AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Percentage Accurate: 60.4% → 87.8%

Time: 11.6s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+289}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) (+ y (+ x t))))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 5e+289) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 5e+289) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 5e+289) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t))
	t_2 = (z + a) - b
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 5e+289:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 5e+289)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 5e+289)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 5e+289], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.00000000000000031e289 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.9%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 71.1%

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

   5. Simplified 71.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000031e289

   1. Initial program 99.1%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+289}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - \left(b - z\right)\right) \cdot \frac{y}{x + \left(y + t\right)}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-152}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{t \cdot a}{z \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+32}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a (- b z)) (/ y (+ x (+ y t))))))
   (if (<= y -9.5e+23)
     t_1
     (if (<= y 3.8e-152)
       (* z (+ (/ x (+ x t)) (/ (* t a) (* z (+ x t)))))
       (if (<= y 2.15e+32) (/ (- (* z (+ x y)) (* y b)) (+ y (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - (b - z)) * (y / (x + (y + t)));
	double tmp;
	if (y <= -9.5e+23) {
		tmp = t_1;
	} else if (y <= 3.8e-152) {
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	} else if (y <= 2.15e+32) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - (b - z)) * (y / (x + (y + t)))
    if (y <= (-9.5d+23)) then
        tmp = t_1
    else if (y <= 3.8d-152) then
        tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))))
    else if (y <= 2.15d+32) then
        tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - (b - z)) * (y / (x + (y + t)));
	double tmp;
	if (y <= -9.5e+23) {
		tmp = t_1;
	} else if (y <= 3.8e-152) {
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	} else if (y <= 2.15e+32) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - (b - z)) * (y / (x + (y + t)))
	tmp = 0
	if y <= -9.5e+23:
		tmp = t_1
	elif y <= 3.8e-152:
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))))
	elif y <= 2.15e+32:
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - Float64(b - z)) * Float64(y / Float64(x + Float64(y + t))))
	tmp = 0.0
	if (y <= -9.5e+23)
		tmp = t_1;
	elseif (y <= 3.8e-152)
		tmp = Float64(z * Float64(Float64(x / Float64(x + t)) + Float64(Float64(t * a) / Float64(z * Float64(x + t)))));
	elseif (y <= 2.15e+32)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - (b - z)) * (y / (x + (y + t)));
	tmp = 0.0;
	if (y <= -9.5e+23)
		tmp = t_1;
	elseif (y <= 3.8e-152)
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	elseif (y <= 2.15e+32)
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - N[(b - z), $MachinePrecision]), $MachinePrecision] * N[(y / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+23], t$95$1, If[LessEqual[y, 3.8e-152], N[(z * N[(N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] / N[(z * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+32], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000038e23 or 2.1499999999999999e32 < y

   1. Initial program 30.4%

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

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. +-lowering-+.f64 25.6%

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

   5. Simplified 25.6%

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. associate--l+ N/A

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

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

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

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

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

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

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

      11. associate-+r+ N/A

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

      12. +-commutative N/A

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

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

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

      14. +-commutative N/A

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

      15. +-lowering-+.f64 77.8%

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

   7. Applied egg-rr 77.8%

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

   if -9.50000000000000038e23 < y < 3.80000000000000012e-152

   1. Initial program 81.3%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   4. Step-by-step derivation

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

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

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

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

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

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

      4. *-commutative N/A

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

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

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

      6. +-lowering-+.f64 67.4%

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

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{a \cdot t + z \cdot x}{t + x}} \]

   6. Taylor expanded in z around inf

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      8. +-lowering-+.f64 68.8%

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

   8. Simplified 68.8%

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

   if 3.80000000000000012e-152 < y < 2.1499999999999999e32

   1. Initial program 76.4%

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

   3. Taylor expanded in z around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+23}:\\ \;\;\;\;\left(a - \left(b - z\right)\right) \cdot \frac{y}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-152}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{t \cdot a}{z \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+32}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a - \left(b - z\right)\right) \cdot \frac{y}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - \left(b - z\right)\right) \cdot \frac{y}{x + \left(y + t\right)}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-148}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a (- b z)) (/ y (+ x (+ y t))))))
   (if (<= y -3e+22)
     t_1
     (if (<= y 9e-148)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 7.5e+34) (/ (- (* z (+ x y)) (* y b)) (+ y (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - (b - z)) * (y / (x + (y + t)));
	double tmp;
	if (y <= -3e+22) {
		tmp = t_1;
	} else if (y <= 9e-148) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 7.5e+34) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - (b - z)) * (y / (x + (y + t)))
    if (y <= (-3d+22)) then
        tmp = t_1
    else if (y <= 9d-148) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 7.5d+34) then
        tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - (b - z)) * (y / (x + (y + t)));
	double tmp;
	if (y <= -3e+22) {
		tmp = t_1;
	} else if (y <= 9e-148) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 7.5e+34) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - (b - z)) * (y / (x + (y + t)))
	tmp = 0
	if y <= -3e+22:
		tmp = t_1
	elif y <= 9e-148:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 7.5e+34:
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - Float64(b - z)) * Float64(y / Float64(x + Float64(y + t))))
	tmp = 0.0
	if (y <= -3e+22)
		tmp = t_1;
	elseif (y <= 9e-148)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 7.5e+34)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - (b - z)) * (y / (x + (y + t)));
	tmp = 0.0;
	if (y <= -3e+22)
		tmp = t_1;
	elseif (y <= 9e-148)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 7.5e+34)
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - N[(b - z), $MachinePrecision]), $MachinePrecision] * N[(y / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e+22], t$95$1, If[LessEqual[y, 9e-148], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+34], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e22 or 7.49999999999999976e34 < y

   1. Initial program 30.4%

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

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. +-lowering-+.f64 25.6%

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

   5. Simplified 25.6%

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. associate--l+ N/A

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

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

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

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

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

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

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

      11. associate-+r+ N/A

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

      12. +-commutative N/A

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

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

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

      14. +-commutative N/A

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

      15. +-lowering-+.f64 77.8%

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

   7. Applied egg-rr 77.8%

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

   if -3e22 < y < 9.00000000000000029e-148

   1. Initial program 80.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   4. Step-by-step derivation

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

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

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

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

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

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

      4. *-commutative N/A

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

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

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

      6. +-lowering-+.f64 66.8%

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

   5. Simplified 66.8%

      \[\leadsto \color{blue}{\frac{a \cdot t + z \cdot x}{t + x}} \]

   if 9.00000000000000029e-148 < y < 7.49999999999999976e34

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 61.9%

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

   5. Simplified 61.9%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+22}:\\ \;\;\;\;\left(a - \left(b - z\right)\right) \cdot \frac{y}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-148}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a - \left(b - z\right)\right) \cdot \frac{y}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := a - \left(b - z\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;t\_2 \cdot \frac{y}{t\_1}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{\left(t \cdot a + x \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t\_2}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (- a (- b z))))
   (if (<= y -4.4e+49)
     (* t_2 (/ y t_1))
     (if (<= y 7.4e-19)
       (/ (- (+ (* t a) (* x z)) (* y b)) (+ y (+ x t)))
       (if (<= y 9.5e+59)
         (* z (/ (+ x y) (+ t (+ x y))))
         (* y (/ t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = a - (b - z);
	double tmp;
	if (y <= -4.4e+49) {
		tmp = t_2 * (y / t_1);
	} else if (y <= 7.4e-19) {
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t));
	} else if (y <= 9.5e+59) {
		tmp = z * ((x + y) / (t + (x + y)));
	} else {
		tmp = y * (t_2 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = a - (b - z)
    if (y <= (-4.4d+49)) then
        tmp = t_2 * (y / t_1)
    else if (y <= 7.4d-19) then
        tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t))
    else if (y <= 9.5d+59) then
        tmp = z * ((x + y) / (t + (x + y)))
    else
        tmp = y * (t_2 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = a - (b - z);
	double tmp;
	if (y <= -4.4e+49) {
		tmp = t_2 * (y / t_1);
	} else if (y <= 7.4e-19) {
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t));
	} else if (y <= 9.5e+59) {
		tmp = z * ((x + y) / (t + (x + y)));
	} else {
		tmp = y * (t_2 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = a - (b - z)
	tmp = 0
	if y <= -4.4e+49:
		tmp = t_2 * (y / t_1)
	elif y <= 7.4e-19:
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t))
	elif y <= 9.5e+59:
		tmp = z * ((x + y) / (t + (x + y)))
	else:
		tmp = y * (t_2 / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(a - Float64(b - z))
	tmp = 0.0
	if (y <= -4.4e+49)
		tmp = Float64(t_2 * Float64(y / t_1));
	elseif (y <= 7.4e-19)
		tmp = Float64(Float64(Float64(Float64(t * a) + Float64(x * z)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (y <= 9.5e+59)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(t + Float64(x + y))));
	else
		tmp = Float64(y * Float64(t_2 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = a - (b - z);
	tmp = 0.0;
	if (y <= -4.4e+49)
		tmp = t_2 * (y / t_1);
	elseif (y <= 7.4e-19)
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t));
	elseif (y <= 9.5e+59)
		tmp = z * ((x + y) / (t + (x + y)));
	else
		tmp = y * (t_2 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+49], N[(t$95$2 * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4e-19], N[(N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+59], N[(z * N[(N[(x + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4000000000000001e49

   1. Initial program 29.7%

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

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. +-lowering-+.f64 28.6%

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

   5. Simplified 28.6%

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. associate--l+ N/A

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

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

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

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

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

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

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

      11. associate-+r+ N/A

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

      12. +-commutative N/A

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

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

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

      14. +-commutative N/A

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

      15. +-lowering-+.f64 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -4.4000000000000001e49 < y < 7.40000000000000011e-19

   1. Initial program 82.0%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 73.5%

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

   5. Simplified 73.5%

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

   if 7.40000000000000011e-19 < y < 9.50000000000000023e59

   1. Initial program 51.0%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

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

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

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

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

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)\right)\right)\right) \]

      6. unsub-neg N/A

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

   5. Simplified 83.0%

      \[\leadsto \color{blue}{0 - z \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 65.8%

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

   8. Simplified 65.8%

      \[\leadsto 0 - z \cdot \color{blue}{\frac{\left(y + x\right) \cdot -1}{t + \left(y + x\right)}} \]

   if 9.50000000000000023e59 < y

   1. Initial program 24.1%

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

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. +-lowering-+.f64 20.0%

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

   5. Simplified 20.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

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

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

      8. associate--l+ N/A

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

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

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

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

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

      11. associate-+r+ N/A

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

      12. +-commutative N/A

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

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

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

      14. +-commutative N/A

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

      15. +-lowering-+.f64 77.4%

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

   7. Applied egg-rr 77.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;\left(a - \left(b - z\right)\right) \cdot \frac{y}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{\left(t \cdot a + x \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a - \left(b - z\right)}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - \left(b - z\right)\right) \cdot \frac{y}{x + \left(y + t\right)}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-145}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a (- b z)) (/ y (+ x (+ y t))))))
   (if (<= y -3e+22)
     t_1
     (if (<= y 1.56e-145) (/ (+ (* t a) (* x z)) (+ x t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - (b - z)) * (y / (x + (y + t)));
	double tmp;
	if (y <= -3e+22) {
		tmp = t_1;
	} else if (y <= 1.56e-145) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - (b - z)) * (y / (x + (y + t)))
    if (y <= (-3d+22)) then
        tmp = t_1
    else if (y <= 1.56d-145) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - (b - z)) * (y / (x + (y + t)));
	double tmp;
	if (y <= -3e+22) {
		tmp = t_1;
	} else if (y <= 1.56e-145) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - (b - z)) * (y / (x + (y + t)))
	tmp = 0
	if y <= -3e+22:
		tmp = t_1
	elif y <= 1.56e-145:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - Float64(b - z)) * Float64(y / Float64(x + Float64(y + t))))
	tmp = 0.0
	if (y <= -3e+22)
		tmp = t_1;
	elseif (y <= 1.56e-145)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - (b - z)) * (y / (x + (y + t)));
	tmp = 0.0;
	if (y <= -3e+22)
		tmp = t_1;
	elseif (y <= 1.56e-145)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - N[(b - z), $MachinePrecision]), $MachinePrecision] * N[(y / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e+22], t$95$1, If[LessEqual[y, 1.56e-145], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3e22 or 1.56000000000000001e-145 < y

   1. Initial program 41.0%

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

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. +-lowering-+.f64 31.5%

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

   5. Simplified 31.5%

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. associate--l+ N/A

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

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

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

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

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

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

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

      11. associate-+r+ N/A

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

      12. +-commutative N/A

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

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

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

      14. +-commutative N/A

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

      15. +-lowering-+.f64 71.3%

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

   7. Applied egg-rr 71.3%

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

   if -3e22 < y < 1.56000000000000001e-145

   1. Initial program 80.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   4. Step-by-step derivation

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

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

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

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

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

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

      4. *-commutative N/A

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

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

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

      6. +-lowering-+.f64 67.1%

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

   5. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{a \cdot t + z \cdot x}{t + x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+22}:\\ \;\;\;\;\left(a - \left(b - z\right)\right) \cdot \frac{y}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-145}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(a - \left(b - z\right)\right) \cdot \frac{y}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -6.5e+62)
     t_1
     (if (<= y 1.3e-12) (/ (+ (* t a) (* x z)) (+ x t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6.5e+62) {
		tmp = t_1;
	} else if (y <= 1.3e-12) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-6.5d+62)) then
        tmp = t_1
    else if (y <= 1.3d-12) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6.5e+62) {
		tmp = t_1;
	} else if (y <= 1.3e-12) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -6.5e+62:
		tmp = t_1
	elif y <= 1.3e-12:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6.5e+62)
		tmp = t_1;
	elseif (y <= 1.3e-12)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.5e+62)
		tmp = t_1;
	elseif (y <= 1.3e-12)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.5e+62], t$95$1, If[LessEqual[y, 1.3e-12], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000003e62 or 1.29999999999999991e-12 < y

   1. Initial program 29.4%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 72.8%

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

   5. Simplified 72.8%

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

   if -6.5000000000000003e62 < y < 1.29999999999999991e-12

   1. Initial program 81.2%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   4. Step-by-step derivation

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

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

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

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

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

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

      4. *-commutative N/A

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

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

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

      6. +-lowering-+.f64 59.7%

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

   5. Simplified 59.7%

      \[\leadsto \color{blue}{\frac{a \cdot t + z \cdot x}{t + x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+62}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{t}{x + t}\\ \mathbf{if}\;t \leq -6 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+29}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ t (+ x t)))))
   (if (<= t -6e+191) t_1 (if (<= t 5.3e+29) (- (+ z a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t / (x + t));
	double tmp;
	if (t <= -6e+191) {
		tmp = t_1;
	} else if (t <= 5.3e+29) {
		tmp = (z + a) - 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 = a * (t / (x + t))
    if (t <= (-6d+191)) then
        tmp = t_1
    else if (t <= 5.3d+29) then
        tmp = (z + a) - 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 = a * (t / (x + t));
	double tmp;
	if (t <= -6e+191) {
		tmp = t_1;
	} else if (t <= 5.3e+29) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t / (x + t))
	tmp = 0
	if t <= -6e+191:
		tmp = t_1
	elif t <= 5.3e+29:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t / Float64(x + t)))
	tmp = 0.0
	if (t <= -6e+191)
		tmp = t_1;
	elseif (t <= 5.3e+29)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t / (x + t));
	tmp = 0.0;
	if (t <= -6e+191)
		tmp = t_1;
	elseif (t <= 5.3e+29)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+191], t$95$1, If[LessEqual[t, 5.3e+29], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.9999999999999995e191 or 5.3e29 < t

   1. Initial program 52.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   4. Step-by-step derivation

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

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

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

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

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

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

      4. *-commutative N/A

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

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

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

      6. +-lowering-+.f64 42.5%

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

   5. Simplified 42.5%

      \[\leadsto \color{blue}{\frac{a \cdot t + z \cdot x}{t + x}} \]

   6. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{a \cdot t}{t + x}} \]
   7. Step-by-step derivation

      1. associate-/l* N/A

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

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

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

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

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

      4. +-lowering-+.f64 65.0%

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

   8. Simplified 65.0%

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

   if -5.9999999999999995e191 < t < 5.3e29

   1. Initial program 59.6%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 59.8%

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

   5. Simplified 59.8%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+191}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+29}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+195}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+118}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - \frac{x}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.6e+195)
   a
   (if (<= t 1.95e+118) (- (+ z a) b) (* a (- 1.0 (/ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.6e+195) {
		tmp = a;
	} else if (t <= 1.95e+118) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (1.0 - (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.6d+195)) then
        tmp = a
    else if (t <= 1.95d+118) then
        tmp = (z + a) - b
    else
        tmp = a * (1.0d0 - (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.6e+195) {
		tmp = a;
	} else if (t <= 1.95e+118) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (1.0 - (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.6e+195:
		tmp = a
	elif t <= 1.95e+118:
		tmp = (z + a) - b
	else:
		tmp = a * (1.0 - (x / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.6e+195)
		tmp = a;
	elseif (t <= 1.95e+118)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(1.0 - Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.6e+195)
		tmp = a;
	elseif (t <= 1.95e+118)
		tmp = (z + a) - b;
	else
		tmp = a * (1.0 - (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.6e+195], a, If[LessEqual[t, 1.95e+118], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(1.0 - N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.60000000000000002e195

   1. Initial program 44.7%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 63.6%

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

   if -2.60000000000000002e195 < t < 1.95e118

   1. Initial program 60.6%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 57.7%

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

   5. Simplified 57.7%

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

   if 1.95e118 < t

   1. Initial program 49.1%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

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

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

      7. associate-/l* N/A

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

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

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

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

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

      10. +-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 74.1%

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

   6. Taylor expanded in a around inf

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

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

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

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

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

      3. /-lowering-/.f64 64.7%

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

   8. Simplified 64.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+195}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+118}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - \frac{x}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+188}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.8e+188) a (if (<= t 1.65e+151) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.8e+188) {
		tmp = a;
	} else if (t <= 1.65e+151) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.8d+188)) then
        tmp = a
    else if (t <= 1.65d+151) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.8e+188) {
		tmp = a;
	} else if (t <= 1.65e+151) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.8e+188:
		tmp = a
	elif t <= 1.65e+151:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.8e+188)
		tmp = a;
	elseif (t <= 1.65e+151)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.8e+188)
		tmp = a;
	elseif (t <= 1.65e+151)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.8e+188], a, If[LessEqual[t, 1.65e+151], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7999999999999998e188 or 1.65000000000000012e151 < t

   1. Initial program 48.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 66.9%

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

   if -3.7999999999999998e188 < t < 1.65000000000000012e151

   1. Initial program 59.9%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 57.1%

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

   5. Simplified 57.1%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+188}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+167}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+80}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.5e+167) a (if (<= t 9e+80) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e+167) {
		tmp = a;
	} else if (t <= 9e+80) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.5d+167)) then
        tmp = a
    else if (t <= 9d+80) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e+167) {
		tmp = a;
	} else if (t <= 9e+80) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.5e+167:
		tmp = a
	elif t <= 9e+80:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.5e+167)
		tmp = a;
	elseif (t <= 9e+80)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.5e+167)
		tmp = a;
	elseif (t <= 9e+80)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.5e+167], a, If[LessEqual[t, 9e+80], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.50000000000000006e167 or 9.00000000000000013e80 < t

   1. Initial program 50.5%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 62.6%

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

   if -1.50000000000000006e167 < t < 9.00000000000000013e80

   1. Initial program 60.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 43.9%

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

Alternative 11: 32.0% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 57.1%

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

3. Taylor expanded in t around inf

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

5. Simplified 31.5%

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

Developer Target 1: 82.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t\_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
        (t_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b))))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))