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

Percentage Accurate: 95.2% → 98.0%

Time: 12.5s

Alternatives: 25

Speedup: 0.8×

• 35.6% 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: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $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[(y * N[(b - z), $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 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 64.3%

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

   5. Simplified 64.3%

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

4. Final simplification 98.4%

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

Alternative 2: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+71}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (+ (* y (- b z)) (* b (+ t -2.0))))))
   (if (<= b -5.8e+150)
     t_1
     (if (<= b 1.1e+71)
       (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))
       (if (<= b 1.6e+154) t_1 (+ x (* (- (+ y t) 2.0) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (b - z)) + (b * (t + -2.0)));
	double tmp;
	if (b <= -5.8e+150) {
		tmp = t_1;
	} else if (b <= 1.1e+71) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else if (b <= 1.6e+154) {
		tmp = t_1;
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + ((y * (b - z)) + (b * (t + (-2.0d0))))
    if (b <= (-5.8d+150)) then
        tmp = t_1
    else if (b <= 1.1d+71) then
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    else if (b <= 1.6d+154) then
        tmp = t_1
    else
        tmp = x + (((y + t) - 2.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (b - z)) + (b * (t + -2.0)));
	double tmp;
	if (b <= -5.8e+150) {
		tmp = t_1;
	} else if (b <= 1.1e+71) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else if (b <= 1.6e+154) {
		tmp = t_1;
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + ((y * (b - z)) + (b * (t + -2.0)))
	tmp = 0
	if b <= -5.8e+150:
		tmp = t_1
	elif b <= 1.1e+71:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	elif b <= 1.6e+154:
		tmp = t_1
	else:
		tmp = x + (((y + t) - 2.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(b - z)) + Float64(b * Float64(t + -2.0))))
	tmp = 0.0
	if (b <= -5.8e+150)
		tmp = t_1;
	elseif (b <= 1.1e+71)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	elseif (b <= 1.6e+154)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + ((y * (b - z)) + (b * (t + -2.0)));
	tmp = 0.0;
	if (b <= -5.8e+150)
		tmp = t_1;
	elseif (b <= 1.1e+71)
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	elseif (b <= 1.6e+154)
		tmp = t_1;
	else
		tmp = x + (((y + t) - 2.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+150], t$95$1, If[LessEqual[b, 1.1e+71], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+154], t$95$1, N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.80000000000000022e150 or 1.09999999999999997e71 < b < 1.6e154

   1. Initial program 92.7%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

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

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

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

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-lowering-+.f64 89.6%

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

   8. Simplified 89.6%

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

   if -5.80000000000000022e150 < b < 1.09999999999999997e71

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

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

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

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

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. sub-neg N/A

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

      21. metadata-eval N/A

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

      22. distribute-lft-in N/A

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

      23. metadata-eval N/A

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

      24. +-commutative N/A

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

      25. neg-mul-1 N/A

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

      26. sub-neg N/A

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

   5. Simplified 79.6%

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

   if 1.6e154 < b

   1. Initial program 91.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 99.2%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+150}:\\ \;\;\;\;z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+71}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+154}:\\ \;\;\;\;z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{+255}:\\ \;\;\;\;\left(x + b \cdot \left(t + -2\right)\right) + \left(y \cdot \left(b - z\right) + \left(z + a \cdot \left(1 - t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1e+255)
   (+ (+ x (* b (+ t -2.0))) (+ (* y (- b z)) (+ z (* a (- 1.0 t)))))
   (* t (- b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1e+255) {
		tmp = (x + (b * (t + -2.0))) + ((y * (b - z)) + (z + (a * (1.0 - t))));
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1d+255) then
        tmp = (x + (b * (t + (-2.0d0)))) + ((y * (b - z)) + (z + (a * (1.0d0 - t))))
    else
        tmp = t * (b - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1e+255) {
		tmp = (x + (b * (t + -2.0))) + ((y * (b - z)) + (z + (a * (1.0 - t))));
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1e+255:
		tmp = (x + (b * (t + -2.0))) + ((y * (b - z)) + (z + (a * (1.0 - t))))
	else:
		tmp = t * (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1e+255)
		tmp = Float64(Float64(x + Float64(b * Float64(t + -2.0))) + Float64(Float64(y * Float64(b - z)) + Float64(z + Float64(a * Float64(1.0 - t)))));
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1e+255)
		tmp = (x + (b * (t + -2.0))) + ((y * (b - z)) + (z + (a * (1.0 - t))));
	else
		tmp = t * (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1e+255], N[(N[(x + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.99999999999999988e254

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. sub-neg N/A

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

   5. Simplified 97.5%

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

   if 9.99999999999999988e254 < t

   1. Initial program 69.2%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   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 92.7%

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

   5. Simplified 92.7%

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

Alternative 4: 87.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b + \left(x + z \cdot \left(1 - y\right)\right)\\ \mathbf{if}\;y \leq -13200000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+26}:\\ \;\;\;\;\left(t \cdot \left(b - a\right) + \left(z + b \cdot -2\right)\right) + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* (- (+ y t) 2.0) b) (+ x (* z (- 1.0 y))))))
   (if (<= y -13200000.0)
     t_1
     (if (<= y 8.2e+26) (+ (+ (* t (- b a)) (+ z (* b -2.0))) (+ x a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((y + t) - 2.0) * b) + (x + (z * (1.0 - y)));
	double tmp;
	if (y <= -13200000.0) {
		tmp = t_1;
	} else if (y <= 8.2e+26) {
		tmp = ((t * (b - a)) + (z + (b * -2.0))) + (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 = (((y + t) - 2.0d0) * b) + (x + (z * (1.0d0 - y)))
    if (y <= (-13200000.0d0)) then
        tmp = t_1
    else if (y <= 8.2d+26) then
        tmp = ((t * (b - a)) + (z + (b * (-2.0d0)))) + (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 = (((y + t) - 2.0) * b) + (x + (z * (1.0 - y)));
	double tmp;
	if (y <= -13200000.0) {
		tmp = t_1;
	} else if (y <= 8.2e+26) {
		tmp = ((t * (b - a)) + (z + (b * -2.0))) + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((y + t) - 2.0) * b) + (x + (z * (1.0 - y)))
	tmp = 0
	if y <= -13200000.0:
		tmp = t_1
	elif y <= 8.2e+26:
		tmp = ((t * (b - a)) + (z + (b * -2.0))) + (x + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) + Float64(x + Float64(z * Float64(1.0 - y))))
	tmp = 0.0
	if (y <= -13200000.0)
		tmp = t_1;
	elseif (y <= 8.2e+26)
		tmp = Float64(Float64(Float64(t * Float64(b - a)) + Float64(z + Float64(b * -2.0))) + Float64(x + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((y + t) - 2.0) * b) + (x + (z * (1.0 - y)));
	tmp = 0.0;
	if (y <= -13200000.0)
		tmp = t_1;
	elseif (y <= 8.2e+26)
		tmp = ((t * (b - a)) + (z + (b * -2.0))) + (x + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -13200000.0], t$95$1, If[LessEqual[y, 8.2e+26], N[(N[(N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision] + N[(z + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.32e7 or 8.19999999999999967e26 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in a around 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 82.9%

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

   5. Simplified 82.9%

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

   if -1.32e7 < y < 8.19999999999999967e26

   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-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

      12. +-lowering-+.f64 98.9%

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

   8. Simplified 98.9%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13200000:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+26}:\\ \;\;\;\;\left(t \cdot \left(b - a\right) + \left(z + b \cdot -2\right)\right) + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+121}:\\ \;\;\;\;t\_2 + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+42}:\\ \;\;\;\;t\_1 + \left(x + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)) (t_2 (* a (- 1.0 t))))
   (if (<= a -2.3e+121)
     (+ t_2 (+ x (* b (+ y -2.0))))
     (if (<= a 2.55e+42) (+ t_1 (+ x (* z (- 1.0 y)))) (+ t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -2.3e+121) {
		tmp = t_2 + (x + (b * (y + -2.0)));
	} else if (a <= 2.55e+42) {
		tmp = t_1 + (x + (z * (1.0 - y)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    t_2 = a * (1.0d0 - t)
    if (a <= (-2.3d+121)) then
        tmp = t_2 + (x + (b * (y + (-2.0d0))))
    else if (a <= 2.55d+42) then
        tmp = t_1 + (x + (z * (1.0d0 - y)))
    else
        tmp = t_1 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -2.3e+121) {
		tmp = t_2 + (x + (b * (y + -2.0)));
	} else if (a <= 2.55e+42) {
		tmp = t_1 + (x + (z * (1.0 - y)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -2.3e+121:
		tmp = t_2 + (x + (b * (y + -2.0)))
	elif a <= 2.55e+42:
		tmp = t_1 + (x + (z * (1.0 - y)))
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -2.3e+121)
		tmp = Float64(t_2 + Float64(x + Float64(b * Float64(y + -2.0))));
	elseif (a <= 2.55e+42)
		tmp = Float64(t_1 + Float64(x + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -2.3e+121)
		tmp = t_2 + (x + (b * (y + -2.0)));
	elseif (a <= 2.55e+42)
		tmp = t_1 + (x + (z * (1.0 - y)));
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+121], N[(t$95$2 + N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e+42], N[(t$95$1 + N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2999999999999999e121

   1. Initial program 86.8%

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

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

   5. Simplified 92.1%

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

   6. Taylor expanded in a around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 84.1%

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

   8. Simplified 84.1%

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

   if -2.2999999999999999e121 < a < 2.55e42

   1. Initial program 98.8%

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

   3. Taylor expanded in 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 93.1%

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

   5. Simplified 93.1%

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

   if 2.55e42 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 81.2%

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

   5. Simplified 81.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(1 - t\right) + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+42}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-160}:\\ \;\;\;\;\left(x + y \cdot b\right) - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;\left(x + a\right) + \left(z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1e+139)
     t_1
     (if (<= b -1.7e-160)
       (- (+ x (* y b)) (* (+ y -1.0) z))
       (if (<= b 2.4e-24) (+ (+ x a) (- z (* t 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 <= -1e+139) {
		tmp = t_1;
	} else if (b <= -1.7e-160) {
		tmp = (x + (y * b)) - ((y + -1.0) * z);
	} else if (b <= 2.4e-24) {
		tmp = (x + a) + (z - (t * 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 <= (-1d+139)) then
        tmp = t_1
    else if (b <= (-1.7d-160)) then
        tmp = (x + (y * b)) - ((y + (-1.0d0)) * z)
    else if (b <= 2.4d-24) then
        tmp = (x + a) + (z - (t * 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 <= -1e+139) {
		tmp = t_1;
	} else if (b <= -1.7e-160) {
		tmp = (x + (y * b)) - ((y + -1.0) * z);
	} else if (b <= 2.4e-24) {
		tmp = (x + a) + (z - (t * 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 <= -1e+139:
		tmp = t_1
	elif b <= -1.7e-160:
		tmp = (x + (y * b)) - ((y + -1.0) * z)
	elif b <= 2.4e-24:
		tmp = (x + a) + (z - (t * 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 <= -1e+139)
		tmp = t_1;
	elseif (b <= -1.7e-160)
		tmp = Float64(Float64(x + Float64(y * b)) - Float64(Float64(y + -1.0) * z));
	elseif (b <= 2.4e-24)
		tmp = Float64(Float64(x + a) + Float64(z - Float64(t * 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 <= -1e+139)
		tmp = t_1;
	elseif (b <= -1.7e-160)
		tmp = (x + (y * b)) - ((y + -1.0) * z);
	elseif (b <= 2.4e-24)
		tmp = (x + a) + (z - (t * 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, -1e+139], t$95$1, If[LessEqual[b, -1.7e-160], N[(N[(x + N[(y * b), $MachinePrecision]), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-24], N[(N[(x + a), $MachinePrecision] + N[(z - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.00000000000000003e139 or 2.3999999999999998e-24 < b

   1. Initial program 92.5%

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

   3. Taylor expanded in 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 80.5%

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

   if -1.00000000000000003e139 < b < -1.70000000000000011e-160

   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 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-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

   5. Simplified 98.4%

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

   6. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 70.2%

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

   8. Simplified 70.2%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 65.6%

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

   11. Simplified 65.6%

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

   if -1.70000000000000011e-160 < b < 2.3999999999999998e-24

   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 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-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

   5. Simplified 98.6%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

      12. +-lowering-+.f64 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in b around 0

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

       1. mul-1-neg N/A

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

       2. unsub-neg N/A

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

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

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

       4. *-lowering-*.f64 76.5%

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

   11. Simplified 76.5%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+139}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-160}:\\ \;\;\;\;\left(x + y \cdot b\right) - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;\left(x + a\right) + \left(z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \left(1 - y\right) + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-24}:\\ \;\;\;\;\left(x + a\right) + \left(z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -7.4e+41)
     t_1
     (if (<= b -3.8e-60)
       (+ (* z (- 1.0 y)) (* b (- y 2.0)))
       (if (<= b 2.1e-24) (+ (+ x a) (- z (* t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -7.4e+41) {
		tmp = t_1;
	} else if (b <= -3.8e-60) {
		tmp = (z * (1.0 - y)) + (b * (y - 2.0));
	} else if (b <= 2.1e-24) {
		tmp = (x + a) + (z - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-7.4d+41)) then
        tmp = t_1
    else if (b <= (-3.8d-60)) then
        tmp = (z * (1.0d0 - y)) + (b * (y - 2.0d0))
    else if (b <= 2.1d-24) then
        tmp = (x + a) + (z - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -7.4e+41) {
		tmp = t_1;
	} else if (b <= -3.8e-60) {
		tmp = (z * (1.0 - y)) + (b * (y - 2.0));
	} else if (b <= 2.1e-24) {
		tmp = (x + a) + (z - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -7.4e+41:
		tmp = t_1
	elif b <= -3.8e-60:
		tmp = (z * (1.0 - y)) + (b * (y - 2.0))
	elif b <= 2.1e-24:
		tmp = (x + a) + (z - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -7.4e+41)
		tmp = t_1;
	elseif (b <= -3.8e-60)
		tmp = Float64(Float64(z * Float64(1.0 - y)) + Float64(b * Float64(y - 2.0)));
	elseif (b <= 2.1e-24)
		tmp = Float64(Float64(x + a) + Float64(z - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -7.4e+41)
		tmp = t_1;
	elseif (b <= -3.8e-60)
		tmp = (z * (1.0 - y)) + (b * (y - 2.0));
	elseif (b <= 2.1e-24)
		tmp = (x + a) + (z - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e+41], t$95$1, If[LessEqual[b, -3.8e-60], N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-24], N[(N[(x + a), $MachinePrecision] + N[(z - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.39999999999999962e41 or 2.0999999999999999e-24 < b

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 78.8%

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

   if -7.39999999999999962e41 < b < -3.79999999999999994e-60

   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

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 77.1%

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

   if -3.79999999999999994e-60 < b < 2.0999999999999999e-24

   1. Initial program 99.0%

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

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

   5. Simplified 99.0%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

      12. +-lowering-+.f64 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in b around 0

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

       1. mul-1-neg N/A

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

       2. unsub-neg N/A

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

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

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

       4. *-lowering-*.f64 70.5%

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

   11. Simplified 70.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+41}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \left(1 - y\right) + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-24}:\\ \;\;\;\;\left(x + a\right) + \left(z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+150}:\\ \;\;\;\;z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+26}:\\ \;\;\;\;x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -5.8e+150)
     (+ z (+ (* y (- b z)) (* b (+ t -2.0))))
     (if (<= b 2.8e+26)
       (+ x (+ t_1 (* z (- 1.0 y))))
       (+ (* (- (+ 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 = a * (1.0 - t);
	double tmp;
	if (b <= -5.8e+150) {
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	} else if (b <= 2.8e+26) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (((y + t) - 2.0) * b) + 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 (b <= (-5.8d+150)) then
        tmp = z + ((y * (b - z)) + (b * (t + (-2.0d0))))
    else if (b <= 2.8d+26) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = (((y + t) - 2.0d0) * b) + 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 (b <= -5.8e+150) {
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	} else if (b <= 2.8e+26) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (((y + t) - 2.0) * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -5.8e+150:
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)))
	elif b <= 2.8e+26:
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = (((y + t) - 2.0) * b) + 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 (b <= -5.8e+150)
		tmp = Float64(z + Float64(Float64(y * Float64(b - z)) + Float64(b * Float64(t + -2.0))));
	elseif (b <= 2.8e+26)
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) + 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 (b <= -5.8e+150)
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	elseif (b <= 2.8e+26)
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = (((y + t) - 2.0) * b) + 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[b, -5.8e+150], N[(z + N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+26], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.80000000000000022e150

   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 z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

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

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

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

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-lowering-+.f64 91.0%

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

   8. Simplified 91.0%

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

   if -5.80000000000000022e150 < b < 2.8e26

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

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

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

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

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. sub-neg N/A

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

      21. metadata-eval N/A

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

      22. distribute-lft-in N/A

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

      23. metadata-eval N/A

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

      24. +-commutative N/A

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

      25. neg-mul-1 N/A

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

      26. sub-neg N/A

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

   5. Simplified 81.6%

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

   if 2.8e26 < b

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+150}:\\ \;\;\;\;z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+26}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+68}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -2.05e-25)
     t_1
     (if (<= b 9.5e+68) (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.05e-25) {
		tmp = t_1;
	} else if (b <= 9.5e+68) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-2.05d-25)) then
        tmp = t_1
    else if (b <= 9.5d+68) then
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.05e-25) {
		tmp = t_1;
	} else if (b <= 9.5e+68) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -2.05e-25:
		tmp = t_1
	elif b <= 9.5e+68:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -2.05e-25)
		tmp = t_1;
	elseif (b <= 9.5e+68)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -2.05e-25)
		tmp = t_1;
	elseif (b <= 9.5e+68)
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e-25], t$95$1, If[LessEqual[b, 9.5e+68], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.04999999999999994e-25 or 9.50000000000000069e68 < b

   1. Initial program 92.9%

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

   3. Taylor expanded in 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 81.0%

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

   if -2.04999999999999994e-25 < b < 9.50000000000000069e68

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

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

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

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

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. sub-neg N/A

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

      21. metadata-eval N/A

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

      22. distribute-lft-in N/A

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

      23. metadata-eval N/A

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

      24. +-commutative N/A

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

      25. neg-mul-1 N/A

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

      26. sub-neg N/A

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

   5. Simplified 83.9%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{-25}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+68}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1900000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-69}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;y \leq 600000000:\\ \;\;\;\;z + b \cdot \left(t + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1900000000.0)
     t_1
     (if (<= y -1.45e-69)
       (+ z (+ x a))
       (if (<= y 600000000.0) (+ z (* b (+ t -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 <= -1900000000.0) {
		tmp = t_1;
	} else if (y <= -1.45e-69) {
		tmp = z + (x + a);
	} else if (y <= 600000000.0) {
		tmp = z + (b * (t + -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 <= (-1900000000.0d0)) then
        tmp = t_1
    else if (y <= (-1.45d-69)) then
        tmp = z + (x + a)
    else if (y <= 600000000.0d0) then
        tmp = z + (b * (t + (-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 <= -1900000000.0) {
		tmp = t_1;
	} else if (y <= -1.45e-69) {
		tmp = z + (x + a);
	} else if (y <= 600000000.0) {
		tmp = z + (b * (t + -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 <= -1900000000.0:
		tmp = t_1
	elif y <= -1.45e-69:
		tmp = z + (x + a)
	elif y <= 600000000.0:
		tmp = z + (b * (t + -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 <= -1900000000.0)
		tmp = t_1;
	elseif (y <= -1.45e-69)
		tmp = Float64(z + Float64(x + a));
	elseif (y <= 600000000.0)
		tmp = Float64(z + Float64(b * Float64(t + -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 <= -1900000000.0)
		tmp = t_1;
	elseif (y <= -1.45e-69)
		tmp = z + (x + a);
	elseif (y <= 600000000.0)
		tmp = z + (b * (t + -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, -1900000000.0], t$95$1, If[LessEqual[y, -1.45e-69], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 600000000.0], N[(z + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9e9 or 6e8 < y

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 67.1%

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

   5. Simplified 67.1%

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

   if -1.9e9 < y < -1.4499999999999999e-69

   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 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-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

      12. +-lowering-+.f64 98.3%

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

   8. Simplified 98.3%

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

   9. Taylor expanded in z around inf

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

   11. Simplified 65.3%

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

   if -1.4499999999999999e-69 < y < 6e8

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 55.7%

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

   8. Simplified 55.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1900000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-69}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;y \leq 600000000:\\ \;\;\;\;z + b \cdot \left(t + -2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1700000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-229}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1700000000.0)
     t_1
     (if (<= y 1.55e-229)
       (+ z (+ x a))
       (if (<= y 5.8e+74) (* t (- b a)) 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 <= -1700000000.0) {
		tmp = t_1;
	} else if (y <= 1.55e-229) {
		tmp = z + (x + a);
	} else if (y <= 5.8e+74) {
		tmp = t * (b - 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 = y * (b - z)
    if (y <= (-1700000000.0d0)) then
        tmp = t_1
    else if (y <= 1.55d-229) then
        tmp = z + (x + a)
    else if (y <= 5.8d+74) then
        tmp = t * (b - 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 = y * (b - z);
	double tmp;
	if (y <= -1700000000.0) {
		tmp = t_1;
	} else if (y <= 1.55e-229) {
		tmp = z + (x + a);
	} else if (y <= 5.8e+74) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1700000000.0:
		tmp = t_1
	elif y <= 1.55e-229:
		tmp = z + (x + a)
	elif y <= 5.8e+74:
		tmp = t * (b - a)
	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 <= -1700000000.0)
		tmp = t_1;
	elseif (y <= 1.55e-229)
		tmp = Float64(z + Float64(x + a));
	elseif (y <= 5.8e+74)
		tmp = Float64(t * Float64(b - a));
	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 <= -1700000000.0)
		tmp = t_1;
	elseif (y <= 1.55e-229)
		tmp = z + (x + a);
	elseif (y <= 5.8e+74)
		tmp = t * (b - a);
	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, -1700000000.0], t$95$1, If[LessEqual[y, 1.55e-229], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+74], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e9 or 5.8000000000000005e74 < y

   1. Initial program 92.3%

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

   3. Taylor expanded in 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 70.0%

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

   5. Simplified 70.0%

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

   if -1.7e9 < y < 1.55e-229

   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 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-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

      12. +-lowering-+.f64 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in z around inf

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

   11. Simplified 54.6%

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

   if 1.55e-229 < y < 5.8000000000000005e74

   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 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 52.2%

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

   5. Simplified 52.2%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1700000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-229}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2050000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-242}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2050000000.0)
     t_1
     (if (<= y 3.2e-242)
       (+ x (* t b))
       (if (<= y 2.1e+76) (* t (- b a)) 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 <= -2050000000.0) {
		tmp = t_1;
	} else if (y <= 3.2e-242) {
		tmp = x + (t * b);
	} else if (y <= 2.1e+76) {
		tmp = t * (b - 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 = y * (b - z)
    if (y <= (-2050000000.0d0)) then
        tmp = t_1
    else if (y <= 3.2d-242) then
        tmp = x + (t * b)
    else if (y <= 2.1d+76) then
        tmp = t * (b - 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 = y * (b - z);
	double tmp;
	if (y <= -2050000000.0) {
		tmp = t_1;
	} else if (y <= 3.2e-242) {
		tmp = x + (t * b);
	} else if (y <= 2.1e+76) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2050000000.0:
		tmp = t_1
	elif y <= 3.2e-242:
		tmp = x + (t * b)
	elif y <= 2.1e+76:
		tmp = t * (b - a)
	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 <= -2050000000.0)
		tmp = t_1;
	elseif (y <= 3.2e-242)
		tmp = Float64(x + Float64(t * b));
	elseif (y <= 2.1e+76)
		tmp = Float64(t * Float64(b - a));
	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 <= -2050000000.0)
		tmp = t_1;
	elseif (y <= 3.2e-242)
		tmp = x + (t * b);
	elseif (y <= 2.1e+76)
		tmp = t * (b - a);
	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, -2050000000.0], t$95$1, If[LessEqual[y, 3.2e-242], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+76], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e9 or 2.10000000000000007e76 < y

   1. Initial program 92.3%

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

   3. Taylor expanded in 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 70.0%

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

   5. Simplified 70.0%

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

   if -2.05e9 < y < 3.19999999999999999e-242

   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 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 55.1%

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

   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 41.6%

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

   if 3.19999999999999999e-242 < y < 2.10000000000000007e76

   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 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 51.3%

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

   5. Simplified 51.3%

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

Alternative 13: 38.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + -2\right)\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.95 \cdot 10^{+105}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t -2.0))))
   (if (<= b -1.35e-72)
     t_1
     (if (<= b 1.3e+84) (* a (- 1.0 t)) (if (<= b 3.95e+105) (* y b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + -2.0);
	double tmp;
	if (b <= -1.35e-72) {
		tmp = t_1;
	} else if (b <= 1.3e+84) {
		tmp = a * (1.0 - t);
	} else if (b <= 3.95e+105) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t + (-2.0d0))
    if (b <= (-1.35d-72)) then
        tmp = t_1
    else if (b <= 1.3d+84) then
        tmp = a * (1.0d0 - t)
    else if (b <= 3.95d+105) then
        tmp = y * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + -2.0);
	double tmp;
	if (b <= -1.35e-72) {
		tmp = t_1;
	} else if (b <= 1.3e+84) {
		tmp = a * (1.0 - t);
	} else if (b <= 3.95e+105) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + -2.0)
	tmp = 0
	if b <= -1.35e-72:
		tmp = t_1
	elif b <= 1.3e+84:
		tmp = a * (1.0 - t)
	elif b <= 3.95e+105:
		tmp = y * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + -2.0))
	tmp = 0.0
	if (b <= -1.35e-72)
		tmp = t_1;
	elseif (b <= 1.3e+84)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 3.95e+105)
		tmp = Float64(y * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + -2.0);
	tmp = 0.0;
	if (b <= -1.35e-72)
		tmp = t_1;
	elseif (b <= 1.3e+84)
		tmp = a * (1.0 - t);
	elseif (b <= 3.95e+105)
		tmp = y * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.35e-72], t$95$1, If[LessEqual[b, 1.3e+84], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.95e+105], N[(y * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.35e-72 or 3.95e105 < 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 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-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

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

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

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

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

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

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

      13. distribute-neg-in N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

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

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

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

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

      18. mul-1-neg N/A

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

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

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

      20. mul-1-neg N/A

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

   5. Simplified 92.2%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

      12. +-lowering-+.f64 69.9%

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

   8. Simplified 69.9%

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

   9. Taylor expanded in b around inf

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

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

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

       2. sub-neg N/A

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

       3. metadata-eval N/A

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

       4. +-commutative N/A

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

       5. +-lowering-+.f64 43.9%

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

   11. Simplified 43.9%

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

   if -1.35e-72 < b < 1.3000000000000001e84

   1. Initial program 97.5%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 39.9%

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

   5. Simplified 39.9%

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

   if 1.3000000000000001e84 < b < 3.95e105

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   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 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in b around inf

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

   8. Simplified 100.0%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-72}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.95 \cdot 10^{+105}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+204}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+85}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e+204)
   (* t b)
   (if (<= b -4.4e+38) x (if (<= b 3.8e+85) (* a (- 1.0 t)) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e+204) {
		tmp = t * b;
	} else if (b <= -4.4e+38) {
		tmp = x;
	} else if (b <= 3.8e+85) {
		tmp = a * (1.0 - t);
	} 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 (b <= (-3d+204)) then
        tmp = t * b
    else if (b <= (-4.4d+38)) then
        tmp = x
    else if (b <= 3.8d+85) then
        tmp = a * (1.0d0 - t)
    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 (b <= -3e+204) {
		tmp = t * b;
	} else if (b <= -4.4e+38) {
		tmp = x;
	} else if (b <= 3.8e+85) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e+204:
		tmp = t * b
	elif b <= -4.4e+38:
		tmp = x
	elif b <= 3.8e+85:
		tmp = a * (1.0 - t)
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e+204)
		tmp = Float64(t * b);
	elseif (b <= -4.4e+38)
		tmp = x;
	elseif (b <= 3.8e+85)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e+204)
		tmp = t * b;
	elseif (b <= -4.4e+38)
		tmp = x;
	elseif (b <= 3.8e+85)
		tmp = a * (1.0 - t);
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3e+204], N[(t * b), $MachinePrecision], If[LessEqual[b, -4.4e+38], x, If[LessEqual[b, 3.8e+85], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.99999999999999983e204

   1. Initial program 95.6%

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

   3. Taylor expanded in 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 91.5%

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

   6. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 53.2%

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

   8. Simplified 53.2%

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

   if -2.99999999999999983e204 < b < -4.40000000000000013e38

   1. Initial program 94.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 30.4%

      \[\leadsto \color{blue}{x} \]

   if -4.40000000000000013e38 < b < 3.79999999999999992e85

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto a \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto a \cdot \left(1 + -1 \cdot \color{blue}{t}\right) \]

      3. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + \color{blue}{-1} \cdot t\right) \]

      4. distribute-lft-in N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(-1 + t\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \color{blue}{-1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t - \color{blue}{1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 37.6%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 37.6%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if 3.79999999999999992e85 < b

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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 51.1%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{b}\right) \]
   7. Step-by-step derivation

   8. Simplified 45.5%

      \[\leadsto y \cdot \color{blue}{b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+204}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+85}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-24}:\\ \;\;\;\;\left(x + a\right) + \left(z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -8.2e-64) t_1 (if (<= b 2.1e-24) (+ (+ x a) (- z (* t 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 <= -8.2e-64) {
		tmp = t_1;
	} else if (b <= 2.1e-24) {
		tmp = (x + a) + (z - (t * 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 <= (-8.2d-64)) then
        tmp = t_1
    else if (b <= 2.1d-24) then
        tmp = (x + a) + (z - (t * 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 <= -8.2e-64) {
		tmp = t_1;
	} else if (b <= 2.1e-24) {
		tmp = (x + a) + (z - (t * 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 <= -8.2e-64:
		tmp = t_1
	elif b <= 2.1e-24:
		tmp = (x + a) + (z - (t * 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 <= -8.2e-64)
		tmp = t_1;
	elseif (b <= 2.1e-24)
		tmp = Float64(Float64(x + a) + Float64(z - Float64(t * 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 <= -8.2e-64)
		tmp = t_1;
	elseif (b <= 2.1e-24)
		tmp = (x + a) + (z - (t * 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, -8.2e-64], t$95$1, If[LessEqual[b, 2.1e-24], N[(N[(x + a), $MachinePrecision] + N[(z - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.2000000000000001e-64 or 2.0999999999999999e-24 < b

   1. Initial program 93.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 75.1%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -8.2000000000000001e-64 < b < 2.0999999999999999e-24

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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-+r+ N/A

         \[\leadsto \left(\left(x + b \cdot \left(y - 2\right)\right) + t \cdot \left(b - a\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + \color{blue}{\left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + b \cdot \left(y - 2\right)\right), \color{blue}{\left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(y - 2\right)\right)\right), \left(\color{blue}{t \cdot \left(b - a\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(y - 2\right)\right)\right), \left(t \cdot \color{blue}{\left(b - a\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \left(t \cdot \left(b - \color{blue}{a}\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \left(t \cdot \left(b - \color{blue}{a}\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \left(t \cdot \left(b - a\right) + \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\left(t \cdot \left(b - a\right)\right), \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b - a\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\mathsf{neg}\left(\left(-1 \cdot a + \color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right)\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\left(\mathsf{neg}\left(-1 \cdot a\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z} \cdot \left(y - 1\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(a + \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 99.0%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y + -2\right)\right) + \left(t \cdot \left(b - a\right) + \left(a + z \cdot \left(1 - y\right)\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(x + \left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right) + \color{blue}{\left(a + x\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right), \color{blue}{\left(a + x\right)}\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z + -2 \cdot b\right) + t \cdot \left(b - a\right)\right), \left(\color{blue}{a} + x\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(b - a\right) + \left(z + -2 \cdot b\right)\right), \left(\color{blue}{a} + x\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(b - a\right)\right), \left(z + -2 \cdot b\right)\right), \left(\color{blue}{a} + x\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b - a\right)\right), \left(z + -2 \cdot b\right)\right), \left(a + x\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(z + -2 \cdot b\right)\right), \left(a + x\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \left(-2 \cdot b\right)\right)\right), \left(a + x\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \left(b \cdot -2\right)\right)\right), \left(a + x\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(b, -2\right)\right)\right), \left(a + x\right)\right) \]

      12. +-lowering-+.f64 75.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(b, -2\right)\right)\right), \mathsf{+.f64}\left(a, \color{blue}{x}\right)\right) \]

   8. Simplified 75.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(z + b \cdot -2\right)\right) + \left(a + x\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z + -1 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(a, x\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right), \mathsf{+.f64}\left(a, x\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(z - a \cdot t\right), \mathsf{+.f64}\left(\color{blue}{a}, x\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(z, \left(a \cdot t\right)\right), \mathsf{+.f64}\left(\color{blue}{a}, x\right)\right) \]

       4. *-lowering-*.f64 71.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, t\right)\right), \mathsf{+.f64}\left(a, x\right)\right) \]

   11. Simplified 71.1%

       \[\leadsto \color{blue}{\left(z - a \cdot t\right)} + \left(a + x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-64}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-24}:\\ \;\;\;\;\left(x + a\right) + \left(z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+48}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))))
   (if (<= z -1.65e+132)
     t_1
     (if (<= z 3.4e+48) (+ 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 <= -1.65e+132) {
		tmp = t_1;
	} else if (z <= 3.4e+48) {
		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 <= (-1.65d+132)) then
        tmp = t_1
    else if (z <= 3.4d+48) 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 <= -1.65e+132) {
		tmp = t_1;
	} else if (z <= 3.4e+48) {
		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 <= -1.65e+132:
		tmp = t_1
	elif z <= 3.4e+48:
		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 <= -1.65e+132)
		tmp = t_1;
	elseif (z <= 3.4e+48)
		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 <= -1.65e+132)
		tmp = t_1;
	elseif (z <= 3.4e+48)
		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, -1.65e+132], t$95$1, If[LessEqual[z, 3.4e+48], 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 < -1.65000000000000015e132 or 3.4000000000000003e48 < z

   1. Initial program 88.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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-+r+ N/A

         \[\leadsto \left(\left(x + b \cdot \left(y - 2\right)\right) + t \cdot \left(b - a\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + \color{blue}{\left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + b \cdot \left(y - 2\right)\right), \color{blue}{\left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(y - 2\right)\right)\right), \left(\color{blue}{t \cdot \left(b - a\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(y - 2\right)\right)\right), \left(t \cdot \color{blue}{\left(b - a\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \left(t \cdot \left(b - \color{blue}{a}\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \left(t \cdot \left(b - \color{blue}{a}\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \left(t \cdot \left(b - a\right) + \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\left(t \cdot \left(b - a\right)\right), \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b - a\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\mathsf{neg}\left(\left(-1 \cdot a + \color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right)\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\left(\mathsf{neg}\left(-1 \cdot a\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z} \cdot \left(y - 1\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(a + \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 91.0%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y + -2\right)\right) + \left(t \cdot \left(b - a\right) + \left(a + z \cdot \left(1 - y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      2. --lowering--.f64 72.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 72.4%

      \[\leadsto \left(x + b \cdot \left(y + -2\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   10. Step-by-step derivation

       1. *-lft-identity N/A

          \[\leadsto 1 \cdot x + \color{blue}{z} \cdot \left(1 - y\right) \]

       2. fma-define N/A

          \[\leadsto \mathsf{fma}\left(1, \color{blue}{x}, z \cdot \left(1 - y\right)\right) \]

       3. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(\left(\mathsf{neg}\left(z \cdot \left(1 - y\right)\right)\right)\right)\right) \]

       4. distribute-rgt-neg-out N/A

          \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(z \cdot \left(\mathsf{neg}\left(\left(1 - y\right)\right)\right)\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(z \cdot \left(-1 \cdot \left(1 - y\right)\right)\right)\right) \]

       6. fmm-undef N/A

          \[\leadsto 1 \cdot x - \color{blue}{z \cdot \left(-1 \cdot \left(1 - y\right)\right)} \]

       7. *-lft-identity N/A

          \[\leadsto x - \color{blue}{z} \cdot \left(-1 \cdot \left(1 - y\right)\right) \]

       8. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot \left(-1 \cdot \left(1 - y\right)\right)\right)}\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(1 - y\right)\right)}\right)\right) \]

       10. mul-1-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(1 - y\right)\right)\right)\right)\right) \]

       11. neg-sub0 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(0 - \color{blue}{\left(1 - y\right)}\right)\right)\right) \]

       12. associate--r- N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(0 - 1\right) + \color{blue}{y}\right)\right)\right) \]

       13. metadata-eval N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(-1 + y\right)\right)\right) \]

       14. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + \color{blue}{-1}\right)\right)\right) \]

       15. +-lowering-+.f64 70.3%

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   11. Simplified 70.3%

       \[\leadsto \color{blue}{x - z \cdot \left(y + -1\right)} \]

   if -1.65000000000000015e132 < z < 3.4000000000000003e48

   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 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 68.9%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+48}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 27.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2700000000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1150000000000:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2700000000.0)
   (* y b)
   (if (<= y -7e-70) x (if (<= y 1150000000000.0) (* t b) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2700000000.0) {
		tmp = y * b;
	} else if (y <= -7e-70) {
		tmp = x;
	} else if (y <= 1150000000000.0) {
		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 <= (-2700000000.0d0)) then
        tmp = y * b
    else if (y <= (-7d-70)) then
        tmp = x
    else if (y <= 1150000000000.0d0) 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 <= -2700000000.0) {
		tmp = y * b;
	} else if (y <= -7e-70) {
		tmp = x;
	} else if (y <= 1150000000000.0) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2700000000.0:
		tmp = y * b
	elif y <= -7e-70:
		tmp = x
	elif y <= 1150000000000.0:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2700000000.0)
		tmp = Float64(y * b);
	elseif (y <= -7e-70)
		tmp = x;
	elseif (y <= 1150000000000.0)
		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 <= -2700000000.0)
		tmp = y * b;
	elseif (y <= -7e-70)
		tmp = x;
	elseif (y <= 1150000000000.0)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2700000000.0], N[(y * b), $MachinePrecision], If[LessEqual[y, -7e-70], x, If[LessEqual[y, 1150000000000.0], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e9 or 1.15e12 < y

   1. Initial program 93.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 67.1%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 67.1%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{b}\right) \]
   7. Step-by-step derivation

   8. Simplified 40.8%

      \[\leadsto y \cdot \color{blue}{b} \]

   if -2.7e9 < y < -6.99999999999999949e-70

   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

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 35.3%

      \[\leadsto \color{blue}{x} \]

   if -6.99999999999999949e-70 < y < 1.15e12

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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 56.3%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot t} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 24.7%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{t}\right) \]

   8. Simplified 24.7%

      \[\leadsto \color{blue}{b \cdot t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2700000000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1150000000000:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 55.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+110}:\\ \;\;\;\;x + b \cdot \left(y + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -8.5e+72) t_1 (if (<= t 2e+110) (+ x (* b (+ y -2.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -8.5e+72) {
		tmp = t_1;
	} else if (t <= 2e+110) {
		tmp = x + (b * (y + -2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-8.5d+72)) then
        tmp = t_1
    else if (t <= 2d+110) then
        tmp = x + (b * (y + (-2.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -8.5e+72) {
		tmp = t_1;
	} else if (t <= 2e+110) {
		tmp = x + (b * (y + -2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -8.5e+72:
		tmp = t_1
	elif t <= 2e+110:
		tmp = x + (b * (y + -2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.5e+72)
		tmp = t_1;
	elseif (t <= 2e+110)
		tmp = Float64(x + Float64(b * Float64(y + -2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -8.5e+72)
		tmp = t_1;
	elseif (t <= 2e+110)
		tmp = x + (b * (y + -2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+72], t$95$1, If[LessEqual[t, 2e+110], N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5000000000000004e72 or 2e110 < t

   1. Initial program 92.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 80.6%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -8.5000000000000004e72 < t < 2e110

   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 61.0%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + b \cdot \left(y - 2\right)} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto b \cdot \left(y - 2\right) + \color{blue}{x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \color{blue}{x}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), x\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), x\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + -2\right)\right), x\right) \]

      6. +-lowering-+.f64 56.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), x\right) \]

   8. Simplified 56.8%

      \[\leadsto \color{blue}{b \cdot \left(y + -2\right) + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+110}:\\ \;\;\;\;x + b \cdot \left(y + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 49.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+110}:\\ \;\;\;\;x + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -6e+72) t_1 (if (<= t 2e+110) (+ x (* y b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -6e+72) {
		tmp = t_1;
	} else if (t <= 2e+110) {
		tmp = x + (y * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-6d+72)) then
        tmp = t_1
    else if (t <= 2d+110) then
        tmp = x + (y * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -6e+72) {
		tmp = t_1;
	} else if (t <= 2e+110) {
		tmp = x + (y * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -6e+72:
		tmp = t_1
	elif t <= 2e+110:
		tmp = x + (y * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6e+72)
		tmp = t_1;
	elseif (t <= 2e+110)
		tmp = Float64(x + Float64(y * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -6e+72)
		tmp = t_1;
	elseif (t <= 2e+110)
		tmp = x + (y * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+72], t$95$1, If[LessEqual[t, 2e+110], N[(x + N[(y * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.00000000000000006e72 or 2e110 < t

   1. Initial program 92.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 80.6%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -6.00000000000000006e72 < t < 2e110

   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 61.0%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, b\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 45.1%

      \[\leadsto x + \color{blue}{y} \cdot b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 51.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.1e+73) t_1 (if (<= t 2.55e+17) (* y (- b z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.1e+73) {
		tmp = t_1;
	} else if (t <= 2.55e+17) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1.1d+73)) then
        tmp = t_1
    else if (t <= 2.55d+17) then
        tmp = y * (b - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.1e+73) {
		tmp = t_1;
	} else if (t <= 2.55e+17) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.1e+73:
		tmp = t_1
	elif t <= 2.55e+17:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.1e+73)
		tmp = t_1;
	elseif (t <= 2.55e+17)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.1e+73)
		tmp = t_1;
	elseif (t <= 2.55e+17)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+73], t$95$1, If[LessEqual[t, 2.55e+17], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e73 or 2.55e17 < t

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 72.6%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 72.6%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -1.1e73 < t < 2.55e17

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 41.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 48.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -900000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -900000000.0) t_1 (if (<= t 1.75e+15) (* b (+ y -2.0)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -900000000.0) {
		tmp = t_1;
	} else if (t <= 1.75e+15) {
		tmp = b * (y + -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-900000000.0d0)) then
        tmp = t_1
    else if (t <= 1.75d+15) then
        tmp = b * (y + (-2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -900000000.0) {
		tmp = t_1;
	} else if (t <= 1.75e+15) {
		tmp = b * (y + -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -900000000.0:
		tmp = t_1
	elif t <= 1.75e+15:
		tmp = b * (y + -2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -900000000.0)
		tmp = t_1;
	elseif (t <= 1.75e+15)
		tmp = Float64(b * Float64(y + -2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -900000000.0)
		tmp = t_1;
	elseif (t <= 1.75e+15)
		tmp = b * (y + -2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -900000000.0], t$95$1, If[LessEqual[t, 1.75e+15], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9e8 or 1.75e15 < t

   1. Initial program 93.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 68.7%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -9e8 < t < 1.75e15

   1. Initial program 97.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(1 - y\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + -1 \cdot -1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(-1 + y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      16. --lowering--.f64 65.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 65.3%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{y}, 2\right), b\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 65.3%

      \[\leadsto z \cdot \left(1 - y\right) + \left(\color{blue}{y} - 2\right) \cdot b \]

   9. Taylor expanded in z around 0

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y - 2\right)}\right) \]

       2. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(y + -2\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(-2 + \color{blue}{y}\right)\right) \]

       5. +-lowering-+.f64 40.5%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-2, \color{blue}{y}\right)\right) \]

   11. Simplified 40.5%

       \[\leadsto \color{blue}{b \cdot \left(-2 + y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -900000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-73}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.2e-73)
   (* b (+ t -2.0))
   (if (<= b 1.4e+69) (* a (- 1.0 t)) (* b (+ y -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.2e-73) {
		tmp = b * (t + -2.0);
	} else if (b <= 1.4e+69) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (y + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.2d-73)) then
        tmp = b * (t + (-2.0d0))
    else if (b <= 1.4d+69) then
        tmp = a * (1.0d0 - t)
    else
        tmp = b * (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.2e-73) {
		tmp = b * (t + -2.0);
	} else if (b <= 1.4e+69) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.2e-73:
		tmp = b * (t + -2.0)
	elif b <= 1.4e+69:
		tmp = a * (1.0 - t)
	else:
		tmp = b * (y + -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.2e-73)
		tmp = Float64(b * Float64(t + -2.0));
	elseif (b <= 1.4e+69)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(b * Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.2e-73)
		tmp = b * (t + -2.0);
	elseif (b <= 1.4e+69)
		tmp = a * (1.0 - t);
	else
		tmp = b * (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.2e-73], N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+69], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.1999999999999997e-73

   1. Initial program 96.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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-+r+ N/A

         \[\leadsto \left(\left(x + b \cdot \left(y - 2\right)\right) + t \cdot \left(b - a\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + \color{blue}{\left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + b \cdot \left(y - 2\right)\right), \color{blue}{\left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(y - 2\right)\right)\right), \left(\color{blue}{t \cdot \left(b - a\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(y - 2\right)\right)\right), \left(t \cdot \color{blue}{\left(b - a\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \left(t \cdot \left(b - \color{blue}{a}\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \left(t \cdot \left(b - \color{blue}{a}\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \left(t \cdot \left(b - a\right) + \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\left(t \cdot \left(b - a\right)\right), \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b - a\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\mathsf{neg}\left(\left(-1 \cdot a + \color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right)\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\left(\mathsf{neg}\left(-1 \cdot a\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z} \cdot \left(y - 1\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(a + \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 97.4%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y + -2\right)\right) + \left(t \cdot \left(b - a\right) + \left(a + z \cdot \left(1 - y\right)\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(x + \left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right) + \color{blue}{\left(a + x\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right), \color{blue}{\left(a + x\right)}\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z + -2 \cdot b\right) + t \cdot \left(b - a\right)\right), \left(\color{blue}{a} + x\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(b - a\right) + \left(z + -2 \cdot b\right)\right), \left(\color{blue}{a} + x\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(b - a\right)\right), \left(z + -2 \cdot b\right)\right), \left(\color{blue}{a} + x\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b - a\right)\right), \left(z + -2 \cdot b\right)\right), \left(a + x\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(z + -2 \cdot b\right)\right), \left(a + x\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \left(-2 \cdot b\right)\right)\right), \left(a + x\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \left(b \cdot -2\right)\right)\right), \left(a + x\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(b, -2\right)\right)\right), \left(a + x\right)\right) \]

      12. +-lowering-+.f64 73.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(b, -2\right)\right)\right), \mathsf{+.f64}\left(a, \color{blue}{x}\right)\right) \]

   8. Simplified 73.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(z + b \cdot -2\right)\right) + \left(a + x\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(t - 2\right)}\right) \]

       2. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(t + -2\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(-2 + \color{blue}{t}\right)\right) \]

       5. +-lowering-+.f64 38.3%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-2, \color{blue}{t}\right)\right) \]

   11. Simplified 38.3%

       \[\leadsto \color{blue}{b \cdot \left(-2 + t\right)} \]

   if -4.1999999999999997e-73 < b < 1.39999999999999991e69

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto a \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto a \cdot \left(1 + -1 \cdot \color{blue}{t}\right) \]

      3. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + \color{blue}{-1} \cdot t\right) \]

      4. distribute-lft-in N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(-1 + t\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \color{blue}{-1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t - \color{blue}{1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 40.3%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 40.3%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if 1.39999999999999991e69 < b

   1. Initial program 90.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(1 - y\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + -1 \cdot -1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(-1 + y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      16. --lowering--.f64 83.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 83.4%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\color{blue}{y}, 2\right), b\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 59.3%

      \[\leadsto z \cdot \left(1 - y\right) + \left(\color{blue}{y} - 2\right) \cdot b \]

   9. Taylor expanded in z around 0

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y - 2\right)}\right) \]

       2. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(y + -2\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(-2 + \color{blue}{y}\right)\right) \]

       5. +-lowering-+.f64 57.7%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-2, \color{blue}{y}\right)\right) \]

   11. Simplified 57.7%

       \[\leadsto \color{blue}{b \cdot \left(-2 + y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-73}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 25.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+72}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.6e+72) (* t b) (if (<= t 1.02e+33) x (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.6e+72) {
		tmp = t * b;
	} else if (t <= 1.02e+33) {
		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 <= (-5.6d+72)) then
        tmp = t * b
    else if (t <= 1.02d+33) 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 <= -5.6e+72) {
		tmp = t * b;
	} else if (t <= 1.02e+33) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.6e+72:
		tmp = t * b
	elif t <= 1.02e+33:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.6e+72)
		tmp = Float64(t * b);
	elseif (t <= 1.02e+33)
		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 <= -5.6e+72)
		tmp = t * b;
	elseif (t <= 1.02e+33)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.6e+72], N[(t * b), $MachinePrecision], If[LessEqual[t, 1.02e+33], x, N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5999999999999998e72 or 1.02000000000000001e33 < t

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 55.1%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot t} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 39.7%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{t}\right) \]

   8. Simplified 39.7%

      \[\leadsto \color{blue}{b \cdot t} \]

   if -5.5999999999999998e72 < t < 1.02000000000000001e33

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 22.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+72}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 20.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+118}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+143}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.55e+118) z (if (<= z 1.05e+143) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.55e+118) {
		tmp = z;
	} else if (z <= 1.05e+143) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.55d+118)) then
        tmp = z
    else if (z <= 1.05d+143) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.55e+118) {
		tmp = z;
	} else if (z <= 1.05e+143) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.55e+118:
		tmp = z
	elif z <= 1.05e+143:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.55e+118)
		tmp = z;
	elseif (z <= 1.05e+143)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.55e+118)
		tmp = z;
	elseif (z <= 1.05e+143)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.55e+118], z, If[LessEqual[z, 1.05e+143], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999993e118 or 1.04999999999999994e143 < z

   1. Initial program 87.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 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-+r+ N/A

         \[\leadsto \left(\left(x + b \cdot \left(y - 2\right)\right) + t \cdot \left(b - a\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + \color{blue}{\left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + b \cdot \left(y - 2\right)\right), \color{blue}{\left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(y - 2\right)\right)\right), \left(\color{blue}{t \cdot \left(b - a\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(y - 2\right)\right)\right), \left(t \cdot \color{blue}{\left(b - a\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \left(t \cdot \left(b - \color{blue}{a}\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \left(t \cdot \left(b - \color{blue}{a}\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \left(t \cdot \left(b - a\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \left(t \cdot \left(b - a\right) + \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\left(t \cdot \left(b - a\right)\right), \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b - a\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\mathsf{neg}\left(\left(-1 \cdot a + \color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right)\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\left(\mathsf{neg}\left(-1 \cdot a\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z} \cdot \left(y - 1\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(a + \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right)\right) \]

      20. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 88.8%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y + -2\right)\right) + \left(t \cdot \left(b - a\right) + \left(a + z \cdot \left(1 - y\right)\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(x + \left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right) + \color{blue}{\left(a + x\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z + \left(-2 \cdot b + t \cdot \left(b - a\right)\right)\right), \color{blue}{\left(a + x\right)}\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z + -2 \cdot b\right) + t \cdot \left(b - a\right)\right), \left(\color{blue}{a} + x\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(b - a\right) + \left(z + -2 \cdot b\right)\right), \left(\color{blue}{a} + x\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(b - a\right)\right), \left(z + -2 \cdot b\right)\right), \left(\color{blue}{a} + x\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b - a\right)\right), \left(z + -2 \cdot b\right)\right), \left(a + x\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \left(z + -2 \cdot b\right)\right), \left(a + x\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \left(-2 \cdot b\right)\right)\right), \left(a + x\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \left(b \cdot -2\right)\right)\right), \left(a + x\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(b, -2\right)\right)\right), \left(a + x\right)\right) \]

      12. +-lowering-+.f64 60.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(b, -2\right)\right)\right), \mathsf{+.f64}\left(a, \color{blue}{x}\right)\right) \]

   8. Simplified 60.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(z + b \cdot -2\right)\right) + \left(a + x\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} \]
   10. Step-by-step derivation

   11. Simplified 28.4%

       \[\leadsto \color{blue}{z} \]

   if -1.54999999999999993e118 < z < 1.04999999999999994e143

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 19.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 15.6% 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 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

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 15.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(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)))