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

Percentage Accurate: 60.3% → 91.8%

Time: 19.6s

Alternatives: 21

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.3% 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: 91.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+120}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(\frac{y}{\frac{t_1}{a - b}} + \frac{t \cdot a}{t_1}\right)\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{+140}:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(\frac{a}{\frac{t_1}{y + t}} + \frac{x \cdot z}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}} + \mathsf{fma}\left(t, \frac{a}{x + y} - \left(\frac{z}{x + y} + \frac{y}{\frac{{\left(x + y\right)}^{2}}{a - b}}\right), z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= x -5.6e+120)
     (+ (/ (+ x y) (/ t_1 z)) (+ (/ y (/ t_1 (- a b))) (/ (* t a) t_1)))
     (if (<= x 3.75e+140)
       (+ (/ (- z b) (/ t_1 y)) (+ (/ a (/ t_1 (+ y t))) (/ (* x z) t_1)))
       (+
        (/ y (/ (+ x y) (- a b)))
        (fma
         t
         (-
          (/ a (+ x y))
          (+ (/ z (+ x y)) (/ y (/ (pow (+ x y) 2.0) (- a b)))))
         z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (x <= -5.6e+120) {
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + ((t * a) / t_1));
	} else if (x <= 3.75e+140) {
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	} else {
		tmp = (y / ((x + y) / (a - b))) + fma(t, ((a / (x + y)) - ((z / (x + y)) + (y / (pow((x + y), 2.0) / (a - b))))), z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (x <= -5.6e+120)
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(y / Float64(t_1 / Float64(a - b))) + Float64(Float64(t * a) / t_1)));
	elseif (x <= 3.75e+140)
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(Float64(x * z) / t_1)));
	else
		tmp = Float64(Float64(y / Float64(Float64(x + y) / Float64(a - b))) + fma(t, Float64(Float64(a / Float64(x + y)) - Float64(Float64(z / Float64(x + y)) + Float64(y / Float64((Float64(x + y) ^ 2.0) / Float64(a - b))))), z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.6e+120], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.75e+140], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(N[(x + y), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a / N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(N[(z / N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[Power[N[(x + y), $MachinePrecision], 2.0], $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.6000000000000001e120

   1. Initial program 53.6%

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

   3. Simplified 53.7%

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

   4. Taylor expanded in z around inf 53.7%

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

      1. associate-/l* 77.8%

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

      2. associate-/l* 91.5%

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

   6. Simplified 91.5%

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

   if -5.6000000000000001e120 < x < 3.7499999999999999e140

   1. Initial program 72.1%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in a around inf 72.3%

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

      1. associate-/l* 79.0%

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

      2. +-commutative 79.0%

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

      3. associate-/l* 95.2%

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

   6. Simplified 95.2%

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

   if 3.7499999999999999e140 < x

   1. Initial program 47.8%

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

      1. *-commutative 47.8%

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

      2. distribute-rgt-in 47.6%

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

      3. associate-+r+ 47.6%

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

      4. associate--l+ 47.6%

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

      5. +-commutative 47.6%

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

      6. +-commutative 47.6%

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

      7. distribute-lft-out-- 47.9%

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

      8. fma-def 48.5%

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

      9. +-commutative 48.5%

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

      10. fma-def 48.8%

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

      11. associate-+l+ 48.8%

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

      12. +-commutative 48.8%

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

   3. Simplified 48.8%

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

   4. Taylor expanded in t around 0 73.0%

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

      1. associate-/l* 65.4%

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

      2. *-commutative 65.4%

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

      3. fma-def 65.4%

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

      4. +-commutative 65.4%

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

      5. associate-/l* 84.6%

         \[\leadsto \frac{y}{\frac{y + x}{a - b}} + \mathsf{fma}\left(t, \frac{a}{y + x} - \left(\frac{z}{y + x} + \color{blue}{\frac{y}{\frac{{\left(y + x\right)}^{2}}{a - b}}}\right), z\right) \]

   6. Simplified 84.6%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+120}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + \frac{t \cdot a}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{+140}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{x \cdot z}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}} + \mathsf{fma}\left(t, \frac{a}{x + y} - \left(\frac{z}{x + y} + \frac{y}{\frac{{\left(x + y\right)}^{2}}{a - b}}\right), z\right)\\ \end{array} \]

Alternative 2: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+246}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_1} + z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \mathsf{fma}\left(y, a + \left(z - b\right), t \cdot a\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(\frac{y}{\frac{t_1}{a - b}} + \frac{t \cdot a}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1)))
   (if (<= t_2 -1e+246)
     (+ (* (+ y t) (/ a t_1)) (* z (/ (+ x y) t_1)))
     (if (<= t_2 2e+307)
       (/ (fma x z (fma y (+ a (- z b)) (* t a))) (+ x (+ y t)))
       (+ (/ (+ x y) (/ t_1 z)) (+ (/ y (/ t_1 (- a b))) (/ (* t a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -1e+246) {
		tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1));
	} else if (t_2 <= 2e+307) {
		tmp = fma(x, z, fma(y, (a + (z - b)), (t * a))) / (x + (y + t));
	} else {
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + ((t * a) / t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= -1e+246)
		tmp = Float64(Float64(Float64(y + t) * Float64(a / t_1)) + Float64(z * Float64(Float64(x + y) / t_1)));
	elseif (t_2 <= 2e+307)
		tmp = Float64(fma(x, z, fma(y, Float64(a + Float64(z - b)), Float64(t * a))) / Float64(x + Float64(y + t)));
	else
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(y / Float64(t_1 / Float64(a - b))) + Float64(Float64(t * a) / t_1)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+246], N[(N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+307], N[(N[(x * z + N[(y * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $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)) < -1.00000000000000007e246

   1. Initial program 11.7%

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

   2. Taylor expanded in b around 0 11.5%

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

   3. Taylor expanded in a around inf 11.5%

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

      1. associate-/l* 47.2%

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

      2. +-commutative 47.2%

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

      3. associate-/r/ 47.0%

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

      4. *-commutative 47.0%

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

      5. associate-*l/ 85.8%

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

      6. *-commutative 85.8%

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

   5. Simplified 85.8%

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

   if -1.00000000000000007e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999997e307

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   if 1.99999999999999997e307 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.5%

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

   3. Simplified 6.0%

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

   4. Taylor expanded in z around inf 4.5%

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

      1. associate-/l* 31.0%

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

      2. associate-/l* 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+246}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)} + z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \mathsf{fma}\left(y, a + \left(z - b\right), t \cdot a\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + \frac{t \cdot a}{y + \left(x + t\right)}\right)\\ \end{array} \]

Alternative 3: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+246}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_1} + z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, a - b, \mathsf{fma}\left(x + y, z, t \cdot a\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(\frac{y}{\frac{t_1}{a - b}} + \frac{t \cdot a}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1)))
   (if (<= t_2 -1e+246)
     (+ (* (+ y t) (/ a t_1)) (* z (/ (+ x y) t_1)))
     (if (<= t_2 2e+307)
       (/ (fma y (- a b) (fma (+ x y) z (* t a))) (+ x (+ y t)))
       (+ (/ (+ x y) (/ t_1 z)) (+ (/ y (/ t_1 (- a b))) (/ (* t a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -1e+246) {
		tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1));
	} else if (t_2 <= 2e+307) {
		tmp = fma(y, (a - b), fma((x + y), z, (t * a))) / (x + (y + t));
	} else {
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + ((t * a) / t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= -1e+246)
		tmp = Float64(Float64(Float64(y + t) * Float64(a / t_1)) + Float64(z * Float64(Float64(x + y) / t_1)));
	elseif (t_2 <= 2e+307)
		tmp = Float64(fma(y, Float64(a - b), fma(Float64(x + y), z, Float64(t * a))) / Float64(x + Float64(y + t)));
	else
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(y / Float64(t_1 / Float64(a - b))) + Float64(Float64(t * a) / t_1)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+246], N[(N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+307], N[(N[(y * N[(a - b), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $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)) < -1.00000000000000007e246

   1. Initial program 11.7%

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

   2. Taylor expanded in b around 0 11.5%

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

   3. Taylor expanded in a around inf 11.5%

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

      1. associate-/l* 47.2%

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

      2. +-commutative 47.2%

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

      3. associate-/r/ 47.0%

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

      4. *-commutative 47.0%

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

      5. associate-*l/ 85.8%

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

      6. *-commutative 85.8%

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

   5. Simplified 85.8%

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

   if -1.00000000000000007e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999997e307

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. distribute-rgt-in 99.7%

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

      3. associate-+r+ 99.7%

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

      4. associate--l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. fma-def 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-def 99.7%

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

      11. associate-+l+ 99.7%

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

      12. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   if 1.99999999999999997e307 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.5%

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

   3. Simplified 6.0%

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

   4. Taylor expanded in z around inf 4.5%

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

      1. associate-/l* 31.0%

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

      2. associate-/l* 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+246}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)} + z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, a - b, \mathsf{fma}\left(x + y, z, t \cdot a\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + \frac{t \cdot a}{y + \left(x + t\right)}\right)\\ \end{array} \]

Alternative 4: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+246}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_1} + z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(\frac{y}{\frac{t_1}{a - b}} + \frac{t \cdot a}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1)))
   (if (<= t_2 -1e+246)
     (+ (* (+ y t) (/ a t_1)) (* z (/ (+ x y) t_1)))
     (if (<= t_2 2e+307)
       t_2
       (+ (/ (+ x y) (/ t_1 z)) (+ (/ y (/ t_1 (- a b))) (/ (* t a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -1e+246) {
		tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1));
	} else if (t_2 <= 2e+307) {
		tmp = t_2;
	} else {
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + ((t * a) / 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 = y + (x + t)
    t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
    if (t_2 <= (-1d+246)) then
        tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1))
    else if (t_2 <= 2d+307) then
        tmp = t_2
    else
        tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + ((t * a) / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -1e+246) {
		tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1));
	} else if (t_2 <= 2e+307) {
		tmp = t_2;
	} else {
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + ((t * a) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -1e+246:
		tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1))
	elif t_2 <= 2e+307:
		tmp = t_2
	else:
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + ((t * a) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= -1e+246)
		tmp = Float64(Float64(Float64(y + t) * Float64(a / t_1)) + Float64(z * Float64(Float64(x + y) / t_1)));
	elseif (t_2 <= 2e+307)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(y / Float64(t_1 / Float64(a - b))) + Float64(Float64(t * a) / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -1e+246)
		tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1));
	elseif (t_2 <= 2e+307)
		tmp = t_2;
	else
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + ((t * a) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+246], N[(N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+307], t$95$2, N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $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)) < -1.00000000000000007e246

   1. Initial program 11.7%

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

   2. Taylor expanded in b around 0 11.5%

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

   3. Taylor expanded in a around inf 11.5%

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

      1. associate-/l* 47.2%

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

      2. +-commutative 47.2%

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

      3. associate-/r/ 47.0%

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

      4. *-commutative 47.0%

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

      5. associate-*l/ 85.8%

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

      6. *-commutative 85.8%

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

   5. Simplified 85.8%

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

   if -1.00000000000000007e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999997e307

   1. Initial program 99.7%

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

   if 1.99999999999999997e307 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.5%

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

   3. Simplified 6.0%

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

   4. Taylor expanded in z around inf 4.5%

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

      1. associate-/l* 31.0%

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

      2. associate-/l* 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+246}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)} + z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + \frac{t \cdot a}{y + \left(x + t\right)}\right)\\ \end{array} \]

Alternative 5: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+246} \lor \neg \left(t_2 \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_1} + z \cdot \frac{x + y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 -1e+246) (not (<= t_2 2e+296)))
     (+ (* (+ y t) (/ a t_1)) (* z (/ (+ x y) t_1)))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -1e+246) || !(t_2 <= 2e+296)) {
		tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
    if ((t_2 <= (-1d+246)) .or. (.not. (t_2 <= 2d+296))) then
        tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -1e+246) || !(t_2 <= 2e+296)) {
		tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -1e+246) or not (t_2 <= 2e+296):
		tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= -1e+246) || !(t_2 <= 2e+296))
		tmp = Float64(Float64(Float64(y + t) * Float64(a / t_1)) + Float64(z * Float64(Float64(x + y) / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -1e+246) || ~((t_2 <= 2e+296)))
		tmp = ((y + t) * (a / t_1)) + (z * ((x + y) / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e+246], N[Not[LessEqual[t$95$2, 2e+296]], $MachinePrecision]], N[(N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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)) < -1.00000000000000007e246 or 1.99999999999999996e296 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.1%

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

   2. Taylor expanded in b around 0 7.8%

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

   3. Taylor expanded in a around inf 7.8%

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

      1. associate-/l* 33.0%

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

      2. +-commutative 33.0%

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

      3. associate-/r/ 32.8%

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

      4. *-commutative 32.8%

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

      5. associate-*l/ 79.1%

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

      6. *-commutative 79.1%

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

   5. Simplified 79.1%

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

   if -1.00000000000000007e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999996e296

   1. Initial program 99.7%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+246} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)} + z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 6: 88.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+307))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+307)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+307)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+307):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+307))
		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 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+307)))
		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[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+307]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

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 1.99999999999999997e307 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.1%

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

   2. Taylor expanded in y around inf 66.3%

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

      1. +-commutative 66.3%

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

   4. Simplified 66.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999997e307

   1. Initial program 99.7%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 7: 56.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{a}{\frac{t_1}{y + t}}\\ t_3 := \left(z + a\right) - b\\ t_4 := \frac{x \cdot z - y \cdot b}{t_1}\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-180}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-209}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-229}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-266}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-43}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ a (/ t_1 (+ y t))))
        (t_3 (- (+ z a) b))
        (t_4 (/ (- (* x z) (* y b)) t_1)))
   (if (<= y -2.65e+36)
     t_3
     (if (<= y -1.3e-69)
       t_2
       (if (<= y -4.3e-180)
         (* z (/ (+ x y) t_1))
         (if (<= y -4e-209)
           (/ (- (* t a) (* y b)) t_1)
           (if (<= y -9.5e-229)
             (+ z a)
             (if (<= y -4.1e-274)
               t_2
               (if (<= y 5.5e-266)
                 t_4
                 (if (<= y 1.8e-184) t_2 (if (<= y 4.6e-43) t_4 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z + a) - b;
	double t_4 = ((x * z) - (y * b)) / t_1;
	double tmp;
	if (y <= -2.65e+36) {
		tmp = t_3;
	} else if (y <= -1.3e-69) {
		tmp = t_2;
	} else if (y <= -4.3e-180) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -4e-209) {
		tmp = ((t * a) - (y * b)) / t_1;
	} else if (y <= -9.5e-229) {
		tmp = z + a;
	} else if (y <= -4.1e-274) {
		tmp = t_2;
	} else if (y <= 5.5e-266) {
		tmp = t_4;
	} else if (y <= 1.8e-184) {
		tmp = t_2;
	} else if (y <= 4.6e-43) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	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 = y + (x + t)
    t_2 = a / (t_1 / (y + t))
    t_3 = (z + a) - b
    t_4 = ((x * z) - (y * b)) / t_1
    if (y <= (-2.65d+36)) then
        tmp = t_3
    else if (y <= (-1.3d-69)) then
        tmp = t_2
    else if (y <= (-4.3d-180)) then
        tmp = z * ((x + y) / t_1)
    else if (y <= (-4d-209)) then
        tmp = ((t * a) - (y * b)) / t_1
    else if (y <= (-9.5d-229)) then
        tmp = z + a
    else if (y <= (-4.1d-274)) then
        tmp = t_2
    else if (y <= 5.5d-266) then
        tmp = t_4
    else if (y <= 1.8d-184) then
        tmp = t_2
    else if (y <= 4.6d-43) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z + a) - b;
	double t_4 = ((x * z) - (y * b)) / t_1;
	double tmp;
	if (y <= -2.65e+36) {
		tmp = t_3;
	} else if (y <= -1.3e-69) {
		tmp = t_2;
	} else if (y <= -4.3e-180) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -4e-209) {
		tmp = ((t * a) - (y * b)) / t_1;
	} else if (y <= -9.5e-229) {
		tmp = z + a;
	} else if (y <= -4.1e-274) {
		tmp = t_2;
	} else if (y <= 5.5e-266) {
		tmp = t_4;
	} else if (y <= 1.8e-184) {
		tmp = t_2;
	} else if (y <= 4.6e-43) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a / (t_1 / (y + t))
	t_3 = (z + a) - b
	t_4 = ((x * z) - (y * b)) / t_1
	tmp = 0
	if y <= -2.65e+36:
		tmp = t_3
	elif y <= -1.3e-69:
		tmp = t_2
	elif y <= -4.3e-180:
		tmp = z * ((x + y) / t_1)
	elif y <= -4e-209:
		tmp = ((t * a) - (y * b)) / t_1
	elif y <= -9.5e-229:
		tmp = z + a
	elif y <= -4.1e-274:
		tmp = t_2
	elif y <= 5.5e-266:
		tmp = t_4
	elif y <= 1.8e-184:
		tmp = t_2
	elif y <= 4.6e-43:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a / Float64(t_1 / Float64(y + t)))
	t_3 = Float64(Float64(z + a) - b)
	t_4 = Float64(Float64(Float64(x * z) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (y <= -2.65e+36)
		tmp = t_3;
	elseif (y <= -1.3e-69)
		tmp = t_2;
	elseif (y <= -4.3e-180)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	elseif (y <= -4e-209)
		tmp = Float64(Float64(Float64(t * a) - Float64(y * b)) / t_1);
	elseif (y <= -9.5e-229)
		tmp = Float64(z + a);
	elseif (y <= -4.1e-274)
		tmp = t_2;
	elseif (y <= 5.5e-266)
		tmp = t_4;
	elseif (y <= 1.8e-184)
		tmp = t_2;
	elseif (y <= 4.6e-43)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a / (t_1 / (y + t));
	t_3 = (z + a) - b;
	t_4 = ((x * z) - (y * b)) / t_1;
	tmp = 0.0;
	if (y <= -2.65e+36)
		tmp = t_3;
	elseif (y <= -1.3e-69)
		tmp = t_2;
	elseif (y <= -4.3e-180)
		tmp = z * ((x + y) / t_1);
	elseif (y <= -4e-209)
		tmp = ((t * a) - (y * b)) / t_1;
	elseif (y <= -9.5e-229)
		tmp = z + a;
	elseif (y <= -4.1e-274)
		tmp = t_2;
	elseif (y <= 5.5e-266)
		tmp = t_4;
	elseif (y <= 1.8e-184)
		tmp = t_2;
	elseif (y <= 4.6e-43)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[y, -2.65e+36], t$95$3, If[LessEqual[y, -1.3e-69], t$95$2, If[LessEqual[y, -4.3e-180], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-209], N[(N[(N[(t * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, -9.5e-229], N[(z + a), $MachinePrecision], If[LessEqual[y, -4.1e-274], t$95$2, If[LessEqual[y, 5.5e-266], t$95$4, If[LessEqual[y, 1.8e-184], t$95$2, If[LessEqual[y, 4.6e-43], t$95$4, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.65e36 or 4.5999999999999998e-43 < y

   1. Initial program 47.6%

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

   2. Taylor expanded in y around inf 70.0%

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

      1. +-commutative 70.0%

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

   4. Simplified 70.0%

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

   if -2.65e36 < y < -1.3000000000000001e-69 or -9.4999999999999997e-229 < y < -4.09999999999999987e-274 or 5.50000000000000026e-266 < y < 1.8000000000000001e-184

   1. Initial program 77.0%

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

   2. Taylor expanded in a around inf 47.4%

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

      1. associate-/l* 60.3%

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

   4. Simplified 60.3%

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

   if -1.3000000000000001e-69 < y < -4.2999999999999996e-180

   1. Initial program 86.2%

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

   2. Taylor expanded in z around inf 63.2%

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

      1. associate-/l* 52.4%

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

   4. Simplified 52.4%

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

      1. associate-/r/ 74.7%

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

   6. Applied egg-rr 74.7%

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

   if -4.2999999999999996e-180 < y < -4.0000000000000002e-209

   1. Initial program 99.5%

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

   2. Taylor expanded in t around inf 87.8%

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

   if -4.0000000000000002e-209 < y < -9.4999999999999997e-229

   1. Initial program 62.3%

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

   2. Taylor expanded in b around 0 62.3%

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

   3. Taylor expanded in y around inf 81.3%

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

      1. +-commutative 81.3%

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

   5. Simplified 81.3%

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

   if -4.09999999999999987e-274 < y < 5.50000000000000026e-266 or 1.8000000000000001e-184 < y < 4.5999999999999998e-43

   1. Initial program 91.6%

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

   2. Taylor expanded in x around inf 72.2%

      \[\leadsto \frac{\color{blue}{z \cdot x} - y \cdot b}{\left(x + t\right) + y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+36}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-69}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-180}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-209}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-229}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-274}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-266}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-184}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 8: 56.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{t \cdot a - y \cdot b}{t_1}\\ t_3 := \left(z + a\right) - b\\ t_4 := z \cdot \frac{x + y}{t_1}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-172}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-293}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (* t a) (* y b)) t_1))
        (t_3 (- (+ z a) b))
        (t_4 (* z (/ (+ x y) t_1))))
   (if (<= y -4.1e+36)
     t_3
     (if (<= y -1.2e-69)
       (/ a (/ t_1 (+ y t)))
       (if (<= y -5.1e-172)
         t_4
         (if (<= y -2.05e-209)
           t_2
           (if (<= y 2.5e-293) t_4 (if (<= y 4e-57) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((t * a) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double t_4 = z * ((x + y) / t_1);
	double tmp;
	if (y <= -4.1e+36) {
		tmp = t_3;
	} else if (y <= -1.2e-69) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= -5.1e-172) {
		tmp = t_4;
	} else if (y <= -2.05e-209) {
		tmp = t_2;
	} else if (y <= 2.5e-293) {
		tmp = t_4;
	} else if (y <= 4e-57) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 = y + (x + t)
    t_2 = ((t * a) - (y * b)) / t_1
    t_3 = (z + a) - b
    t_4 = z * ((x + y) / t_1)
    if (y <= (-4.1d+36)) then
        tmp = t_3
    else if (y <= (-1.2d-69)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= (-5.1d-172)) then
        tmp = t_4
    else if (y <= (-2.05d-209)) then
        tmp = t_2
    else if (y <= 2.5d-293) then
        tmp = t_4
    else if (y <= 4d-57) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((t * a) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double t_4 = z * ((x + y) / t_1);
	double tmp;
	if (y <= -4.1e+36) {
		tmp = t_3;
	} else if (y <= -1.2e-69) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= -5.1e-172) {
		tmp = t_4;
	} else if (y <= -2.05e-209) {
		tmp = t_2;
	} else if (y <= 2.5e-293) {
		tmp = t_4;
	} else if (y <= 4e-57) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((t * a) - (y * b)) / t_1
	t_3 = (z + a) - b
	t_4 = z * ((x + y) / t_1)
	tmp = 0
	if y <= -4.1e+36:
		tmp = t_3
	elif y <= -1.2e-69:
		tmp = a / (t_1 / (y + t))
	elif y <= -5.1e-172:
		tmp = t_4
	elif y <= -2.05e-209:
		tmp = t_2
	elif y <= 2.5e-293:
		tmp = t_4
	elif y <= 4e-57:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(t * a) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	t_4 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (y <= -4.1e+36)
		tmp = t_3;
	elseif (y <= -1.2e-69)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= -5.1e-172)
		tmp = t_4;
	elseif (y <= -2.05e-209)
		tmp = t_2;
	elseif (y <= 2.5e-293)
		tmp = t_4;
	elseif (y <= 4e-57)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((t * a) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	t_4 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (y <= -4.1e+36)
		tmp = t_3;
	elseif (y <= -1.2e-69)
		tmp = a / (t_1 / (y + t));
	elseif (y <= -5.1e-172)
		tmp = t_4;
	elseif (y <= -2.05e-209)
		tmp = t_2;
	elseif (y <= 2.5e-293)
		tmp = t_4;
	elseif (y <= 4e-57)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+36], t$95$3, If[LessEqual[y, -1.2e-69], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.1e-172], t$95$4, If[LessEqual[y, -2.05e-209], t$95$2, If[LessEqual[y, 2.5e-293], t$95$4, If[LessEqual[y, 4e-57], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.10000000000000013e36 or 3.99999999999999982e-57 < y

   1. Initial program 49.2%

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

   2. Taylor expanded in y around inf 69.5%

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

      1. +-commutative 69.5%

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

   4. Simplified 69.5%

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

   if -4.10000000000000013e36 < y < -1.2000000000000001e-69

   1. Initial program 79.6%

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

   2. Taylor expanded in a around inf 43.7%

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

      1. associate-/l* 57.2%

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

   4. Simplified 57.2%

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

   if -1.2000000000000001e-69 < y < -5.0999999999999998e-172 or -2.04999999999999989e-209 < y < 2.5000000000000001e-293

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 56.5%

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

      1. associate-/l* 47.7%

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

   4. Simplified 47.7%

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

      1. associate-/r/ 63.7%

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

   6. Applied egg-rr 63.7%

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

   if -5.0999999999999998e-172 < y < -2.04999999999999989e-209 or 2.5000000000000001e-293 < y < 3.99999999999999982e-57

   1. Initial program 84.6%

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

   2. Taylor expanded in t around inf 55.4%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+36}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-172}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-209}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-293}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-57}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 9: 57.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6700000:\\ \;\;\;\;z \cdot \frac{x + y}{t_2}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{-y}{\frac{t_2}{b}}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-202}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (- z (* y (- (/ b x) (/ a x))))))
   (if (<= x -3.8e+70)
     t_3
     (if (<= x -6700000.0)
       (* z (/ (+ x y) t_2))
       (if (<= x -6.6e-59)
         (/ (- y) (/ t_2 b))
         (if (<= x -4.2e-130)
           t_1
           (if (<= x -1.6e-202) a (if (<= x 4.8e+18) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = z - (y * ((b / x) - (a / x)));
	double tmp;
	if (x <= -3.8e+70) {
		tmp = t_3;
	} else if (x <= -6700000.0) {
		tmp = z * ((x + y) / t_2);
	} else if (x <= -6.6e-59) {
		tmp = -y / (t_2 / b);
	} else if (x <= -4.2e-130) {
		tmp = t_1;
	} else if (x <= -1.6e-202) {
		tmp = a;
	} else if (x <= 4.8e+18) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = z - (y * ((b / x) - (a / x)))
    if (x <= (-3.8d+70)) then
        tmp = t_3
    else if (x <= (-6700000.0d0)) then
        tmp = z * ((x + y) / t_2)
    else if (x <= (-6.6d-59)) then
        tmp = -y / (t_2 / b)
    else if (x <= (-4.2d-130)) then
        tmp = t_1
    else if (x <= (-1.6d-202)) then
        tmp = a
    else if (x <= 4.8d+18) then
        tmp = t_1
    else
        tmp = t_3
    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 t_2 = y + (x + t);
	double t_3 = z - (y * ((b / x) - (a / x)));
	double tmp;
	if (x <= -3.8e+70) {
		tmp = t_3;
	} else if (x <= -6700000.0) {
		tmp = z * ((x + y) / t_2);
	} else if (x <= -6.6e-59) {
		tmp = -y / (t_2 / b);
	} else if (x <= -4.2e-130) {
		tmp = t_1;
	} else if (x <= -1.6e-202) {
		tmp = a;
	} else if (x <= 4.8e+18) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = z - (y * ((b / x) - (a / x)))
	tmp = 0
	if x <= -3.8e+70:
		tmp = t_3
	elif x <= -6700000.0:
		tmp = z * ((x + y) / t_2)
	elif x <= -6.6e-59:
		tmp = -y / (t_2 / b)
	elif x <= -4.2e-130:
		tmp = t_1
	elif x <= -1.6e-202:
		tmp = a
	elif x <= 4.8e+18:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z - Float64(y * Float64(Float64(b / x) - Float64(a / x))))
	tmp = 0.0
	if (x <= -3.8e+70)
		tmp = t_3;
	elseif (x <= -6700000.0)
		tmp = Float64(z * Float64(Float64(x + y) / t_2));
	elseif (x <= -6.6e-59)
		tmp = Float64(Float64(-y) / Float64(t_2 / b));
	elseif (x <= -4.2e-130)
		tmp = t_1;
	elseif (x <= -1.6e-202)
		tmp = a;
	elseif (x <= 4.8e+18)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = z - (y * ((b / x) - (a / x)));
	tmp = 0.0;
	if (x <= -3.8e+70)
		tmp = t_3;
	elseif (x <= -6700000.0)
		tmp = z * ((x + y) / t_2);
	elseif (x <= -6.6e-59)
		tmp = -y / (t_2 / b);
	elseif (x <= -4.2e-130)
		tmp = t_1;
	elseif (x <= -1.6e-202)
		tmp = a;
	elseif (x <= 4.8e+18)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z - N[(y * N[(N[(b / x), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+70], t$95$3, If[LessEqual[x, -6700000.0], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.6e-59], N[((-y) / N[(t$95$2 / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-130], t$95$1, If[LessEqual[x, -1.6e-202], a, If[LessEqual[x, 4.8e+18], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.7999999999999998e70 or 4.8e18 < x

   1. Initial program 58.8%

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

   3. Simplified 59.0%

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

   4. Taylor expanded in x around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. associate-+r+ 51.8%

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

      3. associate-/l* 51.6%

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

      4. associate-/l* 54.7%

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

      5. +-commutative 54.7%

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

   6. Simplified 54.7%

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

   7. Taylor expanded in t around 0 48.2%

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

      1. associate--l+ 49.1%

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

      2. +-commutative 49.1%

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

      3. associate-+r- 49.1%

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

      4. associate-*l/ 51.3%

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

      5. associate-/l* 59.5%

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

   9. Simplified 59.5%

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

   10. Taylor expanded in y around 0 61.7%

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

   if -3.7999999999999998e70 < x < -6.7e6

   1. Initial program 62.0%

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

   2. Taylor expanded in z around inf 48.3%

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

      1. associate-/l* 61.3%

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

   4. Simplified 61.3%

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

      1. associate-/r/ 61.2%

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

   6. Applied egg-rr 61.2%

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

   if -6.7e6 < x < -6.59999999999999964e-59

   1. Initial program 92.4%

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

   2. Taylor expanded in b around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-/l* 75.7%

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

      3. distribute-neg-frac 75.7%

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

   4. Simplified 75.7%

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

   if -6.59999999999999964e-59 < x < -4.20000000000000004e-130 or -1.6000000000000001e-202 < x < 4.8e18

   1. Initial program 67.3%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. +-commutative 65.8%

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

   4. Simplified 65.8%

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

   if -4.20000000000000004e-130 < x < -1.6000000000000001e-202

   1. Initial program 88.5%

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

   2. Taylor expanded in t around inf 66.9%

      \[\leadsto \color{blue}{a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq -6700000:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{-y}{\frac{y + \left(x + t\right)}{b}}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-130}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-202}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \end{array} \]

Alternative 10: 57.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1250000000:\\ \;\;\;\;z \cdot \frac{x + y}{t_2}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{-y}{\frac{t_2}{b}}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-203}:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (- z (* y (- (/ b x) (/ a x))))))
   (if (<= x -8.5e+71)
     t_3
     (if (<= x -1250000000.0)
       (* z (/ (+ x y) t_2))
       (if (<= x -6.6e-59)
         (/ (- y) (/ t_2 b))
         (if (<= x -4e-130)
           t_1
           (if (<= x -1.75e-203)
             (/ a (/ t_2 (+ y t)))
             (if (<= x 4.8e+18) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = z - (y * ((b / x) - (a / x)));
	double tmp;
	if (x <= -8.5e+71) {
		tmp = t_3;
	} else if (x <= -1250000000.0) {
		tmp = z * ((x + y) / t_2);
	} else if (x <= -6.6e-59) {
		tmp = -y / (t_2 / b);
	} else if (x <= -4e-130) {
		tmp = t_1;
	} else if (x <= -1.75e-203) {
		tmp = a / (t_2 / (y + t));
	} else if (x <= 4.8e+18) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = z - (y * ((b / x) - (a / x)))
    if (x <= (-8.5d+71)) then
        tmp = t_3
    else if (x <= (-1250000000.0d0)) then
        tmp = z * ((x + y) / t_2)
    else if (x <= (-6.6d-59)) then
        tmp = -y / (t_2 / b)
    else if (x <= (-4d-130)) then
        tmp = t_1
    else if (x <= (-1.75d-203)) then
        tmp = a / (t_2 / (y + t))
    else if (x <= 4.8d+18) then
        tmp = t_1
    else
        tmp = t_3
    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 t_2 = y + (x + t);
	double t_3 = z - (y * ((b / x) - (a / x)));
	double tmp;
	if (x <= -8.5e+71) {
		tmp = t_3;
	} else if (x <= -1250000000.0) {
		tmp = z * ((x + y) / t_2);
	} else if (x <= -6.6e-59) {
		tmp = -y / (t_2 / b);
	} else if (x <= -4e-130) {
		tmp = t_1;
	} else if (x <= -1.75e-203) {
		tmp = a / (t_2 / (y + t));
	} else if (x <= 4.8e+18) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = z - (y * ((b / x) - (a / x)))
	tmp = 0
	if x <= -8.5e+71:
		tmp = t_3
	elif x <= -1250000000.0:
		tmp = z * ((x + y) / t_2)
	elif x <= -6.6e-59:
		tmp = -y / (t_2 / b)
	elif x <= -4e-130:
		tmp = t_1
	elif x <= -1.75e-203:
		tmp = a / (t_2 / (y + t))
	elif x <= 4.8e+18:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z - Float64(y * Float64(Float64(b / x) - Float64(a / x))))
	tmp = 0.0
	if (x <= -8.5e+71)
		tmp = t_3;
	elseif (x <= -1250000000.0)
		tmp = Float64(z * Float64(Float64(x + y) / t_2));
	elseif (x <= -6.6e-59)
		tmp = Float64(Float64(-y) / Float64(t_2 / b));
	elseif (x <= -4e-130)
		tmp = t_1;
	elseif (x <= -1.75e-203)
		tmp = Float64(a / Float64(t_2 / Float64(y + t)));
	elseif (x <= 4.8e+18)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = z - (y * ((b / x) - (a / x)));
	tmp = 0.0;
	if (x <= -8.5e+71)
		tmp = t_3;
	elseif (x <= -1250000000.0)
		tmp = z * ((x + y) / t_2);
	elseif (x <= -6.6e-59)
		tmp = -y / (t_2 / b);
	elseif (x <= -4e-130)
		tmp = t_1;
	elseif (x <= -1.75e-203)
		tmp = a / (t_2 / (y + t));
	elseif (x <= 4.8e+18)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z - N[(y * N[(N[(b / x), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e+71], t$95$3, If[LessEqual[x, -1250000000.0], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.6e-59], N[((-y) / N[(t$95$2 / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e-130], t$95$1, If[LessEqual[x, -1.75e-203], N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+18], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.4999999999999996e71 or 4.8e18 < x

   1. Initial program 58.8%

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

   3. Simplified 59.0%

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

   4. Taylor expanded in x around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. associate-+r+ 51.8%

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

      3. associate-/l* 51.6%

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

      4. associate-/l* 54.7%

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

      5. +-commutative 54.7%

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

   6. Simplified 54.7%

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

   7. Taylor expanded in t around 0 48.2%

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

      1. associate--l+ 49.1%

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

      2. +-commutative 49.1%

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

      3. associate-+r- 49.1%

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

      4. associate-*l/ 51.3%

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

      5. associate-/l* 59.5%

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

   9. Simplified 59.5%

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

   10. Taylor expanded in y around 0 61.7%

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

   if -8.4999999999999996e71 < x < -1.25e9

   1. Initial program 62.0%

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

   2. Taylor expanded in z around inf 48.3%

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

      1. associate-/l* 61.3%

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

   4. Simplified 61.3%

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

      1. associate-/r/ 61.2%

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

   6. Applied egg-rr 61.2%

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

   if -1.25e9 < x < -6.59999999999999964e-59

   1. Initial program 92.4%

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

   2. Taylor expanded in b around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-/l* 75.7%

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

      3. distribute-neg-frac 75.7%

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

   4. Simplified 75.7%

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

   if -6.59999999999999964e-59 < x < -4.0000000000000003e-130 or -1.7500000000000001e-203 < x < 4.8e18

   1. Initial program 67.3%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. +-commutative 65.8%

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

   4. Simplified 65.8%

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

   if -4.0000000000000003e-130 < x < -1.7500000000000001e-203

   1. Initial program 88.5%

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

   2. Taylor expanded in a around inf 56.2%

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

      1. associate-/l* 67.4%

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

   4. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{a}{\frac{y + \left(t + x\right)}{y + t}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+71}:\\ \;\;\;\;z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq -1250000000:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{-y}{\frac{y + \left(x + t\right)}{b}}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-130}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-203}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \end{array} \]

Alternative 11: 57.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1950000000:\\ \;\;\;\;\frac{x + y}{\frac{t_2}{z}}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{-y}{\frac{t_2}{b}}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-204}:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (- z (* y (- (/ b x) (/ a x))))))
   (if (<= x -2.5e+69)
     t_3
     (if (<= x -1950000000.0)
       (/ (+ x y) (/ t_2 z))
       (if (<= x -6.6e-59)
         (/ (- y) (/ t_2 b))
         (if (<= x -3.5e-130)
           t_1
           (if (<= x -2.2e-204)
             (/ a (/ t_2 (+ y t)))
             (if (<= x 4.8e+18) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = z - (y * ((b / x) - (a / x)));
	double tmp;
	if (x <= -2.5e+69) {
		tmp = t_3;
	} else if (x <= -1950000000.0) {
		tmp = (x + y) / (t_2 / z);
	} else if (x <= -6.6e-59) {
		tmp = -y / (t_2 / b);
	} else if (x <= -3.5e-130) {
		tmp = t_1;
	} else if (x <= -2.2e-204) {
		tmp = a / (t_2 / (y + t));
	} else if (x <= 4.8e+18) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = z - (y * ((b / x) - (a / x)))
    if (x <= (-2.5d+69)) then
        tmp = t_3
    else if (x <= (-1950000000.0d0)) then
        tmp = (x + y) / (t_2 / z)
    else if (x <= (-6.6d-59)) then
        tmp = -y / (t_2 / b)
    else if (x <= (-3.5d-130)) then
        tmp = t_1
    else if (x <= (-2.2d-204)) then
        tmp = a / (t_2 / (y + t))
    else if (x <= 4.8d+18) then
        tmp = t_1
    else
        tmp = t_3
    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 t_2 = y + (x + t);
	double t_3 = z - (y * ((b / x) - (a / x)));
	double tmp;
	if (x <= -2.5e+69) {
		tmp = t_3;
	} else if (x <= -1950000000.0) {
		tmp = (x + y) / (t_2 / z);
	} else if (x <= -6.6e-59) {
		tmp = -y / (t_2 / b);
	} else if (x <= -3.5e-130) {
		tmp = t_1;
	} else if (x <= -2.2e-204) {
		tmp = a / (t_2 / (y + t));
	} else if (x <= 4.8e+18) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = z - (y * ((b / x) - (a / x)))
	tmp = 0
	if x <= -2.5e+69:
		tmp = t_3
	elif x <= -1950000000.0:
		tmp = (x + y) / (t_2 / z)
	elif x <= -6.6e-59:
		tmp = -y / (t_2 / b)
	elif x <= -3.5e-130:
		tmp = t_1
	elif x <= -2.2e-204:
		tmp = a / (t_2 / (y + t))
	elif x <= 4.8e+18:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z - Float64(y * Float64(Float64(b / x) - Float64(a / x))))
	tmp = 0.0
	if (x <= -2.5e+69)
		tmp = t_3;
	elseif (x <= -1950000000.0)
		tmp = Float64(Float64(x + y) / Float64(t_2 / z));
	elseif (x <= -6.6e-59)
		tmp = Float64(Float64(-y) / Float64(t_2 / b));
	elseif (x <= -3.5e-130)
		tmp = t_1;
	elseif (x <= -2.2e-204)
		tmp = Float64(a / Float64(t_2 / Float64(y + t)));
	elseif (x <= 4.8e+18)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = z - (y * ((b / x) - (a / x)));
	tmp = 0.0;
	if (x <= -2.5e+69)
		tmp = t_3;
	elseif (x <= -1950000000.0)
		tmp = (x + y) / (t_2 / z);
	elseif (x <= -6.6e-59)
		tmp = -y / (t_2 / b);
	elseif (x <= -3.5e-130)
		tmp = t_1;
	elseif (x <= -2.2e-204)
		tmp = a / (t_2 / (y + t));
	elseif (x <= 4.8e+18)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z - N[(y * N[(N[(b / x), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+69], t$95$3, If[LessEqual[x, -1950000000.0], N[(N[(x + y), $MachinePrecision] / N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.6e-59], N[((-y) / N[(t$95$2 / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-130], t$95$1, If[LessEqual[x, -2.2e-204], N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+18], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.50000000000000018e69 or 4.8e18 < x

   1. Initial program 58.8%

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

   3. Simplified 59.0%

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

   4. Taylor expanded in x around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. associate-+r+ 51.8%

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

      3. associate-/l* 51.6%

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

      4. associate-/l* 54.7%

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

      5. +-commutative 54.7%

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

   6. Simplified 54.7%

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

   7. Taylor expanded in t around 0 48.2%

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

      1. associate--l+ 49.1%

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

      2. +-commutative 49.1%

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

      3. associate-+r- 49.1%

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

      4. associate-*l/ 51.3%

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

      5. associate-/l* 59.5%

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

   9. Simplified 59.5%

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

   10. Taylor expanded in y around 0 61.7%

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

   if -2.50000000000000018e69 < x < -1.95e9

   1. Initial program 62.0%

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

   2. Taylor expanded in z around inf 48.3%

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

      1. associate-/l* 61.3%

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

   4. Simplified 61.3%

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

   if -1.95e9 < x < -6.59999999999999964e-59

   1. Initial program 92.4%

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

   2. Taylor expanded in b around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-/l* 75.7%

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

      3. distribute-neg-frac 75.7%

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

   4. Simplified 75.7%

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

   if -6.59999999999999964e-59 < x < -3.4999999999999999e-130 or -2.1999999999999998e-204 < x < 4.8e18

   1. Initial program 67.3%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. +-commutative 65.8%

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

   4. Simplified 65.8%

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

   if -3.4999999999999999e-130 < x < -2.1999999999999998e-204

   1. Initial program 88.5%

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

   2. Taylor expanded in a around inf 56.2%

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

      1. associate-/l* 67.4%

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

   4. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{a}{\frac{y + \left(t + x\right)}{y + t}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq -1950000000:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{-y}{\frac{y + \left(x + t\right)}{b}}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-130}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-204}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \end{array} \]

Alternative 12: 58.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1250000:\\ \;\;\;\;\frac{x + y}{\frac{t_2}{z}}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{y \cdot t_1}{t_2}\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-204}:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (- z (* y (- (/ b x) (/ a x))))))
   (if (<= x -1.2e+69)
     t_3
     (if (<= x -1250000.0)
       (/ (+ x y) (/ t_2 z))
       (if (<= x -5.8e-63)
         (/ (* y t_1) t_2)
         (if (<= x -1.4e-128)
           t_1
           (if (<= x -4e-204)
             (/ a (/ t_2 (+ y t)))
             (if (<= x 4.5e+18) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = z - (y * ((b / x) - (a / x)));
	double tmp;
	if (x <= -1.2e+69) {
		tmp = t_3;
	} else if (x <= -1250000.0) {
		tmp = (x + y) / (t_2 / z);
	} else if (x <= -5.8e-63) {
		tmp = (y * t_1) / t_2;
	} else if (x <= -1.4e-128) {
		tmp = t_1;
	} else if (x <= -4e-204) {
		tmp = a / (t_2 / (y + t));
	} else if (x <= 4.5e+18) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = z - (y * ((b / x) - (a / x)))
    if (x <= (-1.2d+69)) then
        tmp = t_3
    else if (x <= (-1250000.0d0)) then
        tmp = (x + y) / (t_2 / z)
    else if (x <= (-5.8d-63)) then
        tmp = (y * t_1) / t_2
    else if (x <= (-1.4d-128)) then
        tmp = t_1
    else if (x <= (-4d-204)) then
        tmp = a / (t_2 / (y + t))
    else if (x <= 4.5d+18) then
        tmp = t_1
    else
        tmp = t_3
    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 t_2 = y + (x + t);
	double t_3 = z - (y * ((b / x) - (a / x)));
	double tmp;
	if (x <= -1.2e+69) {
		tmp = t_3;
	} else if (x <= -1250000.0) {
		tmp = (x + y) / (t_2 / z);
	} else if (x <= -5.8e-63) {
		tmp = (y * t_1) / t_2;
	} else if (x <= -1.4e-128) {
		tmp = t_1;
	} else if (x <= -4e-204) {
		tmp = a / (t_2 / (y + t));
	} else if (x <= 4.5e+18) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = z - (y * ((b / x) - (a / x)))
	tmp = 0
	if x <= -1.2e+69:
		tmp = t_3
	elif x <= -1250000.0:
		tmp = (x + y) / (t_2 / z)
	elif x <= -5.8e-63:
		tmp = (y * t_1) / t_2
	elif x <= -1.4e-128:
		tmp = t_1
	elif x <= -4e-204:
		tmp = a / (t_2 / (y + t))
	elif x <= 4.5e+18:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z - Float64(y * Float64(Float64(b / x) - Float64(a / x))))
	tmp = 0.0
	if (x <= -1.2e+69)
		tmp = t_3;
	elseif (x <= -1250000.0)
		tmp = Float64(Float64(x + y) / Float64(t_2 / z));
	elseif (x <= -5.8e-63)
		tmp = Float64(Float64(y * t_1) / t_2);
	elseif (x <= -1.4e-128)
		tmp = t_1;
	elseif (x <= -4e-204)
		tmp = Float64(a / Float64(t_2 / Float64(y + t)));
	elseif (x <= 4.5e+18)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = z - (y * ((b / x) - (a / x)));
	tmp = 0.0;
	if (x <= -1.2e+69)
		tmp = t_3;
	elseif (x <= -1250000.0)
		tmp = (x + y) / (t_2 / z);
	elseif (x <= -5.8e-63)
		tmp = (y * t_1) / t_2;
	elseif (x <= -1.4e-128)
		tmp = t_1;
	elseif (x <= -4e-204)
		tmp = a / (t_2 / (y + t));
	elseif (x <= 4.5e+18)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z - N[(y * N[(N[(b / x), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+69], t$95$3, If[LessEqual[x, -1250000.0], N[(N[(x + y), $MachinePrecision] / N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-63], N[(N[(y * t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[x, -1.4e-128], t$95$1, If[LessEqual[x, -4e-204], N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+18], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.2000000000000001e69 or 4.5e18 < x

   1. Initial program 58.8%

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

   3. Simplified 59.0%

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

   4. Taylor expanded in x around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. associate-+r+ 51.8%

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

      3. associate-/l* 51.6%

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

      4. associate-/l* 54.7%

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

      5. +-commutative 54.7%

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

   6. Simplified 54.7%

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

   7. Taylor expanded in t around 0 48.2%

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

      1. associate--l+ 49.1%

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

      2. +-commutative 49.1%

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

      3. associate-+r- 49.1%

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

      4. associate-*l/ 51.3%

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

      5. associate-/l* 59.5%

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

   9. Simplified 59.5%

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

   10. Taylor expanded in y around 0 61.7%

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

   if -1.2000000000000001e69 < x < -1.25e6

   1. Initial program 62.0%

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

   2. Taylor expanded in z around inf 48.3%

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

      1. associate-/l* 61.3%

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

   4. Simplified 61.3%

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

   if -1.25e6 < x < -5.7999999999999995e-63

   1. Initial program 93.3%

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

   2. Taylor expanded in y around inf 79.6%

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

      1. +-commutative 79.6%

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

   4. Simplified 79.6%

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

   if -5.7999999999999995e-63 < x < -1.3999999999999999e-128 or -4e-204 < x < 4.5e18

   1. Initial program 66.7%

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

   2. Taylor expanded in y around inf 66.0%

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

      1. +-commutative 66.0%

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

   4. Simplified 66.0%

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

   if -1.3999999999999999e-128 < x < -4e-204

   1. Initial program 88.5%

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

   2. Taylor expanded in a around inf 56.2%

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

      1. associate-/l* 67.4%

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

   4. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{a}{\frac{y + \left(t + x\right)}{y + t}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+69}:\\ \;\;\;\;z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq -1250000:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-128}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-204}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+18}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \left(\frac{b}{x} - \frac{a}{x}\right)\\ \end{array} \]

Alternative 13: 58.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+67} \lor \neg \left(z \leq 1550000000000\right):\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + y \cdot \left(a - b\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (or (<= z -4.7e+67) (not (<= z 1550000000000.0)))
     (* z (/ (+ x y) t_1))
     (/ (+ (* t a) (* y (- a b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((z <= -4.7e+67) || !(z <= 1550000000000.0)) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = ((t * a) + (y * (a - b))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if ((z <= (-4.7d+67)) .or. (.not. (z <= 1550000000000.0d0))) then
        tmp = z * ((x + y) / t_1)
    else
        tmp = ((t * a) + (y * (a - b))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((z <= -4.7e+67) || !(z <= 1550000000000.0)) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = ((t * a) + (y * (a - b))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (z <= -4.7e+67) or not (z <= 1550000000000.0):
		tmp = z * ((x + y) / t_1)
	else:
		tmp = ((t * a) + (y * (a - b))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((z <= -4.7e+67) || !(z <= 1550000000000.0))
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(y * Float64(a - b))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if ((z <= -4.7e+67) || ~((z <= 1550000000000.0)))
		tmp = z * ((x + y) / t_1);
	else
		tmp = ((t * a) + (y * (a - b))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -4.7e+67], N[Not[LessEqual[z, 1550000000000.0]], $MachinePrecision]], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.70000000000000017e67 or 1.55e12 < z

   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. Taylor expanded in z around inf 36.3%

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

      1. associate-/l* 62.2%

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

   4. Simplified 62.2%

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

      1. associate-/r/ 66.1%

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

   6. Applied egg-rr 66.1%

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

   if -4.70000000000000017e67 < z < 1.55e12

   1. Initial program 78.6%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in z around 0 64.1%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+67} \lor \neg \left(z \leq 1550000000000\right):\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + y \cdot \left(a - b\right)}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 14: 60.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z + \left(a - b\right) \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-202}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ z (* (- a b) (/ y x)))))
   (if (<= x -4.5e+80)
     t_2
     (if (<= x -3.5e-130)
       t_1
       (if (<= x -1.6e-202) a (if (<= x 4.8e+18) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + ((a - b) * (y / x));
	double tmp;
	if (x <= -4.5e+80) {
		tmp = t_2;
	} else if (x <= -3.5e-130) {
		tmp = t_1;
	} else if (x <= -1.6e-202) {
		tmp = a;
	} else if (x <= 4.8e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z + ((a - b) * (y / x))
    if (x <= (-4.5d+80)) then
        tmp = t_2
    else if (x <= (-3.5d-130)) then
        tmp = t_1
    else if (x <= (-1.6d-202)) then
        tmp = a
    else if (x <= 4.8d+18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + ((a - b) * (y / x));
	double tmp;
	if (x <= -4.5e+80) {
		tmp = t_2;
	} else if (x <= -3.5e-130) {
		tmp = t_1;
	} else if (x <= -1.6e-202) {
		tmp = a;
	} else if (x <= 4.8e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z + ((a - b) * (y / x))
	tmp = 0
	if x <= -4.5e+80:
		tmp = t_2
	elif x <= -3.5e-130:
		tmp = t_1
	elif x <= -1.6e-202:
		tmp = a
	elif x <= 4.8e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z + Float64(Float64(a - b) * Float64(y / x)))
	tmp = 0.0
	if (x <= -4.5e+80)
		tmp = t_2;
	elseif (x <= -3.5e-130)
		tmp = t_1;
	elseif (x <= -1.6e-202)
		tmp = a;
	elseif (x <= 4.8e+18)
		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 + a) - b;
	t_2 = z + ((a - b) * (y / x));
	tmp = 0.0;
	if (x <= -4.5e+80)
		tmp = t_2;
	elseif (x <= -3.5e-130)
		tmp = t_1;
	elseif (x <= -1.6e-202)
		tmp = a;
	elseif (x <= 4.8e+18)
		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[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(N[(a - b), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+80], t$95$2, If[LessEqual[x, -3.5e-130], t$95$1, If[LessEqual[x, -1.6e-202], a, If[LessEqual[x, 4.8e+18], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.50000000000000007e80 or 4.8e18 < x

   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. Step-by-step derivation

   3. Simplified 59.1%

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

   4. Taylor expanded in x around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. associate-+r+ 51.8%

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

      3. associate-/l* 51.5%

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

      4. associate-/l* 54.7%

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

      5. +-commutative 54.7%

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

   6. Simplified 54.7%

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

   7. Taylor expanded in t around 0 48.1%

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

      1. associate--l+ 49.0%

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

      2. +-commutative 49.0%

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

      3. associate-+r- 49.0%

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

      4. associate-*l/ 51.3%

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

      5. associate-/l* 59.7%

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

   9. Simplified 59.7%

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

   10. Taylor expanded in z around 0 55.1%

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

       1. associate-*l/ 59.7%

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

       2. *-commutative 59.7%

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

   12. Simplified 59.7%

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

   if -4.50000000000000007e80 < x < -3.4999999999999999e-130 or -1.6000000000000001e-202 < x < 4.8e18

   1. Initial program 68.7%

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

   2. Taylor expanded in y around inf 60.8%

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

      1. +-commutative 60.8%

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

   4. Simplified 60.8%

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

   if -3.4999999999999999e-130 < x < -1.6000000000000001e-202

   1. Initial program 88.5%

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

   2. Taylor expanded in t around inf 66.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+80}:\\ \;\;\;\;z + \left(a - b\right) \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-130}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-202}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + \left(a - b\right) \cdot \frac{y}{x}\\ \end{array} \]

Alternative 15: 56.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z + \frac{y \cdot a}{x}\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-202}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ z (/ (* y a) x))))
   (if (<= x -1.95e+173)
     t_2
     (if (<= x -5.6e-130)
       t_1
       (if (<= x -1.6e-202) a (if (<= x 4.8e+18) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + ((y * a) / x);
	double tmp;
	if (x <= -1.95e+173) {
		tmp = t_2;
	} else if (x <= -5.6e-130) {
		tmp = t_1;
	} else if (x <= -1.6e-202) {
		tmp = a;
	} else if (x <= 4.8e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z + ((y * a) / x)
    if (x <= (-1.95d+173)) then
        tmp = t_2
    else if (x <= (-5.6d-130)) then
        tmp = t_1
    else if (x <= (-1.6d-202)) then
        tmp = a
    else if (x <= 4.8d+18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + ((y * a) / x);
	double tmp;
	if (x <= -1.95e+173) {
		tmp = t_2;
	} else if (x <= -5.6e-130) {
		tmp = t_1;
	} else if (x <= -1.6e-202) {
		tmp = a;
	} else if (x <= 4.8e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z + ((y * a) / x)
	tmp = 0
	if x <= -1.95e+173:
		tmp = t_2
	elif x <= -5.6e-130:
		tmp = t_1
	elif x <= -1.6e-202:
		tmp = a
	elif x <= 4.8e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z + Float64(Float64(y * a) / x))
	tmp = 0.0
	if (x <= -1.95e+173)
		tmp = t_2;
	elseif (x <= -5.6e-130)
		tmp = t_1;
	elseif (x <= -1.6e-202)
		tmp = a;
	elseif (x <= 4.8e+18)
		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 + a) - b;
	t_2 = z + ((y * a) / x);
	tmp = 0.0;
	if (x <= -1.95e+173)
		tmp = t_2;
	elseif (x <= -5.6e-130)
		tmp = t_1;
	elseif (x <= -1.6e-202)
		tmp = a;
	elseif (x <= 4.8e+18)
		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[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.95e+173], t$95$2, If[LessEqual[x, -5.6e-130], t$95$1, If[LessEqual[x, -1.6e-202], a, If[LessEqual[x, 4.8e+18], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9499999999999999e173 or 4.8e18 < x

   1. Initial program 57.0%

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

   2. Taylor expanded in b around 0 43.7%

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

   3. Taylor expanded in t around 0 31.7%

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

   4. Taylor expanded in y around 0 48.7%

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

   if -1.9499999999999999e173 < x < -5.60000000000000032e-130 or -1.6000000000000001e-202 < x < 4.8e18

   1. Initial program 68.4%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. +-commutative 59.3%

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

   4. Simplified 59.3%

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

   if -5.60000000000000032e-130 < x < -1.6000000000000001e-202

   1. Initial program 88.5%

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

   2. Taylor expanded in t around inf 66.9%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+173}:\\ \;\;\;\;z + \frac{y \cdot a}{x}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-130}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-202}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + \frac{y \cdot a}{x}\\ \end{array} \]

Alternative 16: 56.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-203}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= x -1.22e-129)
     t_1
     (if (<= x -4.2e-203) a (if (<= x 4.1e+121) t_1 (* z (- 1.0 (/ t x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (x <= -1.22e-129) {
		tmp = t_1;
	} else if (x <= -4.2e-203) {
		tmp = a;
	} else if (x <= 4.1e+121) {
		tmp = t_1;
	} else {
		tmp = z * (1.0 - (t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (x <= (-1.22d-129)) then
        tmp = t_1
    else if (x <= (-4.2d-203)) then
        tmp = a
    else if (x <= 4.1d+121) then
        tmp = t_1
    else
        tmp = z * (1.0d0 - (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (x <= -1.22e-129) {
		tmp = t_1;
	} else if (x <= -4.2e-203) {
		tmp = a;
	} else if (x <= 4.1e+121) {
		tmp = t_1;
	} else {
		tmp = z * (1.0 - (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if x <= -1.22e-129:
		tmp = t_1
	elif x <= -4.2e-203:
		tmp = a
	elif x <= 4.1e+121:
		tmp = t_1
	else:
		tmp = z * (1.0 - (t / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (x <= -1.22e-129)
		tmp = t_1;
	elseif (x <= -4.2e-203)
		tmp = a;
	elseif (x <= 4.1e+121)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(1.0 - Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (x <= -1.22e-129)
		tmp = t_1;
	elseif (x <= -4.2e-203)
		tmp = a;
	elseif (x <= 4.1e+121)
		tmp = t_1;
	else
		tmp = z * (1.0 - (t / x));
	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[x, -1.22e-129], t$95$1, If[LessEqual[x, -4.2e-203], a, If[LessEqual[x, 4.1e+121], t$95$1, N[(z * N[(1.0 - N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.21999999999999999e-129 or -4.20000000000000004e-203 < x < 4.1e121

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. +-commutative 52.3%

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

   4. Simplified 52.3%

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

   if -1.21999999999999999e-129 < x < -4.20000000000000004e-203

   1. Initial program 88.5%

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

   2. Taylor expanded in t around inf 66.9%

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

   if 4.1e121 < x

   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. Step-by-step derivation

   3. Simplified 50.8%

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

   4. Taylor expanded in x around inf 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-+r+ 57.1%

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

      3. associate-/l* 59.7%

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

      4. associate-/l* 63.6%

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

      5. +-commutative 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in z around inf 55.5%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-129}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-203}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+121}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x}\right)\\ \end{array} \]

Alternative 17: 56.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+194} \lor \neg \left(b \leq 6.8 \cdot 10^{+162}\right):\\ \;\;\;\;\frac{-y}{\frac{y + t}{b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.4e+194) (not (<= b 6.8e+162)))
   (/ (- y) (/ (+ y t) b))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.4e+194) || !(b <= 6.8e+162)) {
		tmp = -y / ((y + t) / b);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.4d+194)) .or. (.not. (b <= 6.8d+162))) then
        tmp = -y / ((y + t) / b)
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.4e+194) || !(b <= 6.8e+162)) {
		tmp = -y / ((y + t) / b);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.4e+194) or not (b <= 6.8e+162):
		tmp = -y / ((y + t) / b)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.4e+194) || !(b <= 6.8e+162))
		tmp = Float64(Float64(-y) / Float64(Float64(y + t) / b));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.4e+194) || ~((b <= 6.8e+162)))
		tmp = -y / ((y + t) / b);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.4e+194], N[Not[LessEqual[b, 6.8e+162]], $MachinePrecision]], N[((-y) / N[(N[(y + t), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.40000000000000005e194 or 6.80000000000000006e162 < b

   1. Initial program 58.4%

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

   2. Taylor expanded in b around inf 40.5%

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

      1. mul-1-neg 40.5%

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

      2. associate-/l* 63.0%

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

      3. distribute-neg-frac 63.0%

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

   4. Simplified 63.0%

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

   5. Taylor expanded in x around 0 33.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot b}{y + t}} \]
   6. Step-by-step derivation

      1. mul-1-neg 33.5%

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

      2. associate-/l* 52.4%

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

      3. distribute-neg-frac 52.4%

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

   7. Simplified 52.4%

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

   if -1.40000000000000005e194 < b < 6.80000000000000006e162

   1. Initial program 68.5%

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

   2. Taylor expanded in y around inf 55.9%

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

      1. +-commutative 55.9%

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

   4. Simplified 55.9%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+194} \lor \neg \left(b \leq 6.8 \cdot 10^{+162}\right):\\ \;\;\;\;\frac{-y}{\frac{y + t}{b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 18: 56.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -7 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-204}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= x -7e-130) t_1 (if (<= x -2.5e-204) a (if (<= x 4.4e+121) t_1 z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (x <= -7e-130) {
		tmp = t_1;
	} else if (x <= -2.5e-204) {
		tmp = a;
	} else if (x <= 4.4e+121) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (x <= (-7d-130)) then
        tmp = t_1
    else if (x <= (-2.5d-204)) then
        tmp = a
    else if (x <= 4.4d+121) then
        tmp = t_1
    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 t_1 = (z + a) - b;
	double tmp;
	if (x <= -7e-130) {
		tmp = t_1;
	} else if (x <= -2.5e-204) {
		tmp = a;
	} else if (x <= 4.4e+121) {
		tmp = t_1;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if x <= -7e-130:
		tmp = t_1
	elif x <= -2.5e-204:
		tmp = a
	elif x <= 4.4e+121:
		tmp = t_1
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (x <= -7e-130)
		tmp = t_1;
	elseif (x <= -2.5e-204)
		tmp = a;
	elseif (x <= 4.4e+121)
		tmp = t_1;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (x <= -7e-130)
		tmp = t_1;
	elseif (x <= -2.5e-204)
		tmp = a;
	elseif (x <= 4.4e+121)
		tmp = t_1;
	else
		tmp = z;
	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[x, -7e-130], t$95$1, If[LessEqual[x, -2.5e-204], a, If[LessEqual[x, 4.4e+121], t$95$1, z]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.9999999999999998e-130 or -2.5000000000000001e-204 < x < 4.40000000000000003e121

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. +-commutative 52.3%

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

   4. Simplified 52.3%

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

   if -6.9999999999999998e-130 < x < -2.5000000000000001e-204

   1. Initial program 88.5%

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

   2. Taylor expanded in t around inf 66.9%

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

   if 4.40000000000000003e121 < x

   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. Taylor expanded in x around inf 55.4%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-130}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-204}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+121}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 19: 44.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+130}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+36}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.2e+130) a (if (<= t 2.6e+36) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+130) {
		tmp = a;
	} else if (t <= 2.6e+36) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.2d+130)) then
        tmp = a
    else if (t <= 2.6d+36) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+130) {
		tmp = a;
	} else if (t <= 2.6e+36) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.2e+130:
		tmp = a
	elif t <= 2.6e+36:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.2e+130)
		tmp = a;
	elseif (t <= 2.6e+36)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.2e+130)
		tmp = a;
	elseif (t <= 2.6e+36)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.2e+130], a, If[LessEqual[t, 2.6e+36], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -7.2000000000000002e130 or 2.6000000000000001e36 < t

   1. Initial program 57.1%

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

   2. Taylor expanded in t around inf 44.1%

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

   if -7.2000000000000002e130 < t < 2.6000000000000001e36

   1. Initial program 71.4%

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

   2. Taylor expanded in x around inf 44.5%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+130}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+36}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 20: 52.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{+161}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x 1e+161) (+ z a) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1e+161) {
		tmp = z + 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 <= 1d+161) then
        tmp = z + 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 <= 1e+161) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1e+161:
		tmp = z + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1e+161)
		tmp = Float64(z + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1e+161)
		tmp = z + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1e+161], N[(z + a), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < 1e161

   1. Initial program 68.8%

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

   2. Taylor expanded in b around 0 48.8%

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

   3. Taylor expanded in y around inf 44.8%

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

      1. +-commutative 44.8%

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

   5. Simplified 44.8%

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

   if 1e161 < x

   1. Initial program 47.4%

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

   2. Taylor expanded in x around inf 61.8%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+161}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 21: 32.7% 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 66.1%

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

2. Taylor expanded in t around inf 27.6%

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

3. Final simplification 27.6%

   \[\leadsto a \]

Developer target: 82.4% 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 2023257 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1.0 (/ (+ (+ 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)))