31:
		tmp = t * b
	elif t <= 3.7e+68:
		tmp = y * b
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.4e+31)
		tmp = Float64(t * b);
	elseif (t <= 3.7e+68)
		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 <= -3.4e+31)
		tmp = t * b;
	elseif (t <= 3.7e+68)
		tmp = y * b;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.4e+31], N[(t * b), $MachinePrecision], If[LessEqual[t, 3.7e+68], N[(y * b), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3999999999999998e31 or 3.69999999999999998e68 < t

   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 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 68.0%

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

   5. Simplified 68.0%

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

   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 40.0%

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

   8. Simplified 40.0%

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

   if -3.3999999999999998e31 < t < 3.69999999999999998e68

   1. Initial program 97.9%

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

   3. Taylor expanded in 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 61.0%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 30.4%

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

   8. Simplified 30.4%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+31}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+68}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.22e+60) x (if (<= x 1.8e+52) (* y b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.22e+60) {
		tmp = x;
	} else if (x <= 1.8e+52) {
		tmp = y * b;
	} 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 <= (-1.22d+60)) then
        tmp = x
    else if (x <= 1.8d+52) then
        tmp = y * b
    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 <= -1.22e+60) {
		tmp = x;
	} else if (x <= 1.8e+52) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.22e+60:
		tmp = x
	elif x <= 1.8e+52:
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.22e+60)
		tmp = x;
	elseif (x <= 1.8e+52)
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.22e+60)
		tmp = x;
	elseif (x <= 1.8e+52)
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.22e+60], x, If[LessEqual[x, 1.8e+52], N[(y * b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.21999999999999995e60 or 1.8e52 < x

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 41.7%

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

   if -1.21999999999999995e60 < x < 1.8e52

   1. Initial program 95.4%

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

   3. Taylor expanded in 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 50.2%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 25.0%

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

   8. Simplified 25.0%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 22.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+85}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.2e+49) x (if (<= x 1.5e+85) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.2e+49) {
		tmp = x;
	} else if (x <= 1.5e+85) {
		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 <= (-5.2d+49)) then
        tmp = x
    else if (x <= 1.5d+85) 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 <= -5.2e+49) {
		tmp = x;
	} else if (x <= 1.5e+85) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.2e+49:
		tmp = x
	elif x <= 1.5e+85:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.2e+49)
		tmp = x;
	elseif (x <= 1.5e+85)
		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 <= -5.2e+49)
		tmp = x;
	elseif (x <= 1.5e+85)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.2e+49], x, If[LessEqual[x, 1.5e+85], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.19999999999999977e49 or 1.5e85 < x

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 41.5%

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

   if -5.19999999999999977e49 < x < 1.5e85

   1. Initial program 95.5%

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

   3. Taylor expanded in 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. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 13.2%

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

Alternative 16: 21.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+31}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.45e+56) x (if (<= x 3.4e+31) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.45e+56) {
		tmp = x;
	} else if (x <= 3.4e+31) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.45d+56)) then
        tmp = x
    else if (x <= 3.4d+31) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.45e+56) {
		tmp = x;
	} else if (x <= 3.4e+31) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.45e+56:
		tmp = x
	elif x <= 3.4e+31:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.45e+56)
		tmp = x;
	elseif (x <= 3.4e+31)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.45e+56)
		tmp = x;
	elseif (x <= 3.4e+31)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.45e+56], x, If[LessEqual[x, 3.4e+31], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45000000000000004e56 or 3.3999999999999998e31 < x

   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 x around inf

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

   5. Simplified 40.1%

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

   if -1.45000000000000004e56 < x < 3.3999999999999998e31

   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. neg-mul-1 N/A

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

      3. metadata-eval N/A

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

      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 24.1%

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

   5. Simplified 24.1%

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

   6. Taylor expanded in t around 0

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

   8. Simplified 8.4%

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

Alternative 17: 10.9% 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. neg-mul-1 N/A

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

   3. metadata-eval N/A

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

   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 22.3%

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

5. Simplified 22.3%

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

6. Taylor expanded in t around 0

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

8. Simplified 7.4%

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

Reproduce

herbie shell --seed 2024155 
(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)))