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

Percentage Accurate: 95.3% → 97.8%

Time: 12.9s

Alternatives: 20

Speedup: 1.0×

• 36.3% 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: 95.3% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. div-sub N/A

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

      6. unsub-neg N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. associate--l- N/A

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

      10. div-sub N/A

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

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

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. associate--l+ N/A

          \[\leadsto b \cdot \left(t + \left(y - 2\right)\right) + -1 \cdot \left(a \cdot t\right) \]

       3. distribute-lft-out N/A

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

       4. +-commutative N/A

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

       5. associate-+r+ N/A

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

       6. associate-*r* N/A

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

       7. distribute-rgt-in N/A

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

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

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

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

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

       10. sub-neg N/A

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

       11. metadata-eval N/A

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

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

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

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

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

       14. mul-1-neg N/A

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

       15. sub-neg N/A

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

       16. --lowering--.f64 85.7%

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

   11. Simplified 85.7%

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

4. Final simplification 99.6%

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

Alternative 2: 49.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -9.6 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -0.001:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-77}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - a\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -9.6e+102)
     t_1
     (if (<= b -0.001)
       (+ x (* t b))
       (if (<= b -6e-77)
         (* t (- (/ x t) a))
         (if (<= b 2.1e-27) (* z (- 1.0 y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -9.6e+102) {
		tmp = t_1;
	} else if (b <= -0.001) {
		tmp = x + (t * b);
	} else if (b <= -6e-77) {
		tmp = t * ((x / t) - a);
	} else if (b <= 2.1e-27) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t + (y + (-2.0d0)))
    if (b <= (-9.6d+102)) then
        tmp = t_1
    else if (b <= (-0.001d0)) then
        tmp = x + (t * b)
    else if (b <= (-6d-77)) then
        tmp = t * ((x / t) - a)
    else if (b <= 2.1d-27) then
        tmp = z * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -9.6e+102) {
		tmp = t_1;
	} else if (b <= -0.001) {
		tmp = x + (t * b);
	} else if (b <= -6e-77) {
		tmp = t * ((x / t) - a);
	} else if (b <= 2.1e-27) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -9.6e+102:
		tmp = t_1
	elif b <= -0.001:
		tmp = x + (t * b)
	elif b <= -6e-77:
		tmp = t * ((x / t) - a)
	elif b <= 2.1e-27:
		tmp = z * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -9.6e+102)
		tmp = t_1;
	elseif (b <= -0.001)
		tmp = Float64(x + Float64(t * b));
	elseif (b <= -6e-77)
		tmp = Float64(t * Float64(Float64(x / t) - a));
	elseif (b <= 2.1e-27)
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -9.6e+102)
		tmp = t_1;
	elseif (b <= -0.001)
		tmp = x + (t * b);
	elseif (b <= -6e-77)
		tmp = t * ((x / t) - a);
	elseif (b <= 2.1e-27)
		tmp = z * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.6e+102], t$95$1, If[LessEqual[b, -0.001], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6e-77], N[(t * N[(N[(x / t), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-27], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.59999999999999978e102 or 2.10000000000000015e-27 < b

   1. Initial program 93.7%

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

   3. Taylor expanded in b around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. metadata-eval 71.4%

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

   5. Simplified 71.4%

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

   if -9.59999999999999978e102 < b < -1e-3

   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

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

   5. Simplified 70.1%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 54.7%

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

   if -1e-3 < b < -6.00000000000000033e-77

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. div-sub N/A

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

      6. unsub-neg N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. associate--l- N/A

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

      10. div-sub N/A

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

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

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

   5. Simplified 89.2%

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

   6. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in b around 0

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

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

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

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

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

       3. /-lowering-/.f64 71.8%

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

   11. Simplified 71.8%

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

   if -6.00000000000000033e-77 < b < 2.10000000000000015e-27

   1. Initial program 100.0%

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

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

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      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 48.8%

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

   5. Simplified 48.8%

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

Alternative 3: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b + \left(x + t\_1\right)\\ \mathbf{if}\;b \leq -52000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 110000000:\\ \;\;\;\;x + \left(t\_1 + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (+ (* (- (+ y t) 2.0) b) (+ x t_1))))
   (if (<= b -52000000.0)
     t_2
     (if (<= b 110000000.0) (+ x (+ t_1 (* a (- 1.0 t)))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = (((y + t) - 2.0) * b) + (x + t_1);
	double tmp;
	if (b <= -52000000.0) {
		tmp = t_2;
	} else if (b <= 110000000.0) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} 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 = z * (1.0d0 - y)
    t_2 = (((y + t) - 2.0d0) * b) + (x + t_1)
    if (b <= (-52000000.0d0)) then
        tmp = t_2
    else if (b <= 110000000.0d0) then
        tmp = x + (t_1 + (a * (1.0d0 - t)))
    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 = z * (1.0 - y);
	double t_2 = (((y + t) - 2.0) * b) + (x + t_1);
	double tmp;
	if (b <= -52000000.0) {
		tmp = t_2;
	} else if (b <= 110000000.0) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = (((y + t) - 2.0) * b) + (x + t_1)
	tmp = 0
	if b <= -52000000.0:
		tmp = t_2
	elif b <= 110000000.0:
		tmp = x + (t_1 + (a * (1.0 - t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) + Float64(x + t_1))
	tmp = 0.0
	if (b <= -52000000.0)
		tmp = t_2;
	elseif (b <= 110000000.0)
		tmp = Float64(x + Float64(t_1 + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = (((y + t) - 2.0) * b) + (x + t_1);
	tmp = 0.0;
	if (b <= -52000000.0)
		tmp = t_2;
	elseif (b <= 110000000.0)
		tmp = x + (t_1 + (a * (1.0 - t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + N[(x + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -52000000.0], t$95$2, If[LessEqual[b, 110000000.0], N[(x + N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.2e7 or 1.1e8 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. metadata-eval N/A

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

      12. sub-neg N/A

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

      13. --lowering--.f64 88.5%

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

   5. Simplified 88.5%

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

   if -5.2e7 < b < 1.1e8

   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. sub-neg N/A

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

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

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. --lowering--.f64 N/A

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

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

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

      19. sub-neg N/A

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

      20. metadata-eval N/A

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

      21. +-lowering-+.f64 94.0%

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

   5. Simplified 94.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -52000000:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 110000000:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+92}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -3.4e+75)
     t_1
     (if (<= b 6.4e+92) (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.4e+75) {
		tmp = t_1;
	} else if (b <= 6.4e+92) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-3.4d+75)) then
        tmp = t_1
    else if (b <= 6.4d+92) then
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.4e+75) {
		tmp = t_1;
	} else if (b <= 6.4e+92) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -3.4e+75:
		tmp = t_1
	elif b <= 6.4e+92:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -3.4e+75)
		tmp = t_1;
	elseif (b <= 6.4e+92)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -3.4e+75)
		tmp = t_1;
	elseif (b <= 6.4e+92)
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+75], t$95$1, If[LessEqual[b, 6.4e+92], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.40000000000000011e75 or 6.40000000000000051e92 < b

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 85.5%

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

   if -3.40000000000000011e75 < b < 6.40000000000000051e92

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0

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

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

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

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. --lowering--.f64 N/A

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

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

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

      19. sub-neg N/A

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

      20. metadata-eval N/A

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

      21. +-lowering-+.f64 88.2%

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

   5. Simplified 88.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+75}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+92}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-263}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{+62}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -8.2e+22)
     t_1
     (if (<= y 7e-263)
       (+ x (* b (- t 2.0)))
       (if (<= y 3.35e+62) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -8.2e+22) {
		tmp = t_1;
	} else if (y <= 7e-263) {
		tmp = x + (b * (t - 2.0));
	} else if (y <= 3.35e+62) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-8.2d+22)) then
        tmp = t_1
    else if (y <= 7d-263) then
        tmp = x + (b * (t - 2.0d0))
    else if (y <= 3.35d+62) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -8.2e+22) {
		tmp = t_1;
	} else if (y <= 7e-263) {
		tmp = x + (b * (t - 2.0));
	} else if (y <= 3.35e+62) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -8.2e+22:
		tmp = t_1
	elif y <= 7e-263:
		tmp = x + (b * (t - 2.0))
	elif y <= 3.35e+62:
		tmp = x + (a * (1.0 - t))
	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 <= -8.2e+22)
		tmp = t_1;
	elseif (y <= 7e-263)
		tmp = Float64(x + Float64(b * Float64(t - 2.0)));
	elseif (y <= 3.35e+62)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -8.2e+22)
		tmp = t_1;
	elseif (y <= 7e-263)
		tmp = x + (b * (t - 2.0));
	elseif (y <= 3.35e+62)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+22], t$95$1, If[LessEqual[y, 7e-263], N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.35e+62], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.19999999999999958e22 or 3.3499999999999998e62 < y

   1. Initial program 96.8%

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

   3. Taylor expanded in 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 73.4%

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

   5. Simplified 73.4%

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

   if -8.19999999999999958e22 < y < 6.99999999999999938e-263

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 61.9%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 61.9%

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

   if 6.99999999999999938e-263 < y < 3.3499999999999998e62

   1. Initial program 96.2%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate--l+ N/A

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

      21. sub-neg N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in a around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 63.2%

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

   8. Simplified 63.2%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-263}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{+62}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -1.85 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-139}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -1.85e+103)
     t_1
     (if (<= b 2.55e-139)
       (+ x (* a (- 1.0 t)))
       (if (<= b 4.4e-24) (* y (- b z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -1.85e+103) {
		tmp = t_1;
	} else if (b <= 2.55e-139) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 4.4e-24) {
		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 = b * (t + (y + (-2.0d0)))
    if (b <= (-1.85d+103)) then
        tmp = t_1
    else if (b <= 2.55d-139) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 4.4d-24) 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 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -1.85e+103) {
		tmp = t_1;
	} else if (b <= 2.55e-139) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 4.4e-24) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -1.85e+103:
		tmp = t_1
	elif b <= 2.55e-139:
		tmp = x + (a * (1.0 - t))
	elif b <= 4.4e-24:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -1.85e+103)
		tmp = t_1;
	elseif (b <= 2.55e-139)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 4.4e-24)
		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 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -1.85e+103)
		tmp = t_1;
	elseif (b <= 2.55e-139)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 4.4e-24)
		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[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.85e+103], t$95$1, If[LessEqual[b, 2.55e-139], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e-24], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.85000000000000016e103 or 4.40000000000000003e-24 < b

   1. Initial program 93.7%

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

   3. Taylor expanded in b around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. metadata-eval 71.4%

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

   5. Simplified 71.4%

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

   if -1.85000000000000016e103 < b < 2.55000000000000018e-139

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate--l+ N/A

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

      21. sub-neg N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in a around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 55.2%

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

   8. Simplified 55.2%

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

   if 2.55000000000000018e-139 < b < 4.40000000000000003e-24

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 66.0%

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

   5. Simplified 66.0%

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

Alternative 7: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * (y + (-2.0d0))) + ((t * (b - a)) + (a + (z * (1.0d0 - y)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in t around 0

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

   1. associate--l+ N/A

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

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

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

   3. associate--l+ N/A

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

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

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

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

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

   6. sub-neg N/A

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

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

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

   8. metadata-eval N/A

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

   9. sub-neg N/A

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

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

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

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

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

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

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

   13. distribute-neg-in N/A

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

   14. mul-1-neg N/A

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

   15. remove-double-neg N/A

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

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

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

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

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

   18. mul-1-neg N/A

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

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

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

   20. mul-1-neg N/A

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

   21. sub-neg N/A

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

5. Simplified 96.5%

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

Alternative 8: 48.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;y \leq 114000000000:\\ \;\;\;\;x + b \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.65e+21)
     t_1
     (if (<= y -9e-273)
       (* b (+ t -2.0))
       (if (<= y 114000000000.0) (+ x (* b -2.0)) 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 <= -2.65e+21) {
		tmp = t_1;
	} else if (y <= -9e-273) {
		tmp = b * (t + -2.0);
	} else if (y <= 114000000000.0) {
		tmp = x + (b * -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-2.65d+21)) then
        tmp = t_1
    else if (y <= (-9d-273)) then
        tmp = b * (t + (-2.0d0))
    else if (y <= 114000000000.0d0) then
        tmp = x + (b * (-2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.65e+21) {
		tmp = t_1;
	} else if (y <= -9e-273) {
		tmp = b * (t + -2.0);
	} else if (y <= 114000000000.0) {
		tmp = x + (b * -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2.65e+21:
		tmp = t_1
	elif y <= -9e-273:
		tmp = b * (t + -2.0)
	elif y <= 114000000000.0:
		tmp = x + (b * -2.0)
	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 <= -2.65e+21)
		tmp = t_1;
	elseif (y <= -9e-273)
		tmp = Float64(b * Float64(t + -2.0));
	elseif (y <= 114000000000.0)
		tmp = Float64(x + Float64(b * -2.0));
	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 <= -2.65e+21)
		tmp = t_1;
	elseif (y <= -9e-273)
		tmp = b * (t + -2.0);
	elseif (y <= 114000000000.0)
		tmp = x + (b * -2.0);
	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, -2.65e+21], t$95$1, If[LessEqual[y, -9e-273], N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 114000000000.0], N[(x + N[(b * -2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.65e21 or 1.14e11 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 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 70.1%

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

   5. Simplified 70.1%

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

   if -2.65e21 < y < -8.99999999999999921e-273

   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 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 54.1%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 54.1%

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

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
   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 40.8%

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

   11. Simplified 40.8%

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

   if -8.99999999999999921e-273 < y < 1.14e11

   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 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 62.8%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 62.8%

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

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + -2 \cdot b} \]
   10. Step-by-step derivation

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

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 47.4%

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

   11. Simplified 47.4%

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

Alternative 9: 48.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-262}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;y \leq 560000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.45e+24)
     t_1
     (if (<= y 2.4e-262)
       (* b (+ t -2.0))
       (if (<= y 560000000000.0) (* a (- 1.0 t)) 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 <= -1.45e+24) {
		tmp = t_1;
	} else if (y <= 2.4e-262) {
		tmp = b * (t + -2.0);
	} else if (y <= 560000000000.0) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1.45d+24)) then
        tmp = t_1
    else if (y <= 2.4d-262) then
        tmp = b * (t + (-2.0d0))
    else if (y <= 560000000000.0d0) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.45e+24) {
		tmp = t_1;
	} else if (y <= 2.4e-262) {
		tmp = b * (t + -2.0);
	} else if (y <= 560000000000.0) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.45e+24:
		tmp = t_1
	elif y <= 2.4e-262:
		tmp = b * (t + -2.0)
	elif y <= 560000000000.0:
		tmp = a * (1.0 - t)
	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 <= -1.45e+24)
		tmp = t_1;
	elseif (y <= 2.4e-262)
		tmp = Float64(b * Float64(t + -2.0));
	elseif (y <= 560000000000.0)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.45e+24)
		tmp = t_1;
	elseif (y <= 2.4e-262)
		tmp = b * (t + -2.0);
	elseif (y <= 560000000000.0)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+24], t$95$1, If[LessEqual[y, 2.4e-262], N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 560000000000.0], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4499999999999999e24 or 5.6e11 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 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 70.1%

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

   5. Simplified 70.1%

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

   if -1.4499999999999999e24 < y < 2.4e-262

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 61.9%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 61.9%

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

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
   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 43.4%

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

   11. Simplified 43.4%

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

   if 2.4e-262 < y < 5.6e11

   1. Initial program 97.4%

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

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

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      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 44.0%

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

   5. Simplified 44.0%

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

Alternative 10: 44.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -13:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-301}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+21}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -13.0)
     t_1
     (if (<= t 2.8e-301) (* y b) (if (<= t 2.25e+21) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -13.0) {
		tmp = t_1;
	} else if (t <= 2.8e-301) {
		tmp = y * b;
	} else if (t <= 2.25e+21) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-13.0d0)) then
        tmp = t_1
    else if (t <= 2.8d-301) then
        tmp = y * b
    else if (t <= 2.25d+21) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -13.0) {
		tmp = t_1;
	} else if (t <= 2.8e-301) {
		tmp = y * b;
	} else if (t <= 2.25e+21) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -13.0:
		tmp = t_1
	elif t <= 2.8e-301:
		tmp = y * b
	elif t <= 2.25e+21:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -13.0)
		tmp = t_1;
	elseif (t <= 2.8e-301)
		tmp = Float64(y * b);
	elseif (t <= 2.25e+21)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -13.0)
		tmp = t_1;
	elseif (t <= 2.8e-301)
		tmp = y * b;
	elseif (t <= 2.25e+21)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -13.0], t$95$1, If[LessEqual[t, 2.8e-301], N[(y * b), $MachinePrecision], If[LessEqual[t, 2.25e+21], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -13 or 2.25e21 < t

   1. Initial program 96.6%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   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 62.1%

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

   5. Simplified 62.1%

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

   if -13 < t < 2.8000000000000001e-301

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{b}\right) \]
   7. Step-by-step derivation

   8. Simplified 28.3%

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

   if 2.8000000000000001e-301 < t < 2.25e21

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate--l+ N/A

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

      21. sub-neg N/A

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

   5. Simplified 96.8%

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

   6. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 60.3%

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

   8. Simplified 60.3%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + z} \]
   10. Step-by-step derivation

       1. +-lowering-+.f64 39.2%

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

   11. Simplified 39.2%

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

Alternative 11: 41.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -6.3 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+76}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -6.3e+25)
     t_1
     (if (<= a -7.2e-218) (* b (+ t -2.0)) (if (<= a 1.95e+76) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -6.3e+25) {
		tmp = t_1;
	} else if (a <= -7.2e-218) {
		tmp = b * (t + -2.0);
	} else if (a <= 1.95e+76) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-6.3d+25)) then
        tmp = t_1
    else if (a <= (-7.2d-218)) then
        tmp = b * (t + (-2.0d0))
    else if (a <= 1.95d+76) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -6.3e+25) {
		tmp = t_1;
	} else if (a <= -7.2e-218) {
		tmp = b * (t + -2.0);
	} else if (a <= 1.95e+76) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -6.3e+25:
		tmp = t_1
	elif a <= -7.2e-218:
		tmp = b * (t + -2.0)
	elif a <= 1.95e+76:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -6.3e+25)
		tmp = t_1;
	elseif (a <= -7.2e-218)
		tmp = Float64(b * Float64(t + -2.0));
	elseif (a <= 1.95e+76)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -6.3e+25)
		tmp = t_1;
	elseif (a <= -7.2e-218)
		tmp = b * (t + -2.0);
	elseif (a <= 1.95e+76)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.3e+25], t$95$1, If[LessEqual[a, -7.2e-218], N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e+76], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.29999999999999973e25 or 1.94999999999999995e76 < a

   1. Initial program 94.0%

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

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

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      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 54.4%

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

   5. Simplified 54.4%

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

   if -6.29999999999999973e25 < a < -7.20000000000000023e-218

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 67.8%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 48.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
   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 38.0%

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

   11. Simplified 38.0%

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

   if -7.20000000000000023e-218 < a < 1.94999999999999995e76

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate--l+ N/A

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

      21. sub-neg N/A

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

   5. Simplified 96.9%

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

   6. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 61.7%

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

   8. Simplified 61.7%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + z} \]
   10. Step-by-step derivation

       1. +-lowering-+.f64 32.8%

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

   11. Simplified 32.8%

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

Alternative 12: 40.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-182}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+79}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.75e+44)
     t_1
     (if (<= a -6.4e-182) (* y b) (if (<= a 2.9e+79) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.75e+44) {
		tmp = t_1;
	} else if (a <= -6.4e-182) {
		tmp = y * b;
	} else if (a <= 2.9e+79) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-1.75d+44)) then
        tmp = t_1
    else if (a <= (-6.4d-182)) then
        tmp = y * b
    else if (a <= 2.9d+79) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.75e+44) {
		tmp = t_1;
	} else if (a <= -6.4e-182) {
		tmp = y * b;
	} else if (a <= 2.9e+79) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -1.75e+44:
		tmp = t_1
	elif a <= -6.4e-182:
		tmp = y * b
	elif a <= 2.9e+79:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.75e+44)
		tmp = t_1;
	elseif (a <= -6.4e-182)
		tmp = Float64(y * b);
	elseif (a <= 2.9e+79)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.75e+44)
		tmp = t_1;
	elseif (a <= -6.4e-182)
		tmp = y * b;
	elseif (a <= 2.9e+79)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+44], t$95$1, If[LessEqual[a, -6.4e-182], N[(y * b), $MachinePrecision], If[LessEqual[a, 2.9e+79], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.75e44 or 2.89999999999999992e79 < a

   1. Initial program 93.8%

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

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

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      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 55.5%

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

   5. Simplified 55.5%

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

   if -1.75e44 < a < -6.40000000000000004e-182

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{b}\right) \]
   7. Step-by-step derivation

   8. Simplified 27.3%

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

   if -6.40000000000000004e-182 < a < 2.89999999999999992e79

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate--l+ N/A

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

      21. sub-neg N/A

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

   5. Simplified 97.2%

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

   6. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 60.6%

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

   8. Simplified 60.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + z} \]
   10. Step-by-step derivation

       1. +-lowering-+.f64 31.4%

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

   11. Simplified 31.4%

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

Alternative 13: 71.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -53000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3500000000000:\\ \;\;\;\;z \cdot \left(1 - y\right) + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -53000000.0)
     t_1
     (if (<= b 3500000000000.0) (+ (* z (- 1.0 y)) (+ x 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 <= -53000000.0) {
		tmp = t_1;
	} else if (b <= 3500000000000.0) {
		tmp = (z * (1.0 - y)) + (x + 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 <= (-53000000.0d0)) then
        tmp = t_1
    else if (b <= 3500000000000.0d0) then
        tmp = (z * (1.0d0 - y)) + (x + 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 <= -53000000.0) {
		tmp = t_1;
	} else if (b <= 3500000000000.0) {
		tmp = (z * (1.0 - y)) + (x + 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 <= -53000000.0:
		tmp = t_1
	elif b <= 3500000000000.0:
		tmp = (z * (1.0 - y)) + (x + 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 <= -53000000.0)
		tmp = t_1;
	elseif (b <= 3500000000000.0)
		tmp = Float64(Float64(z * Float64(1.0 - y)) + Float64(x + 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 <= -53000000.0)
		tmp = t_1;
	elseif (b <= 3500000000000.0)
		tmp = (z * (1.0 - y)) + (x + 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, -53000000.0], t$95$1, If[LessEqual[b, 3500000000000.0], N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.3e7 or 3.5e12 < b

   1. Initial program 94.5%

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

   3. Taylor expanded in 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 78.9%

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

   if -5.3e7 < b < 3.5e12

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate--l+ N/A

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

      21. sub-neg N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. mul-1-neg N/A

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

      6. *-rgt-identity N/A

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

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

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

      8. mul-1-neg N/A

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

      9. distribute-lft-in N/A

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

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

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

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

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

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

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

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

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

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

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

      17. --lowering--.f64 94.0%

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

   8. Simplified 94.0%

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

   9. Taylor expanded in t around 0

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

   11. Simplified 72.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -53000000:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 3500000000000:\\ \;\;\;\;z \cdot \left(1 - y\right) + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 80000000000000:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))))
   (if (<= z -4.3e+105)
     t_1
     (if (<= z 80000000000000.0) (+ x (* (- (+ y t) 2.0) b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double tmp;
	if (z <= -4.3e+105) {
		tmp = t_1;
	} else if (z <= 80000000000000.0) {
		tmp = x + (((y + t) - 2.0) * 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 = x + (z * (1.0d0 - y))
    if (z <= (-4.3d+105)) then
        tmp = t_1
    else if (z <= 80000000000000.0d0) then
        tmp = x + (((y + t) - 2.0d0) * 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 = x + (z * (1.0 - y));
	double tmp;
	if (z <= -4.3e+105) {
		tmp = t_1;
	} else if (z <= 80000000000000.0) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	tmp = 0
	if z <= -4.3e+105:
		tmp = t_1
	elif z <= 80000000000000.0:
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (z <= -4.3e+105)
		tmp = t_1;
	elseif (z <= 80000000000000.0)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (z <= -4.3e+105)
		tmp = t_1;
	elseif (z <= 80000000000000.0)
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+105], t$95$1, If[LessEqual[z, 80000000000000.0], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000002e105 or 8e13 < z

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate--l+ N/A

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

      21. sub-neg N/A

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

   5. Simplified 95.0%

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

   6. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 75.0%

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

   8. Simplified 75.0%

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

   if -4.3000000000000002e105 < z < 8e13

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 67.0%

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

Alternative 15: 35.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+69}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-8}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+127}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.7e+69)
   (* y b)
   (if (<= y 6.5e-8) (+ x z) (if (<= y 1.2e+127) (* t b) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e+69) {
		tmp = y * b;
	} else if (y <= 6.5e-8) {
		tmp = x + z;
	} else if (y <= 1.2e+127) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.7d+69)) then
        tmp = y * b
    else if (y <= 6.5d-8) then
        tmp = x + z
    else if (y <= 1.2d+127) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e+69) {
		tmp = y * b;
	} else if (y <= 6.5e-8) {
		tmp = x + z;
	} else if (y <= 1.2e+127) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.7e+69:
		tmp = y * b
	elif y <= 6.5e-8:
		tmp = x + z
	elif y <= 1.2e+127:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.7e+69)
		tmp = Float64(y * b);
	elseif (y <= 6.5e-8)
		tmp = Float64(x + z);
	elseif (y <= 1.2e+127)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.7e+69)
		tmp = y * b;
	elseif (y <= 6.5e-8)
		tmp = x + z;
	elseif (y <= 1.2e+127)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.7e+69], N[(y * b), $MachinePrecision], If[LessEqual[y, 6.5e-8], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.2e+127], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999993e69 or 1.2000000000000001e127 < y

   1. Initial program 95.8%

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

   3. Taylor expanded in 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 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{b}\right) \]
   7. Step-by-step derivation

   8. Simplified 40.1%

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

   if -1.69999999999999993e69 < y < 6.49999999999999997e-8

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate--l+ N/A

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

      21. sub-neg N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + z} \]
   10. Step-by-step derivation

       1. +-lowering-+.f64 33.1%

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

   11. Simplified 33.1%

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

   if 6.49999999999999997e-8 < y < 1.2000000000000001e127

   1. Initial program 96.7%

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

   3. Taylor expanded in 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 41.1%

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

   6. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 24.5%

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

   8. Simplified 24.5%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+69}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-8}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+127}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-302}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.35e+47)
   (* t b)
   (if (<= t 9.5e-302) (* y b) (if (<= t 1.55e+63) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e+47) {
		tmp = t * b;
	} else if (t <= 9.5e-302) {
		tmp = y * b;
	} else if (t <= 1.55e+63) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.35d+47)) then
        tmp = t * b
    else if (t <= 9.5d-302) then
        tmp = y * b
    else if (t <= 1.55d+63) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e+47) {
		tmp = t * b;
	} else if (t <= 9.5e-302) {
		tmp = y * b;
	} else if (t <= 1.55e+63) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.35e+47:
		tmp = t * b
	elif t <= 9.5e-302:
		tmp = y * b
	elif t <= 1.55e+63:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.35e+47)
		tmp = Float64(t * b);
	elseif (t <= 9.5e-302)
		tmp = Float64(y * b);
	elseif (t <= 1.55e+63)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.35e+47)
		tmp = t * b;
	elseif (t <= 9.5e-302)
		tmp = y * b;
	elseif (t <= 1.55e+63)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.35e+47], N[(t * b), $MachinePrecision], If[LessEqual[t, 9.5e-302], N[(y * b), $MachinePrecision], If[LessEqual[t, 1.55e+63], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.34999999999999998e47 or 1.55e63 < t

   1. Initial program 95.8%

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

   3. Taylor expanded in 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 45.7%

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

   6. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 37.1%

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

   8. Simplified 37.1%

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

   if -1.34999999999999998e47 < t < 9.49999999999999991e-302

   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 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 47.8%

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

   5. Simplified 47.8%

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

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{b}\right) \]
   7. Step-by-step derivation

   8. Simplified 27.3%

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

   if 9.49999999999999991e-302 < t < 1.55e63

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 28.1%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-302}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -8.4 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{+78}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -8.4e+102) t_1 (if (<= b 1.38e+78) (+ x (* z (- 1.0 y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -8.4e+102) {
		tmp = t_1;
	} else if (b <= 1.38e+78) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t + (y + (-2.0d0)))
    if (b <= (-8.4d+102)) then
        tmp = t_1
    else if (b <= 1.38d+78) then
        tmp = x + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -8.4e+102) {
		tmp = t_1;
	} else if (b <= 1.38e+78) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -8.4e+102:
		tmp = t_1
	elif b <= 1.38e+78:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -8.4e+102)
		tmp = t_1;
	elseif (b <= 1.38e+78)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -8.4e+102)
		tmp = t_1;
	elseif (b <= 1.38e+78)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.4e+102], t$95$1, If[LessEqual[b, 1.38e+78], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.40000000000000006e102 or 1.37999999999999992e78 < b

   1. Initial program 92.6%

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

   3. Taylor expanded in b around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. metadata-eval 78.9%

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

   5. Simplified 78.9%

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

   if -8.40000000000000006e102 < b < 1.37999999999999992e78

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate--l+ N/A

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

      21. sub-neg N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 58.2%

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

   8. Simplified 58.2%

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

Alternative 18: 52.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+57}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -6.6e+24) t_1 (if (<= y 7.5e+57) (+ 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 <= -6.6e+24) {
		tmp = t_1;
	} else if (y <= 7.5e+57) {
		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 <= (-6.6d+24)) then
        tmp = t_1
    else if (y <= 7.5d+57) 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 <= -6.6e+24) {
		tmp = t_1;
	} else if (y <= 7.5e+57) {
		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 <= -6.6e+24:
		tmp = t_1
	elif y <= 7.5e+57:
		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 <= -6.6e+24)
		tmp = t_1;
	elseif (y <= 7.5e+57)
		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 <= -6.6e+24)
		tmp = t_1;
	elseif (y <= 7.5e+57)
		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, -6.6e+24], t$95$1, If[LessEqual[y, 7.5e+57], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5999999999999998e24 or 7.5000000000000006e57 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in 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 73.1%

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

   5. Simplified 73.1%

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

   if -6.5999999999999998e24 < y < 7.5000000000000006e57

   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 58.2%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 41.4%

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

Alternative 19: 27.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.2e+48) (* t b) (if (<= t 1.02e+66) x (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.2e+48) {
		tmp = t * b;
	} else if (t <= 1.02e+66) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.2d+48)) then
        tmp = t * b
    else if (t <= 1.02d+66) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.2e+48) {
		tmp = t * b;
	} else if (t <= 1.02e+66) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.2e+48:
		tmp = t * b
	elif t <= 1.02e+66:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.2e+48)
		tmp = Float64(t * b);
	elseif (t <= 1.02e+66)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.2e+48)
		tmp = t * b;
	elseif (t <= 1.02e+66)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.2e+48], N[(t * b), $MachinePrecision], If[LessEqual[t, 1.02e+66], x, N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.1999999999999999e48 or 1.01999999999999998e66 < t

   1. Initial program 95.7%

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

   3. Taylor expanded in 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 45.6%

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

   6. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 37.8%

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

   8. Simplified 37.8%

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

   if -5.1999999999999999e48 < t < 1.01999999999999998e66

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 20.1%

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

4. Final simplification 26.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 16.8% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in x around inf

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

5. Simplified 15.3%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024158 
(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)))