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

Percentage Accurate: 61.1% → 98.4%

Time: 14.2s

Alternatives: 14

Speedup: 0.8×

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: 61.1% 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: 98.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ \mathsf{fma}\left(\frac{y + x}{t\_1}, z, a \cdot \left(\frac{1}{t\_1} \cdot \left(y + t\right)\right) - b \cdot \frac{y}{t\_1}\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x))))
   (fma (/ (+ y x) t_1) z (- (* a (* (/ 1.0 t_1) (+ y t))) (* b (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	return fma(((y + x) / t_1), z, ((a * ((1.0 / t_1) * (y + t))) - (b * (y / t_1))));
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	return fma(Float64(Float64(y + x) / t_1), z, Float64(Float64(a * Float64(Float64(1.0 / t_1) * Float64(y + t))) - Float64(b * Float64(y / t_1))))
end

Wolfram

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

Derivation

1. Initial program 58.9%

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

3. Taylor expanded in a around 0

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

   1. associate--l+ N/A

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

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

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

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

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

   4. +-commutative N/A

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

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

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

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

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

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

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

   8. +-commutative N/A

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

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

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

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

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

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

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

   12. +-commutative N/A

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

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

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

5. Simplified 75.1%

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

   1. +-commutative N/A

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

   2. div-sub N/A

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

   3. associate-+l- N/A

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

   4. associate-*r/ N/A

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

   5. +-commutative N/A

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

   6. associate-+r+ N/A

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

   7. +-commutative N/A

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

   8. *-commutative N/A

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

   9. fmm-def N/A

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

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

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

7. Applied egg-rr 98.3%

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

8. Final simplification 98.3%

   \[\leadsto \mathsf{fma}\left(\frac{y + x}{t + \left(y + x\right)}, z, a \cdot \left(\frac{1}{t + \left(y + x\right)} \cdot \left(y + t\right)\right) - b \cdot \frac{y}{t + \left(y + x\right)}\right) \]
9. Add Preprocessing

Alternative 2: 89.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+293}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - b, y \cdot \frac{1}{y + t}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (<= t_1 (- INFINITY))
     (- (+ z a) b)
     (if (<= t_1 4e+293) t_1 (fma (- z b) (* y (/ 1.0 (+ y t))) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (z + a) - b;
	} else if (t_1 <= 4e+293) {
		tmp = t_1;
	} else {
		tmp = fma((z - b), (y * (1.0 / (y + t))), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(z + a) - b);
	elseif (t_1 <= 4e+293)
		tmp = t_1;
	else
		tmp = fma(Float64(z - b), Float64(y * Float64(1.0 / Float64(y + t))), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$1, 4e+293], t$95$1, N[(N[(z - b), $MachinePrecision] * N[(y * N[(1.0 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]]

Derivation

1. Split input into 3 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

   1. Initial program 6.8%

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

   3. Taylor expanded in y around 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 78.8%

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

   5. Simplified 78.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 3.9999999999999997e293

   1. Initial program 99.3%

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

   if 3.9999999999999997e293 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

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

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

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

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

      10. +-lowering-+.f64 8.8%

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

   5. Simplified 8.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

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

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

      9. +-commutative N/A

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

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

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

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

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

      12. --lowering--.f64 8.8%

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

   7. Applied egg-rr 8.8%

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. fma-define N/A

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

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

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

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

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

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

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

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

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

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

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. inv-pow N/A

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

      15. pow-plus N/A

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

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(z, b\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(y, t\right)\right)\right), \left({\left(y + t\right)}^{0} \cdot a\right)\right) \]

      17. metadata-eval N/A

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

      18. *-lowering-*.f64 78.8%

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

   9. Applied egg-rr 78.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+293}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - b, y \cdot \frac{1}{y + t}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+279}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) (+ y (+ x t))))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 5e+279) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + (a * (y + t))) - (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+279) {
		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 = (((z * (y + x)) + (a * (y + t))) - (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+279) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	t_2 = (z + a) - b
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 5e+279:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - 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+279)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 5e+279)
		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[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $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+279], 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 5.0000000000000002e279 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 76.9%

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

   5. Simplified 76.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000002e279

   1. Initial program 99.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+279}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(x \cdot \left(\frac{z}{t} - \frac{a}{t}\right) + \frac{y \cdot z - y \cdot b}{t}\right)\\ t_2 := t + \left(y + x\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-70}:\\ \;\;\;\;z + \left(\frac{y \cdot a}{y + x} - b \cdot \frac{y}{y + x}\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+157}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t\_2} + \frac{t}{t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ (* x (- (/ z t) (/ a t))) (/ (- (* y z) (* y b)) t))))
        (t_2 (+ t (+ y x))))
   (if (<= t -6.2e+64)
     t_1
     (if (<= t 4.6e-70)
       (+ z (- (/ (* y a) (+ y x)) (* b (/ y (+ y x)))))
       (if (<= t 4.5e+157) (+ z (* a (+ (/ y t_2) (/ t t_2)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + ((x * ((z / t) - (a / t))) + (((y * z) - (y * b)) / t));
	double t_2 = t + (y + x);
	double tmp;
	if (t <= -6.2e+64) {
		tmp = t_1;
	} else if (t <= 4.6e-70) {
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))));
	} else if (t <= 4.5e+157) {
		tmp = z + (a * ((y / t_2) + (t / t_2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + ((x * ((z / t) - (a / t))) + (((y * z) - (y * b)) / t))
    t_2 = t + (y + x)
    if (t <= (-6.2d+64)) then
        tmp = t_1
    else if (t <= 4.6d-70) then
        tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))))
    else if (t <= 4.5d+157) then
        tmp = z + (a * ((y / t_2) + (t / t_2)))
    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 + ((x * ((z / t) - (a / t))) + (((y * z) - (y * b)) / t));
	double t_2 = t + (y + x);
	double tmp;
	if (t <= -6.2e+64) {
		tmp = t_1;
	} else if (t <= 4.6e-70) {
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))));
	} else if (t <= 4.5e+157) {
		tmp = z + (a * ((y / t_2) + (t / t_2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + ((x * ((z / t) - (a / t))) + (((y * z) - (y * b)) / t))
	t_2 = t + (y + x)
	tmp = 0
	if t <= -6.2e+64:
		tmp = t_1
	elif t <= 4.6e-70:
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))))
	elif t <= 4.5e+157:
		tmp = z + (a * ((y / t_2) + (t / t_2)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(Float64(x * Float64(Float64(z / t) - Float64(a / t))) + Float64(Float64(Float64(y * z) - Float64(y * b)) / t)))
	t_2 = Float64(t + Float64(y + x))
	tmp = 0.0
	if (t <= -6.2e+64)
		tmp = t_1;
	elseif (t <= 4.6e-70)
		tmp = Float64(z + Float64(Float64(Float64(y * a) / Float64(y + x)) - Float64(b * Float64(y / Float64(y + x)))));
	elseif (t <= 4.5e+157)
		tmp = Float64(z + Float64(a * Float64(Float64(y / t_2) + Float64(t / t_2))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + ((x * ((z / t) - (a / t))) + (((y * z) - (y * b)) / t));
	t_2 = t + (y + x);
	tmp = 0.0;
	if (t <= -6.2e+64)
		tmp = t_1;
	elseif (t <= 4.6e-70)
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))));
	elseif (t <= 4.5e+157)
		tmp = z + (a * ((y / t_2) + (t / t_2)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(N[(x * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+64], t$95$1, If[LessEqual[t, 4.6e-70], N[(z + N[(N[(N[(y * a), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+157], N[(z + N[(a * N[(N[(y / t$95$2), $MachinePrecision] + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.1999999999999998e64 or 4.49999999999999985e157 < 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

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

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

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

      2. associate-*r/ N/A

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

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

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

   5. Simplified 65.7%

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

   6. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate--l+ N/A

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

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

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

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

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

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

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

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

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

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

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

      9. div-sub N/A

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

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

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

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

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

      12. *-commutative N/A

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

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

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

      14. *-commutative N/A

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

      15. *-lowering-*.f64 79.5%

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

   8. Simplified 79.5%

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

   if -6.1999999999999998e64 < t < 4.60000000000000001e-70

   1. Initial program 63.5%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 66.5%

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

   6. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

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

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

      11. +-lowering-+.f64 80.0%

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

   8. Simplified 80.0%

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

   if 4.60000000000000001e-70 < t < 4.49999999999999985e157

   1. Initial program 62.5%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 82.3%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 74.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+64}:\\ \;\;\;\;a + \left(x \cdot \left(\frac{z}{t} - \frac{a}{t}\right) + \frac{y \cdot z - y \cdot b}{t}\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-70}:\\ \;\;\;\;z + \left(\frac{y \cdot a}{y + x} - b \cdot \frac{y}{y + x}\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+157}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{t}{t + \left(y + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x \cdot \left(\frac{z}{t} - \frac{a}{t}\right) + \frac{y \cdot z - y \cdot b}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \frac{t}{x + t} + \frac{x \cdot z}{x + t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-67}:\\ \;\;\;\;z + \left(\frac{y \cdot a}{y + x} - b \cdot \frac{y}{y + x}\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+160}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t\_1} + \frac{t}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x))))
   (if (<= t -4.7e+60)
     (+ (* a (/ t (+ x t))) (/ (* x z) (+ x t)))
     (if (<= t 1.8e-67)
       (+ z (- (/ (* y a) (+ y x)) (* b (/ y (+ y x)))))
       (if (<= t 2.2e+160)
         (+ z (* a (+ (/ y t_1) (/ t t_1))))
         (- a (/ (* y b) t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double tmp;
	if (t <= -4.7e+60) {
		tmp = (a * (t / (x + t))) + ((x * z) / (x + t));
	} else if (t <= 1.8e-67) {
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))));
	} else if (t <= 2.2e+160) {
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	} else {
		tmp = a - ((y * b) / 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) :: t_1
    real(8) :: tmp
    t_1 = t + (y + x)
    if (t <= (-4.7d+60)) then
        tmp = (a * (t / (x + t))) + ((x * z) / (x + t))
    else if (t <= 1.8d-67) then
        tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))))
    else if (t <= 2.2d+160) then
        tmp = z + (a * ((y / t_1) + (t / t_1)))
    else
        tmp = a - ((y * b) / 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 t_1 = t + (y + x);
	double tmp;
	if (t <= -4.7e+60) {
		tmp = (a * (t / (x + t))) + ((x * z) / (x + t));
	} else if (t <= 1.8e-67) {
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))));
	} else if (t <= 2.2e+160) {
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	} else {
		tmp = a - ((y * b) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	tmp = 0
	if t <= -4.7e+60:
		tmp = (a * (t / (x + t))) + ((x * z) / (x + t))
	elif t <= 1.8e-67:
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))))
	elif t <= 2.2e+160:
		tmp = z + (a * ((y / t_1) + (t / t_1)))
	else:
		tmp = a - ((y * b) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	tmp = 0.0
	if (t <= -4.7e+60)
		tmp = Float64(Float64(a * Float64(t / Float64(x + t))) + Float64(Float64(x * z) / Float64(x + t)));
	elseif (t <= 1.8e-67)
		tmp = Float64(z + Float64(Float64(Float64(y * a) / Float64(y + x)) - Float64(b * Float64(y / Float64(y + x)))));
	elseif (t <= 2.2e+160)
		tmp = Float64(z + Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))));
	else
		tmp = Float64(a - Float64(Float64(y * b) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	tmp = 0.0;
	if (t <= -4.7e+60)
		tmp = (a * (t / (x + t))) + ((x * z) / (x + t));
	elseif (t <= 1.8e-67)
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))));
	elseif (t <= 2.2e+160)
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	else
		tmp = a - ((y * b) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.7e+60], N[(N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-67], N[(z + N[(N[(N[(y * a), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+160], N[(z + N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.6999999999999998e60

   1. Initial program 51.7%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 83.7%

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

      1. +-commutative N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      12. div-inv N/A

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

      13. div-inv N/A

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

      14. distribute-rgt-out N/A

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

      15. +-commutative N/A

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

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

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

   7. Applied egg-rr 83.6%

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

   8. Taylor expanded in y around 0

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

      8. +-lowering-+.f64 71.3%

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

   10. Simplified 71.3%

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

   if -4.6999999999999998e60 < t < 1.8e-67

   1. Initial program 63.5%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 66.5%

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

   6. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

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

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

      11. +-lowering-+.f64 80.0%

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

   8. Simplified 80.0%

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

   if 1.8e-67 < t < 2.19999999999999992e160

   1. Initial program 62.5%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 82.3%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 74.6%

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

   if 2.19999999999999992e160 < 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

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

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

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

      2. associate-*r/ N/A

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

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

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

   5. Simplified 69.4%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 72.7%

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

   8. Simplified 72.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \frac{t}{x + t} + \frac{x \cdot z}{x + t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-67}:\\ \;\;\;\;z + \left(\frac{y \cdot a}{y + x} - b \cdot \frac{y}{y + x}\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+160}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{t}{t + \left(y + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{t}{x + t} + \frac{x \cdot z}{x + t}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 120:\\ \;\;\;\;z + \left(\frac{y \cdot a}{y + x} - b \cdot \frac{y}{y + x}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a (/ t (+ x t))) (/ (* x z) (+ x t)))))
   (if (<= t -4.2e+57)
     t_1
     (if (<= t 120.0) (+ z (- (/ (* y a) (+ y x)) (* b (/ y (+ y x))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * (t / (x + t))) + ((x * z) / (x + t));
	double tmp;
	if (t <= -4.2e+57) {
		tmp = t_1;
	} else if (t <= 120.0) {
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))));
	} 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))) + ((x * z) / (x + t))
    if (t <= (-4.2d+57)) then
        tmp = t_1
    else if (t <= 120.0d0) then
        tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))))
    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))) + ((x * z) / (x + t));
	double tmp;
	if (t <= -4.2e+57) {
		tmp = t_1;
	} else if (t <= 120.0) {
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * (t / (x + t))) + ((x * z) / (x + t))
	tmp = 0
	if t <= -4.2e+57:
		tmp = t_1
	elif t <= 120.0:
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * Float64(t / Float64(x + t))) + Float64(Float64(x * z) / Float64(x + t)))
	tmp = 0.0
	if (t <= -4.2e+57)
		tmp = t_1;
	elseif (t <= 120.0)
		tmp = Float64(z + Float64(Float64(Float64(y * a) / Float64(y + x)) - Float64(b * Float64(y / Float64(y + x)))));
	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))) + ((x * z) / (x + t));
	tmp = 0.0;
	if (t <= -4.2e+57)
		tmp = t_1;
	elseif (t <= 120.0)
		tmp = z + (((y * a) / (y + x)) - (b * (y / (y + x))));
	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[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+57], t$95$1, If[LessEqual[t, 120.0], N[(z + N[(N[(N[(y * a), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.19999999999999982e57 or 120 < t

   1. Initial program 53.5%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 83.5%

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

      1. +-commutative N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      12. div-inv N/A

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

      13. div-inv N/A

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

      14. distribute-rgt-out N/A

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

      15. +-commutative N/A

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

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

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

   7. Applied egg-rr 83.4%

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

   8. Taylor expanded in y around 0

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

      8. +-lowering-+.f64 68.7%

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

   10. Simplified 68.7%

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

   if -4.19999999999999982e57 < t < 120

   1. Initial program 63.9%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 67.4%

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

   6. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

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

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

      11. +-lowering-+.f64 78.3%

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

   8. Simplified 78.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \frac{t}{x + t} + \frac{x \cdot z}{x + t}\\ \mathbf{elif}\;t \leq 120:\\ \;\;\;\;z + \left(\frac{y \cdot a}{y + x} - b \cdot \frac{y}{y + x}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t} + \frac{x \cdot z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.85 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{y + x}{t + \left(y + x\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.85e-168)
     t_1
     (if (<= y 9.4e-77)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 6.5e-9) (* (/ (+ y x) (+ t (+ y x))) z) 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 <= -2.85e-168) {
		tmp = t_1;
	} else if (y <= 9.4e-77) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 6.5e-9) {
		tmp = ((y + x) / (t + (y + x))) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.85d-168)) then
        tmp = t_1
    else if (y <= 9.4d-77) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 6.5d-9) then
        tmp = ((y + x) / (t + (y + x))) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.85e-168) {
		tmp = t_1;
	} else if (y <= 9.4e-77) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 6.5e-9) {
		tmp = ((y + x) / (t + (y + x))) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.85e-168:
		tmp = t_1
	elif y <= 9.4e-77:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 6.5e-9:
		tmp = ((y + x) / (t + (y + x))) * z
	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 <= -2.85e-168)
		tmp = t_1;
	elseif (y <= 9.4e-77)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 6.5e-9)
		tmp = Float64(Float64(Float64(y + x) / Float64(t + Float64(y + x))) * z);
	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 <= -2.85e-168)
		tmp = t_1;
	elseif (y <= 9.4e-77)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 6.5e-9)
		tmp = ((y + x) / (t + (y + x))) * z;
	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, -2.85e-168], t$95$1, If[LessEqual[y, 9.4e-77], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-9], N[(N[(N[(y + x), $MachinePrecision] / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.85000000000000004e-168 or 6.5000000000000003e-9 < y

   1. Initial program 46.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 67.0%

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

   5. Simplified 67.0%

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

   if -2.85000000000000004e-168 < y < 9.3999999999999998e-77

   1. Initial program 79.8%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 66.2%

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

   5. Simplified 66.2%

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

   if 9.3999999999999998e-77 < y < 6.5000000000000003e-9

   1. Initial program 60.4%

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

   3. Taylor expanded in z around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 48.6%

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

   5. Simplified 48.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

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

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

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

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

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

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

      10. +-lowering-+.f64 67.2%

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

   7. Applied egg-rr 67.2%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-168}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{y + x}{t + \left(y + x\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.9 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \frac{t}{x + t} + \frac{x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -5.9e+78)
     t_1
     (if (<= y 3.5e-15) (+ (* a (/ t (+ x t))) (/ (* 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 <= -5.9e+78) {
		tmp = t_1;
	} else if (y <= 3.5e-15) {
		tmp = (a * (t / (x + t))) + ((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 <= (-5.9d+78)) then
        tmp = t_1
    else if (y <= 3.5d-15) then
        tmp = (a * (t / (x + t))) + ((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 <= -5.9e+78) {
		tmp = t_1;
	} else if (y <= 3.5e-15) {
		tmp = (a * (t / (x + t))) + ((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 <= -5.9e+78:
		tmp = t_1
	elif y <= 3.5e-15:
		tmp = (a * (t / (x + t))) + ((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 <= -5.9e+78)
		tmp = t_1;
	elseif (y <= 3.5e-15)
		tmp = Float64(Float64(a * Float64(t / Float64(x + t))) + Float64(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 <= -5.9e+78)
		tmp = t_1;
	elseif (y <= 3.5e-15)
		tmp = (a * (t / (x + t))) + ((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, -5.9e+78], t$95$1, If[LessEqual[y, 3.5e-15], N[(N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.9e78 or 3.5000000000000001e-15 < y

   1. Initial program 36.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 73.4%

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

   5. Simplified 73.4%

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

   if -5.9e78 < y < 3.5000000000000001e-15

   1. Initial program 74.4%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 87.8%

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

      1. +-commutative N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      12. div-inv N/A

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

      13. div-inv N/A

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

      14. distribute-rgt-out N/A

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

      15. +-commutative N/A

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

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

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

   7. Applied egg-rr 87.7%

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

   8. Taylor expanded in y around 0

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

      8. +-lowering-+.f64 67.0%

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

   10. Simplified 67.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+78}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \frac{t}{x + t} + \frac{x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+61}:\\ \;\;\;\;a + \frac{z \cdot \left(y + x\right)}{t}\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{+121}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.85e+61)
   (+ a (/ (* z (+ y x)) t))
   (if (<= t 1.92e+121) (- (+ z a) b) (* a (/ t (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.85e+61) {
		tmp = a + ((z * (y + x)) / t);
	} else if (t <= 1.92e+121) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (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 <= (-1.85d+61)) then
        tmp = a + ((z * (y + x)) / t)
    else if (t <= 1.92d+121) then
        tmp = (z + a) - b
    else
        tmp = a * (t / (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 <= -1.85e+61) {
		tmp = a + ((z * (y + x)) / t);
	} else if (t <= 1.92e+121) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.85e+61:
		tmp = a + ((z * (y + x)) / t)
	elif t <= 1.92e+121:
		tmp = (z + a) - b
	else:
		tmp = a * (t / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.85e+61)
		tmp = Float64(a + Float64(Float64(z * Float64(y + x)) / t));
	elseif (t <= 1.92e+121)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(t / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.85e+61)
		tmp = a + ((z * (y + x)) / t);
	elseif (t <= 1.92e+121)
		tmp = (z + a) - b;
	else
		tmp = a * (t / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.85e+61], N[(a + N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.92e+121], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.85000000000000001e61

   1. Initial program 51.7%

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

   3. Taylor expanded in t around -inf

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

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

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

      2. associate-*r/ N/A

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

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

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

   5. Simplified 62.7%

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

   6. Taylor expanded in z around inf

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

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

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

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

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

      3. +-lowering-+.f64 68.5%

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

   8. Simplified 68.5%

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

   if -1.85000000000000001e61 < t < 1.92000000000000001e121

   1. Initial program 63.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 62.7%

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

   5. Simplified 62.7%

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

   if 1.92000000000000001e121 < t

   1. Initial program 49.7%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 86.2%

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

      1. +-commutative N/A

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

      2. div-sub N/A

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

      3. associate-+l- N/A

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

      4. associate-*r/ N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. fmm-def N/A

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

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

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

   7. Applied egg-rr 97.6%

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

   8. Taylor expanded in a around inf

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

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

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

      2. +-commutative N/A

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

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

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

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

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

      5. associate-+r+ N/A

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

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

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

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

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

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

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

      9. associate-+r+ N/A

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

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

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

      11. +-lowering-+.f64 68.4%

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

   10. Simplified 68.4%

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

   11. Taylor expanded in y around 0

       \[\leadsto \color{blue}{\frac{a \cdot t}{t + x}} \]
   12. 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 66.5%

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

   13. Simplified 66.5%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+61}:\\ \;\;\;\;a + \frac{z \cdot \left(y + x\right)}{t}\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{+121}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+161}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+118}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.1e+161)
   (- a (/ (* y b) t))
   (if (<= t 9.6e+118) (- (+ z a) b) (* a (/ t (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.1e+161) {
		tmp = a - ((y * b) / t);
	} else if (t <= 9.6e+118) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (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 <= (-2.1d+161)) then
        tmp = a - ((y * b) / t)
    else if (t <= 9.6d+118) then
        tmp = (z + a) - b
    else
        tmp = a * (t / (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 <= -2.1e+161) {
		tmp = a - ((y * b) / t);
	} else if (t <= 9.6e+118) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.1e+161:
		tmp = a - ((y * b) / t)
	elif t <= 9.6e+118:
		tmp = (z + a) - b
	else:
		tmp = a * (t / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.1e+161)
		tmp = Float64(a - Float64(Float64(y * b) / t));
	elseif (t <= 9.6e+118)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(t / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.1e+161)
		tmp = a - ((y * b) / t);
	elseif (t <= 9.6e+118)
		tmp = (z + a) - b;
	else
		tmp = a * (t / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.1e+161], N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+118], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1e161

   1. Initial program 47.0%

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

   3. Taylor expanded in t around -inf

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

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

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

      2. associate-*r/ N/A

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

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

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

   5. Simplified 62.8%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 71.8%

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

   8. Simplified 71.8%

      \[\leadsto a + \frac{\color{blue}{-y \cdot b}}{t} \]

   if -2.1e161 < t < 9.6e118

   1. Initial program 63.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 62.0%

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

   5. Simplified 62.0%

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

   if 9.6e118 < t

   1. Initial program 49.7%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 86.2%

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

      1. +-commutative N/A

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

      2. div-sub N/A

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

      3. associate-+l- N/A

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

      4. associate-*r/ N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. fmm-def N/A

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

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

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

   7. Applied egg-rr 97.6%

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

   8. Taylor expanded in a around inf

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

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

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

      2. +-commutative N/A

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

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

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

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

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

      5. associate-+r+ N/A

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

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

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

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

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

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

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

      9. associate-+r+ N/A

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

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

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

      11. +-lowering-+.f64 68.4%

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

   10. Simplified 68.4%

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

   11. Taylor expanded in y around 0

       \[\leadsto \color{blue}{\frac{a \cdot t}{t + x}} \]
   12. 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 66.5%

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

   13. Simplified 66.5%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+161}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+118}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{t}{x + t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+120}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ t (+ x t)))))
   (if (<= t -1.4e+163) t_1 (if (<= t 1.16e+120) (- (+ 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 <= -1.4e+163) {
		tmp = t_1;
	} else if (t <= 1.16e+120) {
		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 <= (-1.4d+163)) then
        tmp = t_1
    else if (t <= 1.16d+120) 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 <= -1.4e+163) {
		tmp = t_1;
	} else if (t <= 1.16e+120) {
		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 <= -1.4e+163:
		tmp = t_1
	elif t <= 1.16e+120:
		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 <= -1.4e+163)
		tmp = t_1;
	elseif (t <= 1.16e+120)
		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 <= -1.4e+163)
		tmp = t_1;
	elseif (t <= 1.16e+120)
		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, -1.4e+163], t$95$1, If[LessEqual[t, 1.16e+120], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.40000000000000007e163 or 1.16000000000000003e120 < t

   1. Initial program 48.6%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

   5. Simplified 86.2%

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

      1. +-commutative N/A

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

      2. div-sub N/A

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

      3. associate-+l- N/A

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

      4. associate-*r/ N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. fmm-def N/A

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

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

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

   7. Applied egg-rr 96.1%

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

   8. Taylor expanded in a around inf

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

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

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

      2. +-commutative N/A

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

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

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

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

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

      5. associate-+r+ N/A

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

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

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

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

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

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

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

      9. associate-+r+ N/A

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

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

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

      11. +-lowering-+.f64 68.6%

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

   10. Simplified 68.6%

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

   11. Taylor expanded in y around 0

       \[\leadsto \color{blue}{\frac{a \cdot t}{t + x}} \]
   12. 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 67.5%

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

   13. Simplified 67.5%

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

   if -1.40000000000000007e163 < t < 1.16000000000000003e120

   1. Initial program 63.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 62.0%

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

   5. Simplified 62.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+163}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+120}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+157}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+120}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6e+157) a (if (<= t 1.2e+120) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6e+157) {
		tmp = a;
	} else if (t <= 1.2e+120) {
		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 <= (-6d+157)) then
        tmp = a
    else if (t <= 1.2d+120) 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 <= -6e+157) {
		tmp = a;
	} else if (t <= 1.2e+120) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6e+157:
		tmp = a
	elif t <= 1.2e+120:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6e+157)
		tmp = a;
	elseif (t <= 1.2e+120)
		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 <= -6e+157)
		tmp = a;
	elseif (t <= 1.2e+120)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6e+157], a, If[LessEqual[t, 1.2e+120], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -6.00000000000000021e157 or 1.2e120 < t

   1. Initial program 48.6%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 59.9%

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

   if -6.00000000000000021e157 < t < 1.2e120

   1. Initial program 63.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 62.0%

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

   5. Simplified 62.0%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+157}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+120}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+98}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+47}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.2e+98) z (if (<= x 4.2e+47) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.2e+98) {
		tmp = z;
	} else if (x <= 4.2e+47) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.2d+98)) then
        tmp = z
    else if (x <= 4.2d+47) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.2e+98) {
		tmp = z;
	} else if (x <= 4.2e+47) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.2e+98:
		tmp = z
	elif x <= 4.2e+47:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.2e+98)
		tmp = z;
	elseif (x <= 4.2e+47)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.2e+98)
		tmp = z;
	elseif (x <= 4.2e+47)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.2e+98], z, If[LessEqual[x, 4.2e+47], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000009e98 or 4.2e47 < x

   1. Initial program 48.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 46.4%

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

   if -2.20000000000000009e98 < x < 4.2e47

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 50.2%

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

Alternative 14: 32.1% accurate, 21.0× speedup

Math

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

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 58.9%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{a} \]
4. Step-by-step derivation

5. Simplified 35.9%

   \[\leadsto \color{blue}{a} \]
6. Add Preprocessing

Developer Target 1: 82.9% 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 2024145 
(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)))