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

Percentage Accurate: 61.2% → 84.6%

Time: 14.6s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.2% 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: 84.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z - b\right)\\ t_2 := t + \left(y + x\right)\\ t_3 := \frac{y}{t_2}\\ t_4 := \left(a \cdot \left(t_3 + \frac{t}{t_2}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t_2}\\ t_5 := t_3 \cdot t_1\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+120}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-108}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-129}:\\ \;\;\;\;\frac{1}{\frac{x + \left(y + t\right)}{\mathsf{fma}\left(a, t, \mathsf{fma}\left(y, t_1, x \cdot z\right)\right)}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+110}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- z b)))
        (t_2 (+ t (+ y x)))
        (t_3 (/ y t_2))
        (t_4
         (- (+ (* a (+ t_3 (/ t t_2))) (/ x (/ (+ t x) z))) (/ (* y b) t_2)))
        (t_5 (* t_3 t_1)))
   (if (<= y -2.1e+120)
     t_5
     (if (<= y -1.12e-108)
       t_4
       (if (<= y -2.4e-129)
         (/ 1.0 (/ (+ x (+ y t)) (fma a t (fma y t_1 (* x z)))))
         (if (<= y 5.5e+110) t_4 t_5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double t_2 = t + (y + x);
	double t_3 = y / t_2;
	double t_4 = ((a * (t_3 + (t / t_2))) + (x / ((t + x) / z))) - ((y * b) / t_2);
	double t_5 = t_3 * t_1;
	double tmp;
	if (y <= -2.1e+120) {
		tmp = t_5;
	} else if (y <= -1.12e-108) {
		tmp = t_4;
	} else if (y <= -2.4e-129) {
		tmp = 1.0 / ((x + (y + t)) / fma(a, t, fma(y, t_1, (x * z))));
	} else if (y <= 5.5e+110) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z - b))
	t_2 = Float64(t + Float64(y + x))
	t_3 = Float64(y / t_2)
	t_4 = Float64(Float64(Float64(a * Float64(t_3 + Float64(t / t_2))) + Float64(x / Float64(Float64(t + x) / z))) - Float64(Float64(y * b) / t_2))
	t_5 = Float64(t_3 * t_1)
	tmp = 0.0
	if (y <= -2.1e+120)
		tmp = t_5;
	elseif (y <= -1.12e-108)
		tmp = t_4;
	elseif (y <= -2.4e-129)
		tmp = Float64(1.0 / Float64(Float64(x + Float64(y + t)) / fma(a, t, fma(y, t_1, Float64(x * z)))));
	elseif (y <= 5.5e+110)
		tmp = t_4;
	else
		tmp = t_5;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(a * N[(t$95$3 + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(N[(t + x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 * t$95$1), $MachinePrecision]}, If[LessEqual[y, -2.1e+120], t$95$5, If[LessEqual[y, -1.12e-108], t$95$4, If[LessEqual[y, -2.4e-129], N[(1.0 / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(a * t + N[(y * t$95$1 + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+110], t$95$4, t$95$5]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1e120 or 5.49999999999999996e110 < y

   1. Initial program 36.7%

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

   2. Taylor expanded in y around inf 35.7%

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

      1. *-un-lft-identity 35.7%

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

      2. associate-/l* 85.2%

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

      3. associate-+l+ 85.2%

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

      4. +-commutative 85.2%

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

      5. associate--l+ 85.2%

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

   4. Applied egg-rr 85.2%

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

      1. *-lft-identity 85.2%

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

      2. associate-+r- 85.2%

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

      3. associate-/r/ 93.9%

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

      4. associate-+r+ 93.9%

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

      5. +-commutative 93.9%

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

      6. +-commutative 93.9%

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

      7. associate-+r- 93.9%

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

   6. Simplified 93.9%

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

   if -2.1e120 < y < -1.11999999999999992e-108 or -2.39999999999999989e-129 < y < 5.49999999999999996e110

   1. Initial program 69.0%

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

   2. Taylor expanded in a around 0 83.1%

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

   3. Taylor expanded in y around 0 82.0%

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

      1. associate-/l* 91.2%

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

   5. Simplified 91.2%

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

   if -1.11999999999999992e-108 < y < -2.39999999999999989e-129

   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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-udef 99.8%

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

      7. inv-pow 99.8%

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

   3. Applied egg-rr 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-108}:\\ \;\;\;\;\left(a \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{t}{t + \left(y + x\right)}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-129}:\\ \;\;\;\;\frac{1}{\frac{x + \left(y + t\right)}{\mathsf{fma}\left(a, t, \mathsf{fma}\left(y, a + \left(z - b\right), x \cdot z\right)\right)}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+110}:\\ \;\;\;\;\left(a \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{t}{t + \left(y + x\right)}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]

Alternative 2: 84.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \frac{y}{t_1}\\ t_3 := \left(a \cdot \left(t_2 + \frac{t}{t_1}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t_1}\\ t_4 := t_2 \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+121}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-128}:\\ \;\;\;\;\mathsf{fma}\left(a, y + t, \left(y + x\right) \cdot z - y \cdot b\right) \cdot \frac{1}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x)))
        (t_2 (/ y t_1))
        (t_3
         (- (+ (* a (+ t_2 (/ t t_1))) (/ x (/ (+ t x) z))) (/ (* y b) t_1)))
        (t_4 (* t_2 (+ a (- z b)))))
   (if (<= y -8.5e+121)
     t_4
     (if (<= y -2.3e-108)
       t_3
       (if (<= y -1.16e-128)
         (* (fma a (+ y t) (- (* (+ y x) z) (* y b))) (/ 1.0 (+ x (+ y t))))
         (if (<= y 3.5e+107) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = y / t_1;
	double t_3 = ((a * (t_2 + (t / t_1))) + (x / ((t + x) / z))) - ((y * b) / t_1);
	double t_4 = t_2 * (a + (z - b));
	double tmp;
	if (y <= -8.5e+121) {
		tmp = t_4;
	} else if (y <= -2.3e-108) {
		tmp = t_3;
	} else if (y <= -1.16e-128) {
		tmp = fma(a, (y + t), (((y + x) * z) - (y * b))) * (1.0 / (x + (y + t)));
	} else if (y <= 3.5e+107) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(y / t_1)
	t_3 = Float64(Float64(Float64(a * Float64(t_2 + Float64(t / t_1))) + Float64(x / Float64(Float64(t + x) / z))) - Float64(Float64(y * b) / t_1))
	t_4 = Float64(t_2 * Float64(a + Float64(z - b)))
	tmp = 0.0
	if (y <= -8.5e+121)
		tmp = t_4;
	elseif (y <= -2.3e-108)
		tmp = t_3;
	elseif (y <= -1.16e-128)
		tmp = Float64(fma(a, Float64(y + t), Float64(Float64(Float64(y + x) * z) - Float64(y * b))) * Float64(1.0 / Float64(x + Float64(y + t))));
	elseif (y <= 3.5e+107)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(a * N[(t$95$2 + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(N[(t + x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+121], t$95$4, If[LessEqual[y, -2.3e-108], t$95$3, If[LessEqual[y, -1.16e-128], N[(N[(a * N[(y + t), $MachinePrecision] + N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+107], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5e121 or 3.4999999999999997e107 < y

   1. Initial program 36.7%

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

   2. Taylor expanded in y around inf 35.7%

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

      1. *-un-lft-identity 35.7%

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

      2. associate-/l* 85.2%

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

      3. associate-+l+ 85.2%

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

      4. +-commutative 85.2%

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

      5. associate--l+ 85.2%

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

   4. Applied egg-rr 85.2%

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

      1. *-lft-identity 85.2%

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

      2. associate-+r- 85.2%

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

      3. associate-/r/ 93.9%

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

      4. associate-+r+ 93.9%

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

      5. +-commutative 93.9%

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

      6. +-commutative 93.9%

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

      7. associate-+r- 93.9%

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

   6. Simplified 93.9%

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

   if -8.5e121 < y < -2.29999999999999996e-108 or -1.16000000000000007e-128 < y < 3.4999999999999997e107

   1. Initial program 69.0%

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

   2. Taylor expanded in a around 0 83.1%

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

   3. Taylor expanded in y around 0 82.0%

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

      1. associate-/l* 91.2%

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

   5. Simplified 91.2%

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

   if -2.29999999999999996e-108 < y < -1.16000000000000007e-128

   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. Step-by-step derivation

      1. +-commutative 99.5%

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

      2. associate--l+ 99.5%

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

      3. fma-def 99.5%

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

      4. +-commutative 99.5%

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

      5. +-commutative 99.5%

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

   3. Simplified 99.5%

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

      1. div-inv 99.7%

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

      2. fma-udef 99.7%

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

      3. *-commutative 99.7%

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

      4. fma-def 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-+l+ 99.7%

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

      7. +-commutative 99.7%

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

   5. Applied egg-rr 99.7%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-108}:\\ \;\;\;\;\left(a \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{t}{t + \left(y + x\right)}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-128}:\\ \;\;\;\;\mathsf{fma}\left(a, y + t, \left(y + x\right) \cdot z - y \cdot b\right) \cdot \frac{1}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+107}:\\ \;\;\;\;\left(a \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{t}{t + \left(y + x\right)}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]

Alternative 3: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(a + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+264}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y x) z) (* a (+ y t))) (* y b)) (+ y (+ t x)))))
   (if (<= t_1 (- INFINITY))
     (- (+ a (/ x (/ (+ t x) z))) (/ (* y b) (+ t (+ y x))))
     (if (<= t_1 5e+264) t_1 (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / (y + (t + x));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (a + (x / ((t + x) / z))) - ((y * b) / (t + (y + x)));
	} else if (t_1 <= 5e+264) {
		tmp = t_1;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / (y + (t + x));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (a + (x / ((t + x) / z))) - ((y * b) / (t + (y + x)));
	} else if (t_1 <= 5e+264) {
		tmp = t_1;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / (y + (t + x))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (a + (x / ((t + x) / z))) - ((y * b) / (t + (y + x)))
	elif t_1 <= 5e+264:
		tmp = t_1
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + x) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(t + x)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(a + Float64(x / Float64(Float64(t + x) / z))) - Float64(Float64(y * b) / Float64(t + Float64(y + x))));
	elseif (t_1 <= 5e+264)
		tmp = t_1;
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / (y + (t + x));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (a + (x / ((t + x) / z))) - ((y * b) / (t + (y + x)));
	elseif (t_1 <= 5e+264)
		tmp = t_1;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(a + N[(x / N[(N[(t + x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+264], t$95$1, N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 5.3%

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

   2. Taylor expanded in a around 0 49.0%

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

   3. Taylor expanded in y around 0 51.0%

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

      1. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in t around inf 63.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000033e264

   1. Initial program 98.7%

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

   if 5.00000000000000033e264 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.0%

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

   2. Taylor expanded in y around inf 70.3%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq -\infty:\\ \;\;\;\;\left(a + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{elif}\;\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 4: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \frac{y \cdot b}{t_1}\\ t_3 := \frac{y}{t_1}\\ t_4 := \left(a \cdot \left(t_3 + \frac{t}{t_1}\right) + \frac{x}{\frac{t + x}{z}}\right) - t_2\\ t_5 := t_3 \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+121}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-106}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-129}:\\ \;\;\;\;\left(z \cdot \left(t_3 + \frac{x}{t_1}\right) + \frac{a \cdot \left(y + t\right)}{t_1}\right) - t_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x)))
        (t_2 (/ (* y b) t_1))
        (t_3 (/ y t_1))
        (t_4 (- (+ (* a (+ t_3 (/ t t_1))) (/ x (/ (+ t x) z))) t_2))
        (t_5 (* t_3 (+ a (- z b)))))
   (if (<= y -8.2e+121)
     t_5
     (if (<= y -7e-106)
       t_4
       (if (<= y -2e-129)
         (- (+ (* z (+ t_3 (/ x t_1))) (/ (* a (+ y t)) t_1)) t_2)
         (if (<= y 1.15e+111) t_4 t_5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (y * b) / t_1;
	double t_3 = y / t_1;
	double t_4 = ((a * (t_3 + (t / t_1))) + (x / ((t + x) / z))) - t_2;
	double t_5 = t_3 * (a + (z - b));
	double tmp;
	if (y <= -8.2e+121) {
		tmp = t_5;
	} else if (y <= -7e-106) {
		tmp = t_4;
	} else if (y <= -2e-129) {
		tmp = ((z * (t_3 + (x / t_1))) + ((a * (y + t)) / t_1)) - t_2;
	} else if (y <= 1.15e+111) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	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) :: t_5
    real(8) :: tmp
    t_1 = t + (y + x)
    t_2 = (y * b) / t_1
    t_3 = y / t_1
    t_4 = ((a * (t_3 + (t / t_1))) + (x / ((t + x) / z))) - t_2
    t_5 = t_3 * (a + (z - b))
    if (y <= (-8.2d+121)) then
        tmp = t_5
    else if (y <= (-7d-106)) then
        tmp = t_4
    else if (y <= (-2d-129)) then
        tmp = ((z * (t_3 + (x / t_1))) + ((a * (y + t)) / t_1)) - t_2
    else if (y <= 1.15d+111) then
        tmp = t_4
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (y * b) / t_1;
	double t_3 = y / t_1;
	double t_4 = ((a * (t_3 + (t / t_1))) + (x / ((t + x) / z))) - t_2;
	double t_5 = t_3 * (a + (z - b));
	double tmp;
	if (y <= -8.2e+121) {
		tmp = t_5;
	} else if (y <= -7e-106) {
		tmp = t_4;
	} else if (y <= -2e-129) {
		tmp = ((z * (t_3 + (x / t_1))) + ((a * (y + t)) / t_1)) - t_2;
	} else if (y <= 1.15e+111) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	t_2 = (y * b) / t_1
	t_3 = y / t_1
	t_4 = ((a * (t_3 + (t / t_1))) + (x / ((t + x) / z))) - t_2
	t_5 = t_3 * (a + (z - b))
	tmp = 0
	if y <= -8.2e+121:
		tmp = t_5
	elif y <= -7e-106:
		tmp = t_4
	elif y <= -2e-129:
		tmp = ((z * (t_3 + (x / t_1))) + ((a * (y + t)) / t_1)) - t_2
	elif y <= 1.15e+111:
		tmp = t_4
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(Float64(y * b) / t_1)
	t_3 = Float64(y / t_1)
	t_4 = Float64(Float64(Float64(a * Float64(t_3 + Float64(t / t_1))) + Float64(x / Float64(Float64(t + x) / z))) - t_2)
	t_5 = Float64(t_3 * Float64(a + Float64(z - b)))
	tmp = 0.0
	if (y <= -8.2e+121)
		tmp = t_5;
	elseif (y <= -7e-106)
		tmp = t_4;
	elseif (y <= -2e-129)
		tmp = Float64(Float64(Float64(z * Float64(t_3 + Float64(x / t_1))) + Float64(Float64(a * Float64(y + t)) / t_1)) - t_2);
	elseif (y <= 1.15e+111)
		tmp = t_4;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	t_2 = (y * b) / t_1;
	t_3 = y / t_1;
	t_4 = ((a * (t_3 + (t / t_1))) + (x / ((t + x) / z))) - t_2;
	t_5 = t_3 * (a + (z - b));
	tmp = 0.0;
	if (y <= -8.2e+121)
		tmp = t_5;
	elseif (y <= -7e-106)
		tmp = t_4;
	elseif (y <= -2e-129)
		tmp = ((z * (t_3 + (x / t_1))) + ((a * (y + t)) / t_1)) - t_2;
	elseif (y <= 1.15e+111)
		tmp = t_4;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(a * N[(t$95$3 + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(N[(t + x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+121], t$95$5, If[LessEqual[y, -7e-106], t$95$4, If[LessEqual[y, -2e-129], N[(N[(N[(z * N[(t$95$3 + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[y, 1.15e+111], t$95$4, t$95$5]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.2e121 or 1.15000000000000001e111 < y

   1. Initial program 36.7%

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

   2. Taylor expanded in y around inf 35.7%

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

      1. *-un-lft-identity 35.7%

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

      2. associate-/l* 85.2%

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

      3. associate-+l+ 85.2%

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

      4. +-commutative 85.2%

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

      5. associate--l+ 85.2%

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

   4. Applied egg-rr 85.2%

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

      1. *-lft-identity 85.2%

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

      2. associate-+r- 85.2%

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

      3. associate-/r/ 93.9%

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

      4. associate-+r+ 93.9%

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

      5. +-commutative 93.9%

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

      6. +-commutative 93.9%

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

      7. associate-+r- 93.9%

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

   6. Simplified 93.9%

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

   if -8.2e121 < y < -7e-106 or -1.9999999999999999e-129 < y < 1.15000000000000001e111

   1. Initial program 69.4%

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

   2. Taylor expanded in a around 0 83.5%

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

   3. Taylor expanded in y around 0 82.4%

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

      1. associate-/l* 91.2%

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

   5. Simplified 91.2%

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

   if -7e-106 < y < -1.9999999999999999e-129

   1. Initial program 90.0%

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

   2. Taylor expanded in z around 0 99.5%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+121}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-106}:\\ \;\;\;\;\left(a \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{t}{t + \left(y + x\right)}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-129}:\\ \;\;\;\;\left(z \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{x}{t + \left(y + x\right)}\right) + \frac{a \cdot \left(y + t\right)}{t + \left(y + x\right)}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;\left(a \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{t}{t + \left(y + x\right)}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]

Alternative 5: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \frac{y}{t_1}\\ t_3 := \left(a \cdot \left(t_2 + \frac{t}{t_1}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t_1}\\ t_4 := t_2 \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+122}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-129}:\\ \;\;\;\;\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+111}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x)))
        (t_2 (/ y t_1))
        (t_3
         (- (+ (* a (+ t_2 (/ t t_1))) (/ x (/ (+ t x) z))) (/ (* y b) t_1)))
        (t_4 (* t_2 (+ a (- z b)))))
   (if (<= y -5.8e+122)
     t_4
     (if (<= y -4.3e-109)
       t_3
       (if (<= y -2.45e-129)
         (/ (- (+ (* (+ y x) z) (* a (+ y t))) (* y b)) (+ y (+ t x)))
         (if (<= y 2.2e+111) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = y / t_1;
	double t_3 = ((a * (t_2 + (t / t_1))) + (x / ((t + x) / z))) - ((y * b) / t_1);
	double t_4 = t_2 * (a + (z - b));
	double tmp;
	if (y <= -5.8e+122) {
		tmp = t_4;
	} else if (y <= -4.3e-109) {
		tmp = t_3;
	} else if (y <= -2.45e-129) {
		tmp = ((((y + x) * z) + (a * (y + t))) - (y * b)) / (y + (t + x));
	} else if (y <= 2.2e+111) {
		tmp = t_3;
	} 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 = t + (y + x)
    t_2 = y / t_1
    t_3 = ((a * (t_2 + (t / t_1))) + (x / ((t + x) / z))) - ((y * b) / t_1)
    t_4 = t_2 * (a + (z - b))
    if (y <= (-5.8d+122)) then
        tmp = t_4
    else if (y <= (-4.3d-109)) then
        tmp = t_3
    else if (y <= (-2.45d-129)) then
        tmp = ((((y + x) * z) + (a * (y + t))) - (y * b)) / (y + (t + x))
    else if (y <= 2.2d+111) then
        tmp = t_3
    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 = t + (y + x);
	double t_2 = y / t_1;
	double t_3 = ((a * (t_2 + (t / t_1))) + (x / ((t + x) / z))) - ((y * b) / t_1);
	double t_4 = t_2 * (a + (z - b));
	double tmp;
	if (y <= -5.8e+122) {
		tmp = t_4;
	} else if (y <= -4.3e-109) {
		tmp = t_3;
	} else if (y <= -2.45e-129) {
		tmp = ((((y + x) * z) + (a * (y + t))) - (y * b)) / (y + (t + x));
	} else if (y <= 2.2e+111) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	t_2 = y / t_1
	t_3 = ((a * (t_2 + (t / t_1))) + (x / ((t + x) / z))) - ((y * b) / t_1)
	t_4 = t_2 * (a + (z - b))
	tmp = 0
	if y <= -5.8e+122:
		tmp = t_4
	elif y <= -4.3e-109:
		tmp = t_3
	elif y <= -2.45e-129:
		tmp = ((((y + x) * z) + (a * (y + t))) - (y * b)) / (y + (t + x))
	elif y <= 2.2e+111:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(y / t_1)
	t_3 = Float64(Float64(Float64(a * Float64(t_2 + Float64(t / t_1))) + Float64(x / Float64(Float64(t + x) / z))) - Float64(Float64(y * b) / t_1))
	t_4 = Float64(t_2 * Float64(a + Float64(z - b)))
	tmp = 0.0
	if (y <= -5.8e+122)
		tmp = t_4;
	elseif (y <= -4.3e-109)
		tmp = t_3;
	elseif (y <= -2.45e-129)
		tmp = Float64(Float64(Float64(Float64(Float64(y + x) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(t + x)));
	elseif (y <= 2.2e+111)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	t_2 = y / t_1;
	t_3 = ((a * (t_2 + (t / t_1))) + (x / ((t + x) / z))) - ((y * b) / t_1);
	t_4 = t_2 * (a + (z - b));
	tmp = 0.0;
	if (y <= -5.8e+122)
		tmp = t_4;
	elseif (y <= -4.3e-109)
		tmp = t_3;
	elseif (y <= -2.45e-129)
		tmp = ((((y + x) * z) + (a * (y + t))) - (y * b)) / (y + (t + x));
	elseif (y <= 2.2e+111)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(a * N[(t$95$2 + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(N[(t + x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+122], t$95$4, If[LessEqual[y, -4.3e-109], t$95$3, If[LessEqual[y, -2.45e-129], N[(N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+111], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000002e122 or 2.19999999999999999e111 < y

   1. Initial program 36.7%

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

   2. Taylor expanded in y around inf 35.7%

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

      1. *-un-lft-identity 35.7%

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

      2. associate-/l* 85.2%

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

      3. associate-+l+ 85.2%

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

      4. +-commutative 85.2%

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

      5. associate--l+ 85.2%

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

   4. Applied egg-rr 85.2%

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

      1. *-lft-identity 85.2%

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

      2. associate-+r- 85.2%

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

      3. associate-/r/ 93.9%

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

      4. associate-+r+ 93.9%

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

      5. +-commutative 93.9%

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

      6. +-commutative 93.9%

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

      7. associate-+r- 93.9%

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

   6. Simplified 93.9%

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

   if -5.8000000000000002e122 < y < -4.2999999999999997e-109 or -2.45000000000000001e-129 < y < 2.19999999999999999e111

   1. Initial program 69.0%

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

   2. Taylor expanded in a around 0 83.1%

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

   3. Taylor expanded in y around 0 82.0%

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

      1. associate-/l* 91.2%

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

   5. Simplified 91.2%

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

   if -4.2999999999999997e-109 < y < -2.45000000000000001e-129

   1. Initial program 99.5%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-109}:\\ \;\;\;\;\left(a \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{t}{t + \left(y + x\right)}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-129}:\\ \;\;\;\;\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+111}:\\ \;\;\;\;\left(a \cdot \left(\frac{y}{t + \left(y + x\right)} + \frac{t}{t + \left(y + x\right)}\right) + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]

Alternative 6: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot a + x \cdot z}{t + x}\\ t_2 := \frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-158}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + y \cdot z\right) - y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-218}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{y + x}}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-66}:\\ \;\;\;\;\frac{y \cdot \left(\left(a + z\right) - b\right)}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* t a) (* x z)) (+ t x)))
        (t_2 (* (/ y (+ t (+ y x))) (+ a (- z b)))))
   (if (<= y -2.65e+36)
     t_2
     (if (<= y -9e-158)
       (/ (- (+ (* a (+ y t)) (* y z)) (* y b)) (+ y t))
       (if (<= y -3.4e-218)
         (/ z (/ (+ x (+ y t)) (+ y x)))
         (if (<= y 1.22e-144)
           t_1
           (if (<= y 1.12e-66)
             (/ (* y (- (+ a z) b)) (+ y (+ t x)))
             (if (<= y 1.35e+44) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x * z)) / (t + x);
	double t_2 = (y / (t + (y + x))) * (a + (z - b));
	double tmp;
	if (y <= -2.65e+36) {
		tmp = t_2;
	} else if (y <= -9e-158) {
		tmp = (((a * (y + t)) + (y * z)) - (y * b)) / (y + t);
	} else if (y <= -3.4e-218) {
		tmp = z / ((x + (y + t)) / (y + x));
	} else if (y <= 1.22e-144) {
		tmp = t_1;
	} else if (y <= 1.12e-66) {
		tmp = (y * ((a + z) - b)) / (y + (t + x));
	} else if (y <= 1.35e+44) {
		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 = ((t * a) + (x * z)) / (t + x)
    t_2 = (y / (t + (y + x))) * (a + (z - b))
    if (y <= (-2.65d+36)) then
        tmp = t_2
    else if (y <= (-9d-158)) then
        tmp = (((a * (y + t)) + (y * z)) - (y * b)) / (y + t)
    else if (y <= (-3.4d-218)) then
        tmp = z / ((x + (y + t)) / (y + x))
    else if (y <= 1.22d-144) then
        tmp = t_1
    else if (y <= 1.12d-66) then
        tmp = (y * ((a + z) - b)) / (y + (t + x))
    else if (y <= 1.35d+44) 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 = ((t * a) + (x * z)) / (t + x);
	double t_2 = (y / (t + (y + x))) * (a + (z - b));
	double tmp;
	if (y <= -2.65e+36) {
		tmp = t_2;
	} else if (y <= -9e-158) {
		tmp = (((a * (y + t)) + (y * z)) - (y * b)) / (y + t);
	} else if (y <= -3.4e-218) {
		tmp = z / ((x + (y + t)) / (y + x));
	} else if (y <= 1.22e-144) {
		tmp = t_1;
	} else if (y <= 1.12e-66) {
		tmp = (y * ((a + z) - b)) / (y + (t + x));
	} else if (y <= 1.35e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t * a) + (x * z)) / (t + x)
	t_2 = (y / (t + (y + x))) * (a + (z - b))
	tmp = 0
	if y <= -2.65e+36:
		tmp = t_2
	elif y <= -9e-158:
		tmp = (((a * (y + t)) + (y * z)) - (y * b)) / (y + t)
	elif y <= -3.4e-218:
		tmp = z / ((x + (y + t)) / (y + x))
	elif y <= 1.22e-144:
		tmp = t_1
	elif y <= 1.12e-66:
		tmp = (y * ((a + z) - b)) / (y + (t + x))
	elif y <= 1.35e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(t + x))
	t_2 = Float64(Float64(y / Float64(t + Float64(y + x))) * Float64(a + Float64(z - b)))
	tmp = 0.0
	if (y <= -2.65e+36)
		tmp = t_2;
	elseif (y <= -9e-158)
		tmp = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(y * z)) - Float64(y * b)) / Float64(y + t));
	elseif (y <= -3.4e-218)
		tmp = Float64(z / Float64(Float64(x + Float64(y + t)) / Float64(y + x)));
	elseif (y <= 1.22e-144)
		tmp = t_1;
	elseif (y <= 1.12e-66)
		tmp = Float64(Float64(y * Float64(Float64(a + z) - b)) / Float64(y + Float64(t + x)));
	elseif (y <= 1.35e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t * a) + (x * z)) / (t + x);
	t_2 = (y / (t + (y + x))) * (a + (z - b));
	tmp = 0.0;
	if (y <= -2.65e+36)
		tmp = t_2;
	elseif (y <= -9e-158)
		tmp = (((a * (y + t)) + (y * z)) - (y * b)) / (y + t);
	elseif (y <= -3.4e-218)
		tmp = z / ((x + (y + t)) / (y + x));
	elseif (y <= 1.22e-144)
		tmp = t_1;
	elseif (y <= 1.12e-66)
		tmp = (y * ((a + z) - b)) / (y + (t + x));
	elseif (y <= 1.35e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.65e+36], t$95$2, If[LessEqual[y, -9e-158], N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e-218], N[(z / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e-144], t$95$1, If[LessEqual[y, 1.12e-66], N[(N[(y * N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+44], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.65e36 or 1.35e44 < y

   1. Initial program 39.3%

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

   2. Taylor expanded in y around inf 35.1%

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

      1. *-un-lft-identity 35.1%

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

      2. associate-/l* 77.3%

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

      3. associate-+l+ 77.3%

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

      4. +-commutative 77.3%

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

      5. associate--l+ 77.3%

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

   4. Applied egg-rr 77.3%

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

      1. *-lft-identity 77.3%

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

      2. associate-+r- 77.3%

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

      3. associate-/r/ 84.6%

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

      4. associate-+r+ 84.6%

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

      5. +-commutative 84.6%

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

      6. +-commutative 84.6%

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

      7. associate-+r- 84.6%

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

   6. Simplified 84.6%

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

   if -2.65e36 < y < -9e-158

   1. Initial program 78.8%

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

   2. Taylor expanded in x around 0 59.6%

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

   if -9e-158 < y < -3.39999999999999986e-218

   1. Initial program 65.8%

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

   2. Taylor expanded in z around inf 51.7%

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

      1. associate-/l* 79.0%

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

      2. +-commutative 79.0%

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

      3. associate-+r+ 79.0%

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

      4. +-commutative 79.0%

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

   4. Simplified 79.0%

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

   if -3.39999999999999986e-218 < y < 1.22e-144 or 1.12000000000000004e-66 < y < 1.35e44

   1. Initial program 73.0%

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

   2. Taylor expanded in y around 0 60.5%

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

   if 1.22e-144 < y < 1.12000000000000004e-66

   1. Initial program 77.4%

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

   2. Taylor expanded in y around inf 59.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-158}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + y \cdot z\right) - y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-218}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{y + x}}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-144}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-66}:\\ \;\;\;\;\frac{y \cdot \left(\left(a + z\right) - b\right)}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+44}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]

Alternative 7: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+115} \lor \neg \left(y \leq 1.45 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{y}{t_1} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x))))
   (if (or (<= y -2.8e+115) (not (<= y 1.45e+75)))
     (* (/ y t_1) (+ a (- z b)))
     (- (+ a (/ x (/ (+ t x) z))) (/ (* y b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double tmp;
	if ((y <= -2.8e+115) || !(y <= 1.45e+75)) {
		tmp = (y / t_1) * (a + (z - b));
	} else {
		tmp = (a + (x / ((t + x) / z))) - ((y * 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 = t + (y + x)
    if ((y <= (-2.8d+115)) .or. (.not. (y <= 1.45d+75))) then
        tmp = (y / t_1) * (a + (z - b))
    else
        tmp = (a + (x / ((t + x) / z))) - ((y * 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 = t + (y + x);
	double tmp;
	if ((y <= -2.8e+115) || !(y <= 1.45e+75)) {
		tmp = (y / t_1) * (a + (z - b));
	} else {
		tmp = (a + (x / ((t + x) / z))) - ((y * b) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	tmp = 0
	if (y <= -2.8e+115) or not (y <= 1.45e+75):
		tmp = (y / t_1) * (a + (z - b))
	else:
		tmp = (a + (x / ((t + x) / z))) - ((y * b) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	tmp = 0.0
	if ((y <= -2.8e+115) || !(y <= 1.45e+75))
		tmp = Float64(Float64(y / t_1) * Float64(a + Float64(z - b)));
	else
		tmp = Float64(Float64(a + Float64(x / Float64(Float64(t + x) / z))) - Float64(Float64(y * b) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	tmp = 0.0;
	if ((y <= -2.8e+115) || ~((y <= 1.45e+75)))
		tmp = (y / t_1) * (a + (z - b));
	else
		tmp = (a + (x / ((t + x) / z))) - ((y * b) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -2.8e+115], N[Not[LessEqual[y, 1.45e+75]], $MachinePrecision]], N[(N[(y / t$95$1), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(x / N[(N[(t + x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e115 or 1.4499999999999999e75 < y

   1. Initial program 36.0%

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

   2. Taylor expanded in y around inf 33.9%

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

      1. *-un-lft-identity 33.9%

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

      2. associate-/l* 85.0%

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

      3. associate-+l+ 85.0%

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

      4. +-commutative 85.0%

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

      5. associate--l+ 85.0%

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

   4. Applied egg-rr 85.0%

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

      1. *-lft-identity 85.0%

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

      2. associate-+r- 85.0%

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

      3. associate-/r/ 93.0%

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

      4. associate-+r+ 93.0%

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

      5. +-commutative 93.0%

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

      6. +-commutative 93.0%

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

      7. associate-+r- 93.0%

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

   6. Simplified 93.0%

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

   if -2.8e115 < y < 1.4499999999999999e75

   1. Initial program 71.9%

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

   2. Taylor expanded in a around 0 83.4%

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

   3. Taylor expanded in y around 0 81.8%

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

      1. associate-/l* 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in t around inf 72.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+115} \lor \neg \left(y \leq 1.45 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \frac{x}{\frac{t + x}{z}}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \end{array} \]

Alternative 8: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-11} \lor \neg \left(y \leq 1.22 \cdot 10^{-144}\right) \land \left(y \leq 2.9 \cdot 10^{-67} \lor \neg \left(y \leq 3.1 \cdot 10^{+44}\right)\right):\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.5e-11)
         (and (not (<= y 1.22e-144)) (or (<= y 2.9e-67) (not (<= y 3.1e+44)))))
   (* (/ y (+ t (+ y x))) (+ a (- z b)))
   (/ (+ (* t a) (* x z)) (+ t x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.5e-11) || (!(y <= 1.22e-144) && ((y <= 2.9e-67) || !(y <= 3.1e+44)))) {
		tmp = (y / (t + (y + x))) * (a + (z - b));
	} else {
		tmp = ((t * a) + (x * z)) / (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) :: tmp
    if ((y <= (-3.5d-11)) .or. (.not. (y <= 1.22d-144)) .and. (y <= 2.9d-67) .or. (.not. (y <= 3.1d+44))) then
        tmp = (y / (t + (y + x))) * (a + (z - b))
    else
        tmp = ((t * a) + (x * z)) / (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 tmp;
	if ((y <= -3.5e-11) || (!(y <= 1.22e-144) && ((y <= 2.9e-67) || !(y <= 3.1e+44)))) {
		tmp = (y / (t + (y + x))) * (a + (z - b));
	} else {
		tmp = ((t * a) + (x * z)) / (t + x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.5e-11) or (not (y <= 1.22e-144) and ((y <= 2.9e-67) or not (y <= 3.1e+44))):
		tmp = (y / (t + (y + x))) * (a + (z - b))
	else:
		tmp = ((t * a) + (x * z)) / (t + x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.5e-11) || (!(y <= 1.22e-144) && ((y <= 2.9e-67) || !(y <= 3.1e+44))))
		tmp = Float64(Float64(y / Float64(t + Float64(y + x))) * Float64(a + Float64(z - b)));
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(t + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.5e-11) || (~((y <= 1.22e-144)) && ((y <= 2.9e-67) || ~((y <= 3.1e+44)))))
		tmp = (y / (t + (y + x))) * (a + (z - b));
	else
		tmp = ((t * a) + (x * z)) / (t + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.5e-11], And[N[Not[LessEqual[y, 1.22e-144]], $MachinePrecision], Or[LessEqual[y, 2.9e-67], N[Not[LessEqual[y, 3.1e+44]], $MachinePrecision]]]], N[(N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.50000000000000019e-11 or 1.22e-144 < y < 2.90000000000000005e-67 or 3.09999999999999996e44 < y

   1. Initial program 46.9%

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

   2. Taylor expanded in y around inf 40.4%

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

      1. *-un-lft-identity 40.4%

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

      2. associate-/l* 74.3%

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

      3. associate-+l+ 74.3%

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

      4. +-commutative 74.3%

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

      5. associate--l+ 74.3%

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

   4. Applied egg-rr 74.3%

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

      1. *-lft-identity 74.3%

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

      2. associate-+r- 74.3%

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

      3. associate-/r/ 79.4%

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

      4. associate-+r+ 79.4%

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

      5. +-commutative 79.4%

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

      6. +-commutative 79.4%

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

      7. associate-+r- 79.4%

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

   6. Simplified 79.4%

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

   if -3.50000000000000019e-11 < y < 1.22e-144 or 2.90000000000000005e-67 < y < 3.09999999999999996e44

   1. Initial program 74.1%

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

   2. Taylor expanded in y around 0 57.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-11} \lor \neg \left(y \leq 1.22 \cdot 10^{-144}\right) \land \left(y \leq 2.9 \cdot 10^{-67} \lor \neg \left(y \leq 3.1 \cdot 10^{+44}\right)\right):\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \end{array} \]

Alternative 9: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot a + x \cdot z}{t + x}\\ t_2 := \frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -0.0033:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot \left(\left(a + z\right) - b\right)}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* t a) (* x z)) (+ t x)))
        (t_2 (* (/ y (+ t (+ y x))) (+ a (- z b)))))
   (if (<= y -0.0033)
     t_2
     (if (<= y 1.22e-144)
       t_1
       (if (<= y 4.5e-67)
         (/ (* y (- (+ a z) b)) (+ y (+ t x)))
         (if (<= y 1.25e+44) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x * z)) / (t + x);
	double t_2 = (y / (t + (y + x))) * (a + (z - b));
	double tmp;
	if (y <= -0.0033) {
		tmp = t_2;
	} else if (y <= 1.22e-144) {
		tmp = t_1;
	} else if (y <= 4.5e-67) {
		tmp = (y * ((a + z) - b)) / (y + (t + x));
	} else if (y <= 1.25e+44) {
		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 = ((t * a) + (x * z)) / (t + x)
    t_2 = (y / (t + (y + x))) * (a + (z - b))
    if (y <= (-0.0033d0)) then
        tmp = t_2
    else if (y <= 1.22d-144) then
        tmp = t_1
    else if (y <= 4.5d-67) then
        tmp = (y * ((a + z) - b)) / (y + (t + x))
    else if (y <= 1.25d+44) 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 = ((t * a) + (x * z)) / (t + x);
	double t_2 = (y / (t + (y + x))) * (a + (z - b));
	double tmp;
	if (y <= -0.0033) {
		tmp = t_2;
	} else if (y <= 1.22e-144) {
		tmp = t_1;
	} else if (y <= 4.5e-67) {
		tmp = (y * ((a + z) - b)) / (y + (t + x));
	} else if (y <= 1.25e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t * a) + (x * z)) / (t + x)
	t_2 = (y / (t + (y + x))) * (a + (z - b))
	tmp = 0
	if y <= -0.0033:
		tmp = t_2
	elif y <= 1.22e-144:
		tmp = t_1
	elif y <= 4.5e-67:
		tmp = (y * ((a + z) - b)) / (y + (t + x))
	elif y <= 1.25e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(t + x))
	t_2 = Float64(Float64(y / Float64(t + Float64(y + x))) * Float64(a + Float64(z - b)))
	tmp = 0.0
	if (y <= -0.0033)
		tmp = t_2;
	elseif (y <= 1.22e-144)
		tmp = t_1;
	elseif (y <= 4.5e-67)
		tmp = Float64(Float64(y * Float64(Float64(a + z) - b)) / Float64(y + Float64(t + x)));
	elseif (y <= 1.25e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t * a) + (x * z)) / (t + x);
	t_2 = (y / (t + (y + x))) * (a + (z - b));
	tmp = 0.0;
	if (y <= -0.0033)
		tmp = t_2;
	elseif (y <= 1.22e-144)
		tmp = t_1;
	elseif (y <= 4.5e-67)
		tmp = (y * ((a + z) - b)) / (y + (t + x));
	elseif (y <= 1.25e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0033], t$95$2, If[LessEqual[y, 1.22e-144], t$95$1, If[LessEqual[y, 4.5e-67], N[(N[(y * N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0033 or 1.2499999999999999e44 < y

   1. Initial program 42.4%

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

   2. Taylor expanded in y around inf 37.6%

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

      1. *-un-lft-identity 37.6%

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

      2. associate-/l* 76.5%

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

      3. associate-+l+ 76.5%

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

      4. +-commutative 76.5%

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

      5. associate--l+ 76.5%

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

   4. Applied egg-rr 76.5%

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

      1. *-lft-identity 76.5%

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

      2. associate-+r- 76.5%

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

      3. associate-/r/ 83.2%

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

      4. associate-+r+ 83.2%

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

      5. +-commutative 83.2%

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

      6. +-commutative 83.2%

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

      7. associate-+r- 83.2%

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

   6. Simplified 83.2%

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

   if -0.0033 < y < 1.22e-144 or 4.50000000000000015e-67 < y < 1.2499999999999999e44

   1. Initial program 74.1%

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

   2. Taylor expanded in y around 0 57.9%

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

   if 1.22e-144 < y < 4.50000000000000015e-67

   1. Initial program 77.4%

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

   2. Taylor expanded in y around inf 59.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0033:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-144}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot \left(\left(a + z\right) - b\right)}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]

Alternative 10: 52.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{-b}{\frac{t_1}{y}}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-221}:\\ \;\;\;\;\left(a + \frac{x}{\frac{t + x}{z}}\right) - b\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+188}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))))
   (if (<= b -2e+101)
     (/ (- b) (/ t_1 y))
     (if (<= b 9.5e-221)
       (- (+ a (/ x (/ (+ t x) z))) b)
       (if (<= b 8.5e-109)
         (/ (+ (* t a) (* x z)) (+ t x))
         (if (<= b 8.8e+188) (- (+ a z) b) (/ a (/ t_1 (+ y t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if (b <= -2e+101) {
		tmp = -b / (t_1 / y);
	} else if (b <= 9.5e-221) {
		tmp = (a + (x / ((t + x) / z))) - b;
	} else if (b <= 8.5e-109) {
		tmp = ((t * a) + (x * z)) / (t + x);
	} else if (b <= 8.8e+188) {
		tmp = (a + z) - b;
	} else {
		tmp = a / (t_1 / (y + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y + t)
    if (b <= (-2d+101)) then
        tmp = -b / (t_1 / y)
    else if (b <= 9.5d-221) then
        tmp = (a + (x / ((t + x) / z))) - b
    else if (b <= 8.5d-109) then
        tmp = ((t * a) + (x * z)) / (t + x)
    else if (b <= 8.8d+188) then
        tmp = (a + z) - b
    else
        tmp = a / (t_1 / (y + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if (b <= -2e+101) {
		tmp = -b / (t_1 / y);
	} else if (b <= 9.5e-221) {
		tmp = (a + (x / ((t + x) / z))) - b;
	} else if (b <= 8.5e-109) {
		tmp = ((t * a) + (x * z)) / (t + x);
	} else if (b <= 8.8e+188) {
		tmp = (a + z) - b;
	} else {
		tmp = a / (t_1 / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	tmp = 0
	if b <= -2e+101:
		tmp = -b / (t_1 / y)
	elif b <= 9.5e-221:
		tmp = (a + (x / ((t + x) / z))) - b
	elif b <= 8.5e-109:
		tmp = ((t * a) + (x * z)) / (t + x)
	elif b <= 8.8e+188:
		tmp = (a + z) - b
	else:
		tmp = a / (t_1 / (y + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	tmp = 0.0
	if (b <= -2e+101)
		tmp = Float64(Float64(-b) / Float64(t_1 / y));
	elseif (b <= 9.5e-221)
		tmp = Float64(Float64(a + Float64(x / Float64(Float64(t + x) / z))) - b);
	elseif (b <= 8.5e-109)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(t + x));
	elseif (b <= 8.8e+188)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	tmp = 0.0;
	if (b <= -2e+101)
		tmp = -b / (t_1 / y);
	elseif (b <= 9.5e-221)
		tmp = (a + (x / ((t + x) / z))) - b;
	elseif (b <= 8.5e-109)
		tmp = ((t * a) + (x * z)) / (t + x);
	elseif (b <= 8.8e+188)
		tmp = (a + z) - b;
	else
		tmp = a / (t_1 / (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+101], N[((-b) / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-221], N[(N[(a + N[(x / N[(N[(t + x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[b, 8.5e-109], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.8e+188], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2e101

   1. Initial program 50.2%

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

   2. Taylor expanded in y around inf 34.6%

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

      1. *-un-lft-identity 34.6%

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

      2. associate-/l* 63.9%

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

      3. associate-+l+ 63.9%

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

      4. +-commutative 63.9%

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

      5. associate--l+ 63.9%

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

   4. Applied egg-rr 63.9%

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

      1. *-lft-identity 63.9%

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

      2. associate-+r- 63.9%

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

      3. associate-/r/ 67.4%

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

      4. associate-+r+ 67.4%

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

      5. +-commutative 67.4%

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

      6. +-commutative 67.4%

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

      7. associate-+r- 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in b around inf 33.9%

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

      1. mul-1-neg 33.9%

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

      2. associate-/l* 60.1%

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

      3. distribute-neg-frac 60.1%

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

      4. associate-+r+ 60.1%

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

      5. +-commutative 60.1%

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

      6. associate-+r+ 60.1%

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

   9. Simplified 60.1%

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

   if -2e101 < b < 9.50000000000000022e-221

   1. Initial program 60.0%

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

   2. Taylor expanded in a around 0 72.5%

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

   3. Taylor expanded in y around 0 74.1%

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

      1. associate-/l* 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in t around inf 72.5%

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

   7. Taylor expanded in y around inf 68.5%

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

   if 9.50000000000000022e-221 < b < 8.50000000000000005e-109

   1. Initial program 95.9%

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

   2. Taylor expanded in y around 0 68.8%

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

   if 8.50000000000000005e-109 < b < 8.79999999999999996e188

   1. Initial program 61.3%

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

   2. Taylor expanded in y around inf 65.1%

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

   if 8.79999999999999996e188 < b

   1. Initial program 39.4%

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

   2. Taylor expanded in a around inf 8.4%

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

      1. associate-/l* 48.3%

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

      2. +-commutative 48.3%

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

      3. associate-+r+ 48.3%

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

   4. Simplified 48.3%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{-b}{\frac{x + \left(y + t\right)}{y}}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-221}:\\ \;\;\;\;\left(a + \frac{x}{\frac{t + x}{z}}\right) - b\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+188}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \end{array} \]

Alternative 11: 54.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{-b}{\frac{t_1}{y}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+190}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))))
   (if (<= b -2e+101)
     (/ (- b) (/ t_1 y))
     (if (<= b 5e+190) (- (+ a z) b) (/ a (/ t_1 (+ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if (b <= -2e+101) {
		tmp = -b / (t_1 / y);
	} else if (b <= 5e+190) {
		tmp = (a + z) - b;
	} else {
		tmp = a / (t_1 / (y + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y + t)
    if (b <= (-2d+101)) then
        tmp = -b / (t_1 / y)
    else if (b <= 5d+190) then
        tmp = (a + z) - b
    else
        tmp = a / (t_1 / (y + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if (b <= -2e+101) {
		tmp = -b / (t_1 / y);
	} else if (b <= 5e+190) {
		tmp = (a + z) - b;
	} else {
		tmp = a / (t_1 / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	tmp = 0
	if b <= -2e+101:
		tmp = -b / (t_1 / y)
	elif b <= 5e+190:
		tmp = (a + z) - b
	else:
		tmp = a / (t_1 / (y + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	tmp = 0.0
	if (b <= -2e+101)
		tmp = Float64(Float64(-b) / Float64(t_1 / y));
	elseif (b <= 5e+190)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	tmp = 0.0;
	if (b <= -2e+101)
		tmp = -b / (t_1 / y);
	elseif (b <= 5e+190)
		tmp = (a + z) - b;
	else
		tmp = a / (t_1 / (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+101], N[((-b) / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+190], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2e101

   1. Initial program 50.2%

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

   2. Taylor expanded in y around inf 34.6%

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

      1. *-un-lft-identity 34.6%

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

      2. associate-/l* 63.9%

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

      3. associate-+l+ 63.9%

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

      4. +-commutative 63.9%

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

      5. associate--l+ 63.9%

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

   4. Applied egg-rr 63.9%

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

      1. *-lft-identity 63.9%

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

      2. associate-+r- 63.9%

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

      3. associate-/r/ 67.4%

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

      4. associate-+r+ 67.4%

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

      5. +-commutative 67.4%

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

      6. +-commutative 67.4%

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

      7. associate-+r- 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in b around inf 33.9%

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

      1. mul-1-neg 33.9%

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

      2. associate-/l* 60.1%

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

      3. distribute-neg-frac 60.1%

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

      4. associate-+r+ 60.1%

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

      5. +-commutative 60.1%

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

      6. associate-+r+ 60.1%

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

   9. Simplified 60.1%

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

   if -2e101 < b < 5.00000000000000036e190

   1. Initial program 65.2%

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

   2. Taylor expanded in y around inf 63.8%

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

   if 5.00000000000000036e190 < b

   1. Initial program 39.4%

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

   2. Taylor expanded in a around inf 8.4%

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

      1. associate-/l* 48.3%

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

      2. +-commutative 48.3%

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

      3. associate-+r+ 48.3%

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

   4. Simplified 48.3%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{-b}{\frac{x + \left(y + t\right)}{y}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+190}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \end{array} \]

Alternative 12: 53.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \frac{-b}{t + \left(y + x\right)}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+189}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+101)
   (* y (/ (- b) (+ t (+ y x))))
   (if (<= b 2.1e+189) (- (+ a z) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+101) {
		tmp = y * (-b / (t + (y + x)));
	} else if (b <= 2.1e+189) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2d+101)) then
        tmp = y * (-b / (t + (y + x)))
    else if (b <= 2.1d+189) then
        tmp = (a + z) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+101) {
		tmp = y * (-b / (t + (y + x)));
	} else if (b <= 2.1e+189) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e+101:
		tmp = y * (-b / (t + (y + x)))
	elif b <= 2.1e+189:
		tmp = (a + z) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+101)
		tmp = Float64(y * Float64(Float64(-b) / Float64(t + Float64(y + x))));
	elseif (b <= 2.1e+189)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e+101)
		tmp = y * (-b / (t + (y + x)));
	elseif (b <= 2.1e+189)
		tmp = (a + z) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+101], N[(y * N[((-b) / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+189], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if b < -2e101

   1. Initial program 50.2%

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

   2. Taylor expanded in y around inf 34.6%

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

   3. Taylor expanded in b around inf 33.9%

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

      1. mul-1-neg 33.9%

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

      2. associate-/l* 60.1%

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

      3. +-commutative 60.1%

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

      4. associate-+r+ 60.1%

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

      5. associate-/r/ 56.5%

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

      6. distribute-rgt-neg-in 56.5%

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

      7. associate-+r+ 56.5%

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

      8. +-commutative 56.5%

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

      9. +-commutative 56.5%

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

   5. Simplified 56.5%

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

   if -2e101 < b < 2.09999999999999992e189

   1. Initial program 65.2%

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

   2. Taylor expanded in y around inf 63.8%

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

   if 2.09999999999999992e189 < b

   1. Initial program 39.4%

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

   2. Taylor expanded in t around inf 45.8%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \frac{-b}{t + \left(y + x\right)}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+189}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 13: 54.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.35 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+189}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.35e+100)
   (* (/ y (+ t (+ y x))) (- b))
   (if (<= b 2.05e+189) (- (+ a z) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.35e+100) {
		tmp = (y / (t + (y + x))) * -b;
	} else if (b <= 2.05e+189) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.35d+100)) then
        tmp = (y / (t + (y + x))) * -b
    else if (b <= 2.05d+189) then
        tmp = (a + z) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.35e+100) {
		tmp = (y / (t + (y + x))) * -b;
	} else if (b <= 2.05e+189) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.35e+100:
		tmp = (y / (t + (y + x))) * -b
	elif b <= 2.05e+189:
		tmp = (a + z) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.35e+100)
		tmp = Float64(Float64(y / Float64(t + Float64(y + x))) * Float64(-b));
	elseif (b <= 2.05e+189)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.35e+100)
		tmp = (y / (t + (y + x))) * -b;
	elseif (b <= 2.05e+189)
		tmp = (a + z) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.35e+100], N[(N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[b, 2.05e+189], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3499999999999998e100

   1. Initial program 50.2%

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

   2. Taylor expanded in y around inf 34.6%

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

      1. *-un-lft-identity 34.6%

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

      2. associate-/l* 63.9%

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

      3. associate-+l+ 63.9%

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

      4. +-commutative 63.9%

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

      5. associate--l+ 63.9%

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

   4. Applied egg-rr 63.9%

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

      1. *-lft-identity 63.9%

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

      2. associate-+r- 63.9%

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

      3. associate-/r/ 67.4%

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

      4. associate-+r+ 67.4%

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

      5. +-commutative 67.4%

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

      6. +-commutative 67.4%

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

      7. associate-+r- 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in b around inf 60.0%

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

      1. neg-mul-1 60.0%

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

   9. Simplified 60.0%

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

   if -3.3499999999999998e100 < b < 2.0500000000000001e189

   1. Initial program 65.2%

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

   2. Taylor expanded in y around inf 63.8%

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

   if 2.0500000000000001e189 < b

   1. Initial program 39.4%

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

   2. Taylor expanded in t around inf 45.8%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.35 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+189}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 14: 54.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.35 \cdot 10^{+100}:\\ \;\;\;\;\frac{-b}{\frac{x + \left(y + t\right)}{y}}\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+189}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.35e+100)
   (/ (- b) (/ (+ x (+ y t)) y))
   (if (<= b 2.05e+189) (- (+ a z) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.35e+100) {
		tmp = -b / ((x + (y + t)) / y);
	} else if (b <= 2.05e+189) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.35d+100)) then
        tmp = -b / ((x + (y + t)) / y)
    else if (b <= 2.05d+189) then
        tmp = (a + z) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.35e+100) {
		tmp = -b / ((x + (y + t)) / y);
	} else if (b <= 2.05e+189) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.35e+100:
		tmp = -b / ((x + (y + t)) / y)
	elif b <= 2.05e+189:
		tmp = (a + z) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.35e+100)
		tmp = Float64(Float64(-b) / Float64(Float64(x + Float64(y + t)) / y));
	elseif (b <= 2.05e+189)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.35e+100)
		tmp = -b / ((x + (y + t)) / y);
	elseif (b <= 2.05e+189)
		tmp = (a + z) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.35e+100], N[((-b) / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e+189], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3499999999999998e100

   1. Initial program 50.2%

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

   2. Taylor expanded in y around inf 34.6%

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

      1. *-un-lft-identity 34.6%

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

      2. associate-/l* 63.9%

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

      3. associate-+l+ 63.9%

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

      4. +-commutative 63.9%

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

      5. associate--l+ 63.9%

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

   4. Applied egg-rr 63.9%

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

      1. *-lft-identity 63.9%

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

      2. associate-+r- 63.9%

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

      3. associate-/r/ 67.4%

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

      4. associate-+r+ 67.4%

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

      5. +-commutative 67.4%

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

      6. +-commutative 67.4%

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

      7. associate-+r- 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in b around inf 33.9%

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

      1. mul-1-neg 33.9%

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

      2. associate-/l* 60.1%

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

      3. distribute-neg-frac 60.1%

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

      4. associate-+r+ 60.1%

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

      5. +-commutative 60.1%

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

      6. associate-+r+ 60.1%

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

   9. Simplified 60.1%

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

   if -3.3499999999999998e100 < b < 2.0500000000000001e189

   1. Initial program 65.2%

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

   2. Taylor expanded in y around inf 63.8%

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

   if 2.0500000000000001e189 < b

   1. Initial program 39.4%

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

   2. Taylor expanded in t around inf 45.8%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.35 \cdot 10^{+100}:\\ \;\;\;\;\frac{-b}{\frac{x + \left(y + t\right)}{y}}\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+189}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 15: 43.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-30}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-35}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+79}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -9e-30)
   a
   (if (<= a 2.15e-35) z (if (<= a 2.9e+19) a (if (<= a 7.6e+79) z a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9e-30) {
		tmp = a;
	} else if (a <= 2.15e-35) {
		tmp = z;
	} else if (a <= 2.9e+19) {
		tmp = a;
	} else if (a <= 7.6e+79) {
		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 (a <= (-9d-30)) then
        tmp = a
    else if (a <= 2.15d-35) then
        tmp = z
    else if (a <= 2.9d+19) then
        tmp = a
    else if (a <= 7.6d+79) 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 (a <= -9e-30) {
		tmp = a;
	} else if (a <= 2.15e-35) {
		tmp = z;
	} else if (a <= 2.9e+19) {
		tmp = a;
	} else if (a <= 7.6e+79) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -9e-30:
		tmp = a
	elif a <= 2.15e-35:
		tmp = z
	elif a <= 2.9e+19:
		tmp = a
	elif a <= 7.6e+79:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -9e-30)
		tmp = a;
	elseif (a <= 2.15e-35)
		tmp = z;
	elseif (a <= 2.9e+19)
		tmp = a;
	elseif (a <= 7.6e+79)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -9e-30)
		tmp = a;
	elseif (a <= 2.15e-35)
		tmp = z;
	elseif (a <= 2.9e+19)
		tmp = a;
	elseif (a <= 7.6e+79)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -9e-30], a, If[LessEqual[a, 2.15e-35], z, If[LessEqual[a, 2.9e+19], a, If[LessEqual[a, 7.6e+79], z, a]]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.99999999999999935e-30 or 2.1500000000000001e-35 < a < 2.9e19 or 7.6000000000000005e79 < a

   1. Initial program 48.3%

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

   2. Taylor expanded in t around inf 53.3%

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

   if -8.99999999999999935e-30 < a < 2.1500000000000001e-35 or 2.9e19 < a < 7.6000000000000005e79

   1. Initial program 71.5%

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

   2. Taylor expanded in x around inf 44.8%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-30}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-35}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+79}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16: 53.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.2 \cdot 10^{+190}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 3.2e+190) (- (+ a z) b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.2e+190) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.2d+190) then
        tmp = (a + z) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.2e+190) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.2e+190:
		tmp = (a + z) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.2e+190)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.2e+190)
		tmp = (a + z) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.2e+190], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if b < 3.2000000000000001e190

   1. Initial program 61.7%

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

   2. Taylor expanded in y around inf 58.8%

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

   if 3.2000000000000001e190 < b

   1. Initial program 39.4%

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

   2. Taylor expanded in t around inf 45.8%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.2 \cdot 10^{+190}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17: 32.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 60.1%

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

2. Taylor expanded in t around inf 31.7%

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

3. Final simplification 31.7%

   \[\leadsto a \]

Developer target: 81.6% 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 2023293 
(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)))