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

Percentage Accurate: 60.0% → 98.6%

Time: 18.7s

Alternatives: 19

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{y}{t_1}\\ z \cdot \left(\frac{x}{t_1} + t_2\right) + \left(\frac{a}{\frac{t_1}{t + y}} - b \cdot t_2\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y)) (t_2 (/ y t_1)))
   (+ (* z (+ (/ x t_1) t_2)) (- (/ a (/ t_1 (+ t y))) (* b t_2)))))

C

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

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
    t_1 = (x + t) + y
    t_2 = y / t_1
    code = (z * ((x / t_1) + t_2)) + ((a / (t_1 / (t + y))) - (b * t_2))
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 = y / t_1;
	return (z * ((x / t_1) + t_2)) + ((a / (t_1 / (t + y))) - (b * t_2));
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = y / t_1
	return (z * ((x / t_1) + t_2)) + ((a / (t_1 / (t + y))) - (b * t_2))

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = y / t_1;
	tmp = (z * ((x / t_1) + t_2)) + ((a / (t_1 / (t + y))) - (b * t_2));
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[(y / t$95$1), $MachinePrecision]}, N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(t$95$1 / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 61.6%

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

2. Taylor expanded in z around 0 70.9%

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

   1. associate--l+ 70.9%

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

   2. associate-+r+ 70.9%

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

   3. associate-+r+ 70.9%

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

   4. +-commutative 70.9%

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

   5. +-commutative 70.9%

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

   6. associate-+r+ 70.9%

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

   7. *-commutative 70.9%

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

   8. +-commutative 70.9%

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

   9. associate-+r+ 70.9%

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

   10. div-sub 70.9%

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

4. Simplified 70.9%

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

   1. div-sub 70.9%

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

   2. associate-/l* 87.9%

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

   3. +-commutative 87.9%

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

   4. add-sqr-sqrt 51.6%

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

   5. sqrt-unprod 73.6%

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

   6. sqr-neg 73.6%

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

   7. *-commutative 73.6%

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

   8. distribute-lft-neg-out 73.6%

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

   9. *-commutative 73.6%

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

   10. distribute-lft-neg-out 73.6%

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

   11. sqrt-unprod 43.0%

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

   12. add-sqr-sqrt 78.3%

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

   13. div-inv 78.3%

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

   14. associate-*l* 83.0%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

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

Alternative 2: 94.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + y\right)\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + t_1\right) - y \cdot b}{t_2}\\ t_4 := \frac{y}{t_2}\\ t_5 := \frac{a}{\frac{t_2}{t + y}} - b \cdot t_4\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{+290}:\\ \;\;\;\;t_5 + \frac{y}{\frac{t + y}{z}}\\ \mathbf{elif}\;t_3 \leq 10^{+262}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_2} + t_4\right) + \frac{t_1 - y \cdot b}{t_2}\\ \mathbf{else}:\\ \;\;\;\;z + t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t y)))
        (t_2 (+ (+ x t) y))
        (t_3 (/ (- (+ (* z (+ x y)) t_1) (* y b)) t_2))
        (t_4 (/ y t_2))
        (t_5 (- (/ a (/ t_2 (+ t y))) (* b t_4))))
   (if (<= t_3 -1e+290)
     (+ t_5 (/ y (/ (+ t y) z)))
     (if (<= t_3 1e+262)
       (+ (* z (+ (/ x t_2) t_4)) (/ (- t_1 (* y b)) t_2))
       (+ z t_5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + y);
	double t_2 = (x + t) + y;
	double t_3 = (((z * (x + y)) + t_1) - (y * b)) / t_2;
	double t_4 = y / t_2;
	double t_5 = (a / (t_2 / (t + y))) - (b * t_4);
	double tmp;
	if (t_3 <= -1e+290) {
		tmp = t_5 + (y / ((t + y) / z));
	} else if (t_3 <= 1e+262) {
		tmp = (z * ((x / t_2) + t_4)) + ((t_1 - (y * b)) / t_2);
	} else {
		tmp = z + 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 = a * (t + y)
    t_2 = (x + t) + y
    t_3 = (((z * (x + y)) + t_1) - (y * b)) / t_2
    t_4 = y / t_2
    t_5 = (a / (t_2 / (t + y))) - (b * t_4)
    if (t_3 <= (-1d+290)) then
        tmp = t_5 + (y / ((t + y) / z))
    else if (t_3 <= 1d+262) then
        tmp = (z * ((x / t_2) + t_4)) + ((t_1 - (y * b)) / t_2)
    else
        tmp = z + 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 = a * (t + y);
	double t_2 = (x + t) + y;
	double t_3 = (((z * (x + y)) + t_1) - (y * b)) / t_2;
	double t_4 = y / t_2;
	double t_5 = (a / (t_2 / (t + y))) - (b * t_4);
	double tmp;
	if (t_3 <= -1e+290) {
		tmp = t_5 + (y / ((t + y) / z));
	} else if (t_3 <= 1e+262) {
		tmp = (z * ((x / t_2) + t_4)) + ((t_1 - (y * b)) / t_2);
	} else {
		tmp = z + t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + y)
	t_2 = (x + t) + y
	t_3 = (((z * (x + y)) + t_1) - (y * b)) / t_2
	t_4 = y / t_2
	t_5 = (a / (t_2 / (t + y))) - (b * t_4)
	tmp = 0
	if t_3 <= -1e+290:
		tmp = t_5 + (y / ((t + y) / z))
	elif t_3 <= 1e+262:
		tmp = (z * ((x / t_2) + t_4)) + ((t_1 - (y * b)) / t_2)
	else:
		tmp = z + t_5
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + y))
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + t_1) - Float64(y * b)) / t_2)
	t_4 = Float64(y / t_2)
	t_5 = Float64(Float64(a / Float64(t_2 / Float64(t + y))) - Float64(b * t_4))
	tmp = 0.0
	if (t_3 <= -1e+290)
		tmp = Float64(t_5 + Float64(y / Float64(Float64(t + y) / z)));
	elseif (t_3 <= 1e+262)
		tmp = Float64(Float64(z * Float64(Float64(x / t_2) + t_4)) + Float64(Float64(t_1 - Float64(y * b)) / t_2));
	else
		tmp = Float64(z + t_5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + y);
	t_2 = (x + t) + y;
	t_3 = (((z * (x + y)) + t_1) - (y * b)) / t_2;
	t_4 = y / t_2;
	t_5 = (a / (t_2 / (t + y))) - (b * t_4);
	tmp = 0.0;
	if (t_3 <= -1e+290)
		tmp = t_5 + (y / ((t + y) / z));
	elseif (t_3 <= 1e+262)
		tmp = (z * ((x / t_2) + t_4)) + ((t_1 - (y * b)) / t_2);
	else
		tmp = z + t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(y / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(N[(a / N[(t$95$2 / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+290], N[(t$95$5 + N[(y / N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+262], N[(N[(z * N[(N[(x / t$95$2), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(z + t$95$5), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.00000000000000006e290

   1. Initial program 7.7%

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

   2. Taylor expanded in z around 0 31.8%

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

      1. associate--l+ 31.8%

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

      2. associate-+r+ 31.8%

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

      3. associate-+r+ 31.8%

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

      4. +-commutative 31.8%

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

      5. +-commutative 31.8%

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

      6. associate-+r+ 31.8%

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

      7. *-commutative 31.8%

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

      8. +-commutative 31.8%

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

      9. associate-+r+ 31.8%

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

      10. div-sub 31.8%

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

   4. Simplified 31.8%

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

      1. div-sub 31.8%

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

      2. associate-/l* 80.3%

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

      3. +-commutative 80.3%

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

      4. add-sqr-sqrt 53.8%

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

      5. sqrt-unprod 61.4%

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

      6. sqr-neg 61.4%

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

      7. *-commutative 61.4%

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

      8. distribute-lft-neg-out 61.4%

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

      9. *-commutative 61.4%

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

      10. distribute-lft-neg-out 61.4%

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

      11. sqrt-unprod 30.3%

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

      12. add-sqr-sqrt 76.7%

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

      13. div-inv 76.7%

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

      14. associate-*l* 83.7%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 71.3%

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

      1. associate-/l* 93.2%

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

      2. +-commutative 93.2%

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

   9. Simplified 93.2%

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

   if -1.00000000000000006e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e262

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-+r+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+r+ 99.8%

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

      7. *-commutative 99.8%

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

      8. +-commutative 99.8%

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

      9. associate-+r+ 99.8%

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

      10. div-sub 99.8%

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

   4. Simplified 99.8%

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

   if 1e262 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.1%

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

   2. Taylor expanded in z around 0 27.9%

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

      1. associate--l+ 27.9%

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

      2. associate-+r+ 27.9%

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

      3. associate-+r+ 27.9%

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

      4. +-commutative 27.9%

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

      5. +-commutative 27.9%

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

      6. associate-+r+ 27.9%

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

      7. *-commutative 27.9%

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

      8. +-commutative 27.9%

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

      9. associate-+r+ 27.9%

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

      10. div-sub 27.9%

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

   4. Simplified 27.9%

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

      1. div-sub 27.9%

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

      2. associate-/l* 64.3%

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

      3. +-commutative 64.3%

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

      4. add-sqr-sqrt 28.2%

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

      5. sqrt-unprod 54.6%

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

      6. sqr-neg 54.6%

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

      7. *-commutative 54.6%

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

      8. distribute-lft-neg-out 54.6%

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

      9. *-commutative 54.6%

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

      10. distribute-lft-neg-out 54.6%

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

      11. sqrt-unprod 40.5%

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

      12. add-sqr-sqrt 63.7%

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

      13. div-inv 63.7%

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

      14. associate-*l* 78.2%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 91.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{+290}:\\ \;\;\;\;\left(\frac{a}{\frac{\left(x + t\right) + y}{t + y}} - b \cdot \frac{y}{\left(x + t\right) + y}\right) + \frac{y}{\frac{t + y}{z}}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+262}:\\ \;\;\;\;z \cdot \left(\frac{x}{\left(x + t\right) + y} + \frac{y}{\left(x + t\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;z + \left(\frac{a}{\frac{\left(x + t\right) + y}{t + y}} - b \cdot \frac{y}{\left(x + t\right) + y}\right)\\ \end{array} \]

Alternative 3: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+290} \lor \neg \left(t_2 \leq 10^{+262}\right):\\ \;\;\;\;z + \left(\frac{a}{\frac{t_1}{t + y}} - b \cdot \frac{y}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ t y))) (* y b)) t_1)))
   (if (or (<= t_2 -1e+290) (not (<= t_2 1e+262)))
     (+ z (- (/ a (/ t_1 (+ t y))) (* b (/ y t_1))))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -1e+290) || !(t_2 <= 1e+262)) {
		tmp = z + ((a / (t_1 / (t + y))) - (b * (y / t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1
    if ((t_2 <= (-1d+290)) .or. (.not. (t_2 <= 1d+262))) then
        tmp = z + ((a / (t_1 / (t + y))) - (b * (y / t_1)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -1e+290) || !(t_2 <= 1e+262)) {
		tmp = z + ((a / (t_1 / (t + y))) - (b * (y / t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -1e+290) or not (t_2 <= 1e+262):
		tmp = z + ((a / (t_1 / (t + y))) - (b * (y / t_1)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(t + y))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= -1e+290) || !(t_2 <= 1e+262))
		tmp = Float64(z + Float64(Float64(a / Float64(t_1 / Float64(t + y))) - Float64(b * Float64(y / t_1))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -1e+290) || ~((t_2 <= 1e+262)))
		tmp = z + ((a / (t_1 / (t + y))) - (b * (y / t_1)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e+290], N[Not[LessEqual[t$95$2, 1e+262]], $MachinePrecision]], N[(z + N[(N[(a / N[(t$95$1 / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.00000000000000006e290 or 1e262 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.8%

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

   2. Taylor expanded in z around 0 29.5%

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

      1. associate--l+ 29.5%

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

      2. associate-+r+ 29.5%

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

      3. associate-+r+ 29.5%

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

      4. +-commutative 29.5%

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

      5. +-commutative 29.5%

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

      6. associate-+r+ 29.5%

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

      7. *-commutative 29.5%

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

      8. +-commutative 29.5%

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

      9. associate-+r+ 29.5%

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

      10. div-sub 29.5%

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

   4. Simplified 29.5%

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

      1. div-sub 29.5%

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

      2. associate-/l* 70.9%

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

      3. +-commutative 70.9%

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

      4. add-sqr-sqrt 38.7%

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

      5. sqrt-unprod 57.4%

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

      6. sqr-neg 57.4%

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

      7. *-commutative 57.4%

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

      8. distribute-lft-neg-out 57.4%

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

      9. *-commutative 57.4%

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

      10. distribute-lft-neg-out 57.4%

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

      11. sqrt-unprod 36.3%

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

      12. add-sqr-sqrt 69.0%

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

      13. div-inv 69.0%

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

      14. associate-*l* 80.4%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 90.6%

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

   if -1.00000000000000006e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e262

   1. Initial program 99.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{+290} \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+262}\right):\\ \;\;\;\;z + \left(\frac{a}{\frac{\left(x + t\right) + y}{t + y}} - b \cdot \frac{y}{\left(x + t\right) + y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array} \]

Alternative 4: 94.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{t_1}\\ t_3 := \frac{a}{\frac{t_1}{t + y}} - b \cdot \frac{y}{t_1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+290}:\\ \;\;\;\;t_3 + \frac{y}{\frac{t + y}{z}}\\ \mathbf{elif}\;t_2 \leq 10^{+262}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z + t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ t y))) (* y b)) t_1))
        (t_3 (- (/ a (/ t_1 (+ t y))) (* b (/ y t_1)))))
   (if (<= t_2 -1e+290)
     (+ t_3 (/ y (/ (+ t y) z)))
     (if (<= t_2 1e+262) t_2 (+ z t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1;
	double t_3 = (a / (t_1 / (t + y))) - (b * (y / t_1));
	double tmp;
	if (t_2 <= -1e+290) {
		tmp = t_3 + (y / ((t + y) / z));
	} else if (t_2 <= 1e+262) {
		tmp = t_2;
	} else {
		tmp = z + t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1
    t_3 = (a / (t_1 / (t + y))) - (b * (y / t_1))
    if (t_2 <= (-1d+290)) then
        tmp = t_3 + (y / ((t + y) / z))
    else if (t_2 <= 1d+262) then
        tmp = t_2
    else
        tmp = z + t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1;
	double t_3 = (a / (t_1 / (t + y))) - (b * (y / t_1));
	double tmp;
	if (t_2 <= -1e+290) {
		tmp = t_3 + (y / ((t + y) / z));
	} else if (t_2 <= 1e+262) {
		tmp = t_2;
	} else {
		tmp = z + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1
	t_3 = (a / (t_1 / (t + y))) - (b * (y / t_1))
	tmp = 0
	if t_2 <= -1e+290:
		tmp = t_3 + (y / ((t + y) / z))
	elif t_2 <= 1e+262:
		tmp = t_2
	else:
		tmp = z + t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(t + y))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(a / Float64(t_1 / Float64(t + y))) - Float64(b * Float64(y / t_1)))
	tmp = 0.0
	if (t_2 <= -1e+290)
		tmp = Float64(t_3 + Float64(y / Float64(Float64(t + y) / z)));
	elseif (t_2 <= 1e+262)
		tmp = t_2;
	else
		tmp = Float64(z + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1;
	t_3 = (a / (t_1 / (t + y))) - (b * (y / t_1));
	tmp = 0.0;
	if (t_2 <= -1e+290)
		tmp = t_3 + (y / ((t + y) / z));
	elseif (t_2 <= 1e+262)
		tmp = t_2;
	else
		tmp = z + t_3;
	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[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a / N[(t$95$1 / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+290], N[(t$95$3 + N[(y / N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+262], t$95$2, N[(z + t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.00000000000000006e290

   1. Initial program 7.7%

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

   2. Taylor expanded in z around 0 31.8%

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

      1. associate--l+ 31.8%

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

      2. associate-+r+ 31.8%

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

      3. associate-+r+ 31.8%

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

      4. +-commutative 31.8%

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

      5. +-commutative 31.8%

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

      6. associate-+r+ 31.8%

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

      7. *-commutative 31.8%

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

      8. +-commutative 31.8%

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

      9. associate-+r+ 31.8%

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

      10. div-sub 31.8%

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

   4. Simplified 31.8%

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

      1. div-sub 31.8%

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

      2. associate-/l* 80.3%

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

      3. +-commutative 80.3%

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

      4. add-sqr-sqrt 53.8%

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

      5. sqrt-unprod 61.4%

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

      6. sqr-neg 61.4%

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

      7. *-commutative 61.4%

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

      8. distribute-lft-neg-out 61.4%

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

      9. *-commutative 61.4%

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

      10. distribute-lft-neg-out 61.4%

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

      11. sqrt-unprod 30.3%

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

      12. add-sqr-sqrt 76.7%

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

      13. div-inv 76.7%

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

      14. associate-*l* 83.7%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 71.3%

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

      1. associate-/l* 93.2%

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

      2. +-commutative 93.2%

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

   9. Simplified 93.2%

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

   if -1.00000000000000006e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e262

   1. Initial program 99.7%

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

   if 1e262 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.1%

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

   2. Taylor expanded in z around 0 27.9%

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

      1. associate--l+ 27.9%

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

      2. associate-+r+ 27.9%

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

      3. associate-+r+ 27.9%

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

      4. +-commutative 27.9%

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

      5. +-commutative 27.9%

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

      6. associate-+r+ 27.9%

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

      7. *-commutative 27.9%

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

      8. +-commutative 27.9%

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

      9. associate-+r+ 27.9%

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

      10. div-sub 27.9%

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

   4. Simplified 27.9%

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

      1. div-sub 27.9%

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

      2. associate-/l* 64.3%

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

      3. +-commutative 64.3%

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

      4. add-sqr-sqrt 28.2%

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

      5. sqrt-unprod 54.6%

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

      6. sqr-neg 54.6%

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

      7. *-commutative 54.6%

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

      8. distribute-lft-neg-out 54.6%

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

      9. *-commutative 54.6%

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

      10. distribute-lft-neg-out 54.6%

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

      11. sqrt-unprod 40.5%

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

      12. add-sqr-sqrt 63.7%

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

      13. div-inv 63.7%

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

      14. associate-*l* 78.2%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 91.9%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{+290}:\\ \;\;\;\;\left(\frac{a}{\frac{\left(x + t\right) + y}{t + y}} - b \cdot \frac{y}{\left(x + t\right) + y}\right) + \frac{y}{\frac{t + y}{z}}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+262}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;z + \left(\frac{a}{\frac{\left(x + t\right) + y}{t + y}} - b \cdot \frac{y}{\left(x + t\right) + y}\right)\\ \end{array} \]

Alternative 5: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{t_1}\\ t_3 := \frac{y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{t_1} + t_3\right) + a\\ \mathbf{elif}\;t_2 \leq 10^{+262}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z + \left(\frac{a}{1 + \frac{x}{y}} - b \cdot t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ t y))) (* y b)) t_1))
        (t_3 (/ y t_1)))
   (if (<= t_2 (- INFINITY))
     (+ (* z (+ (/ x t_1) t_3)) a)
     (if (<= t_2 1e+262) t_2 (+ z (- (/ a (+ 1.0 (/ x y))) (* b t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1;
	double t_3 = y / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z * ((x / t_1) + t_3)) + a;
	} else if (t_2 <= 1e+262) {
		tmp = t_2;
	} else {
		tmp = z + ((a / (1.0 + (x / y))) - (b * t_3));
	}
	return tmp;
}

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 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1;
	double t_3 = y / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (z * ((x / t_1) + t_3)) + a;
	} else if (t_2 <= 1e+262) {
		tmp = t_2;
	} else {
		tmp = z + ((a / (1.0 + (x / y))) - (b * t_3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1
	t_3 = y / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (z * ((x / t_1) + t_3)) + a
	elif t_2 <= 1e+262:
		tmp = t_2
	else:
		tmp = z + ((a / (1.0 + (x / y))) - (b * t_3))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(t + y))) - Float64(y * b)) / t_1)
	t_3 = Float64(y / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z * Float64(Float64(x / t_1) + t_3)) + a);
	elseif (t_2 <= 1e+262)
		tmp = t_2;
	else
		tmp = Float64(z + Float64(Float64(a / Float64(1.0 + Float64(x / y))) - Float64(b * t_3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / t_1;
	t_3 = y / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (z * ((x / t_1) + t_3)) + a;
	elseif (t_2 <= 1e+262)
		tmp = t_2;
	else
		tmp = z + ((a / (1.0 + (x / y))) - (b * t_3));
	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[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t$95$2, 1e+262], t$95$2, N[(z + N[(N[(a / N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 5.6%

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

   2. Taylor expanded in z around 0 30.2%

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

      1. associate--l+ 30.2%

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

      2. associate-+r+ 30.2%

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

      3. associate-+r+ 30.2%

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

      4. +-commutative 30.2%

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

      5. +-commutative 30.2%

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

      6. associate-+r+ 30.2%

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

      7. *-commutative 30.2%

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

      8. +-commutative 30.2%

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

      9. associate-+r+ 30.2%

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

      10. div-sub 30.2%

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

   4. Simplified 30.2%

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

   5. Taylor expanded in t around inf 74.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e262

   1. Initial program 99.7%

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

   if 1e262 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.1%

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

   2. Taylor expanded in z around 0 27.9%

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

      1. associate--l+ 27.9%

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

      2. associate-+r+ 27.9%

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

      3. associate-+r+ 27.9%

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

      4. +-commutative 27.9%

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

      5. +-commutative 27.9%

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

      6. associate-+r+ 27.9%

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

      7. *-commutative 27.9%

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

      8. +-commutative 27.9%

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

      9. associate-+r+ 27.9%

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

      10. div-sub 27.9%

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

   4. Simplified 27.9%

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

      1. div-sub 27.9%

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

      2. associate-/l* 64.3%

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

      3. +-commutative 64.3%

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

      4. add-sqr-sqrt 28.2%

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

      5. sqrt-unprod 54.6%

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

      6. sqr-neg 54.6%

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

      7. *-commutative 54.6%

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

      8. distribute-lft-neg-out 54.6%

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

      9. *-commutative 54.6%

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

      10. distribute-lft-neg-out 54.6%

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

      11. sqrt-unprod 40.5%

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

      12. add-sqr-sqrt 63.7%

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

      13. div-inv 63.7%

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

      14. associate-*l* 78.2%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 91.9%

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

   8. Taylor expanded in y around inf 83.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{\left(x + t\right) + y} + \frac{y}{\left(x + t\right) + y}\right) + a\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+262}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;z + \left(\frac{a}{1 + \frac{x}{y}} - b \cdot \frac{y}{\left(x + t\right) + y}\right)\\ \end{array} \]

Alternative 6: 82.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{y}{t_1}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+23} \lor \neg \left(t \leq 1.8 \cdot 10^{+133}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t_1} + t_2\right) + a\\ \mathbf{else}:\\ \;\;\;\;z + \left(\frac{a}{1 + \frac{x}{y}} - b \cdot t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y)) (t_2 (/ y t_1)))
   (if (or (<= t -3.9e+23) (not (<= t 1.8e+133)))
     (+ (* z (+ (/ x t_1) t_2)) a)
     (+ z (- (/ a (+ 1.0 (/ x y))) (* b t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = y / t_1;
	double tmp;
	if ((t <= -3.9e+23) || !(t <= 1.8e+133)) {
		tmp = (z * ((x / t_1) + t_2)) + a;
	} else {
		tmp = z + ((a / (1.0 + (x / y))) - (b * 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 = (x + t) + y
    t_2 = y / t_1
    if ((t <= (-3.9d+23)) .or. (.not. (t <= 1.8d+133))) then
        tmp = (z * ((x / t_1) + t_2)) + a
    else
        tmp = z + ((a / (1.0d0 + (x / y))) - (b * 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 = (x + t) + y;
	double t_2 = y / t_1;
	double tmp;
	if ((t <= -3.9e+23) || !(t <= 1.8e+133)) {
		tmp = (z * ((x / t_1) + t_2)) + a;
	} else {
		tmp = z + ((a / (1.0 + (x / y))) - (b * t_2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = y / t_1
	tmp = 0
	if (t <= -3.9e+23) or not (t <= 1.8e+133):
		tmp = (z * ((x / t_1) + t_2)) + a
	else:
		tmp = z + ((a / (1.0 + (x / y))) - (b * t_2))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(y / t_1)
	tmp = 0.0
	if ((t <= -3.9e+23) || !(t <= 1.8e+133))
		tmp = Float64(Float64(z * Float64(Float64(x / t_1) + t_2)) + a);
	else
		tmp = Float64(z + Float64(Float64(a / Float64(1.0 + Float64(x / y))) - Float64(b * t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = y / t_1;
	tmp = 0.0;
	if ((t <= -3.9e+23) || ~((t <= 1.8e+133)))
		tmp = (z * ((x / t_1) + t_2)) + a;
	else
		tmp = z + ((a / (1.0 + (x / y))) - (b * t_2));
	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[(y / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t, -3.9e+23], N[Not[LessEqual[t, 1.8e+133]], $MachinePrecision]], N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(z + N[(N[(a / N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9e23 or 1.79999999999999989e133 < t

   1. Initial program 52.0%

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

   2. Taylor expanded in z around 0 61.7%

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

      1. associate--l+ 61.7%

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

      2. associate-+r+ 61.7%

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

      3. associate-+r+ 61.7%

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

      4. +-commutative 61.7%

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

      5. +-commutative 61.7%

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

      6. associate-+r+ 61.7%

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

      7. *-commutative 61.7%

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

      8. +-commutative 61.7%

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

      9. associate-+r+ 61.7%

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

      10. div-sub 61.7%

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

   4. Simplified 61.7%

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

   5. Taylor expanded in t around inf 80.3%

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

   if -3.9e23 < t < 1.79999999999999989e133

   1. Initial program 67.7%

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

   2. Taylor expanded in z around 0 76.9%

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

      1. associate--l+ 76.9%

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

      2. associate-+r+ 76.9%

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

      3. associate-+r+ 76.9%

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

      4. +-commutative 76.9%

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

      5. +-commutative 76.9%

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

      6. associate-+r+ 76.9%

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

      7. *-commutative 76.9%

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

      8. +-commutative 76.9%

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

      9. associate-+r+ 76.9%

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

      10. div-sub 76.9%

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

   4. Simplified 76.9%

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

      1. div-sub 76.9%

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

      2. associate-/l* 87.6%

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

      3. +-commutative 87.6%

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

      4. add-sqr-sqrt 50.1%

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

      5. sqrt-unprod 70.0%

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

      6. sqr-neg 70.0%

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

      7. *-commutative 70.0%

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

      8. distribute-lft-neg-out 70.0%

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

      9. *-commutative 70.0%

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

      10. distribute-lft-neg-out 70.0%

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

      11. sqrt-unprod 41.7%

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

      12. add-sqr-sqrt 73.3%

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

      13. div-inv 73.3%

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

      14. associate-*l* 76.4%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around inf 94.1%

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

   8. Taylor expanded in y around inf 86.9%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+23} \lor \neg \left(t \leq 1.8 \cdot 10^{+133}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{\left(x + t\right) + y} + \frac{y}{\left(x + t\right) + y}\right) + a\\ \mathbf{else}:\\ \;\;\;\;z + \left(\frac{a}{1 + \frac{x}{y}} - b \cdot \frac{y}{\left(x + t\right) + y}\right)\\ \end{array} \]

Alternative 7: 76.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+134}:\\ \;\;\;\;a + x \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+135}:\\ \;\;\;\;z + \left(\frac{a}{1 + \frac{x}{y}} - b \cdot \frac{y}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{t_1}{t + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y)))
   (if (<= t -2.6e+134)
     (+ a (* x (- (/ z t) (/ a t))))
     (if (<= t 5e+135)
       (+ z (- (/ a (+ 1.0 (/ x y))) (* b (/ y t_1))))
       (/ a (/ t_1 (+ t y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double tmp;
	if (t <= -2.6e+134) {
		tmp = a + (x * ((z / t) - (a / t)));
	} else if (t <= 5e+135) {
		tmp = z + ((a / (1.0 + (x / y))) - (b * (y / t_1)));
	} else {
		tmp = a / (t_1 / (t + y));
	}
	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 + t) + y
    if (t <= (-2.6d+134)) then
        tmp = a + (x * ((z / t) - (a / t)))
    else if (t <= 5d+135) then
        tmp = z + ((a / (1.0d0 + (x / y))) - (b * (y / t_1)))
    else
        tmp = a / (t_1 / (t + y))
    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 tmp;
	if (t <= -2.6e+134) {
		tmp = a + (x * ((z / t) - (a / t)));
	} else if (t <= 5e+135) {
		tmp = z + ((a / (1.0 + (x / y))) - (b * (y / t_1)));
	} else {
		tmp = a / (t_1 / (t + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	tmp = 0
	if t <= -2.6e+134:
		tmp = a + (x * ((z / t) - (a / t)))
	elif t <= 5e+135:
		tmp = z + ((a / (1.0 + (x / y))) - (b * (y / t_1)))
	else:
		tmp = a / (t_1 / (t + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	tmp = 0.0
	if (t <= -2.6e+134)
		tmp = Float64(a + Float64(x * Float64(Float64(z / t) - Float64(a / t))));
	elseif (t <= 5e+135)
		tmp = Float64(z + Float64(Float64(a / Float64(1.0 + Float64(x / y))) - Float64(b * Float64(y / t_1))));
	else
		tmp = Float64(a / Float64(t_1 / Float64(t + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	tmp = 0.0;
	if (t <= -2.6e+134)
		tmp = a + (x * ((z / t) - (a / t)));
	elseif (t <= 5e+135)
		tmp = z + ((a / (1.0 + (x / y))) - (b * (y / t_1)));
	else
		tmp = a / (t_1 / (t + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -2.6e+134], N[(a + N[(x * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+135], N[(z + N[(N[(a / N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a / N[(t$95$1 / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6000000000000002e134

   1. Initial program 48.4%

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

   2. Taylor expanded in y around 0 44.6%

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

   3. Taylor expanded in x around 0 65.3%

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

   if -2.6000000000000002e134 < t < 5.00000000000000029e135

   1. Initial program 67.1%

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

   2. Taylor expanded in z around 0 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-+r+ 76.2%

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

      3. associate-+r+ 76.2%

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

      4. +-commutative 76.2%

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

      5. +-commutative 76.2%

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

      6. associate-+r+ 76.2%

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

      7. *-commutative 76.2%

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

      8. +-commutative 76.2%

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

      9. associate-+r+ 76.2%

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

      10. div-sub 76.2%

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

   4. Simplified 76.2%

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

      1. div-sub 76.2%

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

      2. associate-/l* 88.7%

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

      3. +-commutative 88.7%

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

      4. add-sqr-sqrt 52.0%

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

      5. sqrt-unprod 70.0%

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

      6. sqr-neg 70.0%

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

      7. *-commutative 70.0%

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

      8. distribute-lft-neg-out 70.0%

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

      9. *-commutative 70.0%

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

      10. distribute-lft-neg-out 70.0%

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

      11. sqrt-unprod 41.4%

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

      12. add-sqr-sqrt 75.6%

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

      13. div-inv 75.6%

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

      14. associate-*l* 78.3%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 92.7%

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

   8. Taylor expanded in y around inf 83.1%

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

   if 5.00000000000000029e135 < t

   1. Initial program 49.3%

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

   2. Taylor expanded in a around inf 38.3%

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

      1. +-commutative 38.3%

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

      2. +-commutative 38.3%

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

      3. associate-+r+ 38.3%

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

      4. associate-/l* 71.0%

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

      5. associate-+r+ 71.0%

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

      6. +-commutative 71.0%

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

      7. associate-+r+ 71.0%

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

      8. +-commutative 71.0%

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

   4. Simplified 71.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+134}:\\ \;\;\;\;a + x \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+135}:\\ \;\;\;\;z + \left(\frac{a}{1 + \frac{x}{y}} - b \cdot \frac{y}{\left(x + t\right) + y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ \end{array} \]

Alternative 8: 57.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + a \cdot \frac{t + y}{x}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-93}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{-b}{\frac{t + y}{y}}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+152}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+226}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (* a (/ (+ t y) x)))) (t_2 (- (+ z a) b)))
   (if (<= x -3.7e+33)
     t_1
     (if (<= x -4.6e-93)
       a
       (if (<= x -1.2e-129)
         (/ (- b) (/ (+ t y) y))
         (if (<= x 1.1e+86)
           t_2
           (if (<= x 8.2e+152)
             (/ z (/ (+ x t) x))
             (if (<= x 1.55e+226) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a * ((t + y) / x));
	double t_2 = (z + a) - b;
	double tmp;
	if (x <= -3.7e+33) {
		tmp = t_1;
	} else if (x <= -4.6e-93) {
		tmp = a;
	} else if (x <= -1.2e-129) {
		tmp = -b / ((t + y) / y);
	} else if (x <= 1.1e+86) {
		tmp = t_2;
	} else if (x <= 8.2e+152) {
		tmp = z / ((x + t) / x);
	} else if (x <= 1.55e+226) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + (a * ((t + y) / x))
    t_2 = (z + a) - b
    if (x <= (-3.7d+33)) then
        tmp = t_1
    else if (x <= (-4.6d-93)) then
        tmp = a
    else if (x <= (-1.2d-129)) then
        tmp = -b / ((t + y) / y)
    else if (x <= 1.1d+86) then
        tmp = t_2
    else if (x <= 8.2d+152) then
        tmp = z / ((x + t) / x)
    else if (x <= 1.55d+226) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a * ((t + y) / x));
	double t_2 = (z + a) - b;
	double tmp;
	if (x <= -3.7e+33) {
		tmp = t_1;
	} else if (x <= -4.6e-93) {
		tmp = a;
	} else if (x <= -1.2e-129) {
		tmp = -b / ((t + y) / y);
	} else if (x <= 1.1e+86) {
		tmp = t_2;
	} else if (x <= 8.2e+152) {
		tmp = z / ((x + t) / x);
	} else if (x <= 1.55e+226) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a * ((t + y) / x))
	t_2 = (z + a) - b
	tmp = 0
	if x <= -3.7e+33:
		tmp = t_1
	elif x <= -4.6e-93:
		tmp = a
	elif x <= -1.2e-129:
		tmp = -b / ((t + y) / y)
	elif x <= 1.1e+86:
		tmp = t_2
	elif x <= 8.2e+152:
		tmp = z / ((x + t) / x)
	elif x <= 1.55e+226:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a * Float64(Float64(t + y) / x)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (x <= -3.7e+33)
		tmp = t_1;
	elseif (x <= -4.6e-93)
		tmp = a;
	elseif (x <= -1.2e-129)
		tmp = Float64(Float64(-b) / Float64(Float64(t + y) / y));
	elseif (x <= 1.1e+86)
		tmp = t_2;
	elseif (x <= 8.2e+152)
		tmp = Float64(z / Float64(Float64(x + t) / x));
	elseif (x <= 1.55e+226)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a * ((t + y) / x));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (x <= -3.7e+33)
		tmp = t_1;
	elseif (x <= -4.6e-93)
		tmp = a;
	elseif (x <= -1.2e-129)
		tmp = -b / ((t + y) / y);
	elseif (x <= 1.1e+86)
		tmp = t_2;
	elseif (x <= 8.2e+152)
		tmp = z / ((x + t) / x);
	elseif (x <= 1.55e+226)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(a * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[x, -3.7e+33], t$95$1, If[LessEqual[x, -4.6e-93], a, If[LessEqual[x, -1.2e-129], N[((-b) / N[(N[(t + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+86], t$95$2, If[LessEqual[x, 8.2e+152], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+226], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.6999999999999999e33 or 1.54999999999999988e226 < x

   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 x around inf 43.5%

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

      1. associate--l+ 43.6%

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

      2. +-commutative 43.6%

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

      3. associate-/l* 49.6%

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

      4. +-commutative 49.6%

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

      5. associate-/l* 49.6%

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

      6. associate-/l* 56.9%

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

      7. +-commutative 56.9%

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

      8. associate-/l* 65.1%

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

      9. +-commutative 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in a around inf 60.4%

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

      1. distribute-lft-in 60.4%

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

      2. associate-*r/ 55.6%

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

      3. *-commutative 55.6%

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

      4. associate-*r/ 60.4%

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

      5. associate-*r/ 56.2%

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

      6. *-commutative 56.2%

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

      7. associate-*r/ 60.8%

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

      8. distribute-rgt-in 60.8%

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

      9. associate-*l/ 51.5%

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

      10. associate-*r/ 60.4%

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

      11. +-commutative 60.4%

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

   7. Simplified 60.4%

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

   if -3.6999999999999999e33 < x < -4.5999999999999996e-93

   1. Initial program 55.4%

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

   2. Taylor expanded in t around inf 59.7%

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

   if -4.5999999999999996e-93 < x < -1.19999999999999994e-129

   1. Initial program 89.3%

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

   2. Taylor expanded in b around inf 56.6%

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

      1. associate-*r* 56.6%

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

      2. mul-1-neg 56.6%

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

   4. Simplified 56.6%

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

   5. Taylor expanded in x around 0 56.6%

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

      1. associate-/l* 66.9%

         \[\leadsto -1 \cdot \color{blue}{\frac{b}{\frac{t + y}{y}}} \]

      2. associate-*r/ 66.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{\frac{t + y}{y}}} \]

      3. mul-1-neg 66.9%

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

      4. +-commutative 66.9%

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

   7. Simplified 66.9%

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

   if -1.19999999999999994e-129 < x < 1.10000000000000002e86 or 8.1999999999999996e152 < x < 1.54999999999999988e226

   1. Initial program 67.3%

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

   2. Taylor expanded in y around inf 63.9%

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

   if 1.10000000000000002e86 < x < 8.1999999999999996e152

   1. Initial program 72.7%

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

   2. Taylor expanded in z around inf 50.5%

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

      1. +-commutative 50.5%

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

   4. Simplified 50.5%

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

   5. Taylor expanded in y around 0 50.5%

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

      1. *-commutative 50.5%

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

      2. associate-/l* 63.8%

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

      3. +-commutative 63.8%

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

   7. Simplified 63.8%

      \[\leadsto \color{blue}{\frac{z}{\frac{x + t}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+33}:\\ \;\;\;\;z + a \cdot \frac{t + y}{x}\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-93}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{-b}{\frac{t + y}{y}}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+86}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+152}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+226}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t + y}{x}\\ \end{array} \]

Alternative 9: 57.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z + a \cdot \frac{t + y}{x}\\ \mathbf{if}\;x \leq -9 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-93}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{-b}{\frac{\left(x + t\right) + y}{y}}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+148}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ z (* a (/ (+ t y) x)))))
   (if (<= x -9e+40)
     t_2
     (if (<= x -4e-93)
       a
       (if (<= x -1.2e-129)
         (/ (- b) (/ (+ (+ x t) y) y))
         (if (<= x 1.9e+86)
           t_1
           (if (<= x 6.2e+148)
             (/ z (/ (+ x t) x))
             (if (<= x 1.7e+226) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + (a * ((t + y) / x));
	double tmp;
	if (x <= -9e+40) {
		tmp = t_2;
	} else if (x <= -4e-93) {
		tmp = a;
	} else if (x <= -1.2e-129) {
		tmp = -b / (((x + t) + y) / y);
	} else if (x <= 1.9e+86) {
		tmp = t_1;
	} else if (x <= 6.2e+148) {
		tmp = z / ((x + t) / x);
	} else if (x <= 1.7e+226) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z + (a * ((t + y) / x))
    if (x <= (-9d+40)) then
        tmp = t_2
    else if (x <= (-4d-93)) then
        tmp = a
    else if (x <= (-1.2d-129)) then
        tmp = -b / (((x + t) + y) / y)
    else if (x <= 1.9d+86) then
        tmp = t_1
    else if (x <= 6.2d+148) then
        tmp = z / ((x + t) / x)
    else if (x <= 1.7d+226) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + (a * ((t + y) / x));
	double tmp;
	if (x <= -9e+40) {
		tmp = t_2;
	} else if (x <= -4e-93) {
		tmp = a;
	} else if (x <= -1.2e-129) {
		tmp = -b / (((x + t) + y) / y);
	} else if (x <= 1.9e+86) {
		tmp = t_1;
	} else if (x <= 6.2e+148) {
		tmp = z / ((x + t) / x);
	} else if (x <= 1.7e+226) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z + (a * ((t + y) / x))
	tmp = 0
	if x <= -9e+40:
		tmp = t_2
	elif x <= -4e-93:
		tmp = a
	elif x <= -1.2e-129:
		tmp = -b / (((x + t) + y) / y)
	elif x <= 1.9e+86:
		tmp = t_1
	elif x <= 6.2e+148:
		tmp = z / ((x + t) / x)
	elif x <= 1.7e+226:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z + Float64(a * Float64(Float64(t + y) / x)))
	tmp = 0.0
	if (x <= -9e+40)
		tmp = t_2;
	elseif (x <= -4e-93)
		tmp = a;
	elseif (x <= -1.2e-129)
		tmp = Float64(Float64(-b) / Float64(Float64(Float64(x + t) + y) / y));
	elseif (x <= 1.9e+86)
		tmp = t_1;
	elseif (x <= 6.2e+148)
		tmp = Float64(z / Float64(Float64(x + t) / x));
	elseif (x <= 1.7e+226)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = z + (a * ((t + y) / x));
	tmp = 0.0;
	if (x <= -9e+40)
		tmp = t_2;
	elseif (x <= -4e-93)
		tmp = a;
	elseif (x <= -1.2e-129)
		tmp = -b / (((x + t) + y) / y);
	elseif (x <= 1.9e+86)
		tmp = t_1;
	elseif (x <= 6.2e+148)
		tmp = z / ((x + t) / x);
	elseif (x <= 1.7e+226)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(a * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+40], t$95$2, If[LessEqual[x, -4e-93], a, If[LessEqual[x, -1.2e-129], N[((-b) / N[(N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+86], t$95$1, If[LessEqual[x, 6.2e+148], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+226], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.00000000000000064e40 or 1.69999999999999989e226 < x

   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 x around inf 43.5%

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

      1. associate--l+ 43.6%

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

      2. +-commutative 43.6%

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

      3. associate-/l* 49.6%

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

      4. +-commutative 49.6%

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

      5. associate-/l* 49.6%

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

      6. associate-/l* 56.9%

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

      7. +-commutative 56.9%

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

      8. associate-/l* 65.1%

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

      9. +-commutative 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in a around inf 60.4%

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

      1. distribute-lft-in 60.4%

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

      2. associate-*r/ 55.6%

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

      3. *-commutative 55.6%

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

      4. associate-*r/ 60.4%

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

      5. associate-*r/ 56.2%

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

      6. *-commutative 56.2%

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

      7. associate-*r/ 60.8%

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

      8. distribute-rgt-in 60.8%

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

      9. associate-*l/ 51.5%

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

      10. associate-*r/ 60.4%

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

      11. +-commutative 60.4%

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

   7. Simplified 60.4%

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

   if -9.00000000000000064e40 < x < -3.9999999999999996e-93

   1. Initial program 55.4%

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

   2. Taylor expanded in t around inf 59.7%

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

   if -3.9999999999999996e-93 < x < -1.19999999999999994e-129

   1. Initial program 89.3%

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

   2. Taylor expanded in b around inf 56.6%

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

      1. *-commutative 56.6%

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

      2. +-commutative 56.6%

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

      3. associate-+r+ 56.6%

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

      4. *-commutative 56.6%

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

      5. associate-/l* 66.9%

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

      6. associate-*r/ 66.9%

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

      7. mul-1-neg 66.9%

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

      8. +-commutative 66.9%

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

      9. associate-+l+ 66.9%

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

   4. Simplified 66.9%

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

   if -1.19999999999999994e-129 < x < 1.89999999999999989e86 or 6.19999999999999951e148 < x < 1.69999999999999989e226

   1. Initial program 67.3%

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

   2. Taylor expanded in y around inf 63.9%

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

   if 1.89999999999999989e86 < x < 6.19999999999999951e148

   1. Initial program 72.7%

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

   2. Taylor expanded in z around inf 50.5%

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

      1. +-commutative 50.5%

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

   4. Simplified 50.5%

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

   5. Taylor expanded in y around 0 50.5%

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

      1. *-commutative 50.5%

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

      2. associate-/l* 63.8%

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

      3. +-commutative 63.8%

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

   7. Simplified 63.8%

      \[\leadsto \color{blue}{\frac{z}{\frac{x + t}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+40}:\\ \;\;\;\;z + a \cdot \frac{t + y}{x}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-93}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{-b}{\frac{\left(x + t\right) + y}{y}}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+86}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+148}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+226}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t + y}{x}\\ \end{array} \]

Alternative 10: 58.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-164}:\\ \;\;\;\;z + a \cdot \frac{t + y}{x}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-123}:\\ \;\;\;\;a + x \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-67}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4e-40)
     t_1
     (if (<= y 4e-164)
       (+ z (* a (/ (+ t y) x)))
       (if (<= y 3.4e-123)
         (+ a (* x (- (/ z t) (/ a t))))
         (if (<= y 2.8e-67) (+ z (* y (- (/ a x) (/ b x)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4e-40) {
		tmp = t_1;
	} else if (y <= 4e-164) {
		tmp = z + (a * ((t + y) / x));
	} else if (y <= 3.4e-123) {
		tmp = a + (x * ((z / t) - (a / t)));
	} else if (y <= 2.8e-67) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-4d-40)) then
        tmp = t_1
    else if (y <= 4d-164) then
        tmp = z + (a * ((t + y) / x))
    else if (y <= 3.4d-123) then
        tmp = a + (x * ((z / t) - (a / t)))
    else if (y <= 2.8d-67) then
        tmp = z + (y * ((a / x) - (b / x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4e-40) {
		tmp = t_1;
	} else if (y <= 4e-164) {
		tmp = z + (a * ((t + y) / x));
	} else if (y <= 3.4e-123) {
		tmp = a + (x * ((z / t) - (a / t)));
	} else if (y <= 2.8e-67) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -4e-40:
		tmp = t_1
	elif y <= 4e-164:
		tmp = z + (a * ((t + y) / x))
	elif y <= 3.4e-123:
		tmp = a + (x * ((z / t) - (a / t)))
	elif y <= 2.8e-67:
		tmp = z + (y * ((a / x) - (b / x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4e-40)
		tmp = t_1;
	elseif (y <= 4e-164)
		tmp = Float64(z + Float64(a * Float64(Float64(t + y) / x)));
	elseif (y <= 3.4e-123)
		tmp = Float64(a + Float64(x * Float64(Float64(z / t) - Float64(a / t))));
	elseif (y <= 2.8e-67)
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4e-40)
		tmp = t_1;
	elseif (y <= 4e-164)
		tmp = z + (a * ((t + y) / x));
	elseif (y <= 3.4e-123)
		tmp = a + (x * ((z / t) - (a / t)));
	elseif (y <= 2.8e-67)
		tmp = z + (y * ((a / x) - (b / x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4e-40], t$95$1, If[LessEqual[y, 4e-164], N[(z + N[(a * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-123], N[(a + N[(x * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-67], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.9999999999999997e-40 or 2.8000000000000001e-67 < y

   1. Initial program 45.7%

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

   2. Taylor expanded in y around inf 69.6%

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

   if -3.9999999999999997e-40 < y < 3.99999999999999985e-164

   1. Initial program 84.0%

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

   2. Taylor expanded in x around inf 48.7%

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

      1. associate--l+ 50.8%

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

      2. +-commutative 50.8%

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

      3. associate-/l* 53.2%

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

      4. +-commutative 53.2%

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

      5. associate-/l* 51.0%

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

      6. associate-/l* 50.8%

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

      7. +-commutative 50.8%

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

      8. associate-/l* 50.9%

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

      9. +-commutative 50.9%

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

   4. Simplified 50.9%

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

   5. Taylor expanded in a around inf 50.4%

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

      1. distribute-lft-in 50.4%

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

      2. associate-*r/ 48.0%

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

      3. *-commutative 48.0%

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

      4. associate-*r/ 46.1%

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

      5. associate-*r/ 46.1%

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

      6. *-commutative 46.1%

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

      7. associate-*r/ 46.0%

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

      8. distribute-rgt-in 46.1%

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

      9. associate-*l/ 48.0%

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

      10. associate-*r/ 50.4%

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

      11. +-commutative 50.4%

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

   7. Simplified 50.4%

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

   if 3.99999999999999985e-164 < y < 3.4000000000000001e-123

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0 25.5%

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

   3. Taylor expanded in x around 0 61.6%

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

   if 3.4000000000000001e-123 < y < 2.8000000000000001e-67

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 56.4%

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

      1. associate--l+ 56.4%

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

      2. +-commutative 56.4%

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

      3. associate-/l* 53.3%

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

      4. +-commutative 53.3%

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

      5. associate-/l* 52.6%

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

      6. associate-/l* 52.6%

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

      7. +-commutative 52.6%

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

      8. associate-/l* 52.7%

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

      9. +-commutative 52.7%

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

   4. Simplified 52.7%

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

   5. Taylor expanded in y around inf 56.9%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-40}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-164}:\\ \;\;\;\;z + a \cdot \frac{t + y}{x}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-123}:\\ \;\;\;\;a + x \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-67}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 58.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-171}:\\ \;\;\;\;z + a \cdot \frac{t + y}{x}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (/ (+ (+ x t) y) (+ t y)))) (t_2 (- (+ z a) b)))
   (if (<= y -1.6e-66)
     t_2
     (if (<= y 3e-285)
       t_1
       (if (<= y 2.7e-171)
         (+ z (* a (/ (+ t y) x)))
         (if (<= y 1.95e+39) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (((x + t) + y) / (t + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.6e-66) {
		tmp = t_2;
	} else if (y <= 3e-285) {
		tmp = t_1;
	} else if (y <= 2.7e-171) {
		tmp = z + (a * ((t + y) / x));
	} else if (y <= 1.95e+39) {
		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 = a / (((x + t) + y) / (t + y))
    t_2 = (z + a) - b
    if (y <= (-1.6d-66)) then
        tmp = t_2
    else if (y <= 3d-285) then
        tmp = t_1
    else if (y <= 2.7d-171) then
        tmp = z + (a * ((t + y) / x))
    else if (y <= 1.95d+39) 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 = a / (((x + t) + y) / (t + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.6e-66) {
		tmp = t_2;
	} else if (y <= 3e-285) {
		tmp = t_1;
	} else if (y <= 2.7e-171) {
		tmp = z + (a * ((t + y) / x));
	} else if (y <= 1.95e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (((x + t) + y) / (t + y))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -1.6e-66:
		tmp = t_2
	elif y <= 3e-285:
		tmp = t_1
	elif y <= 2.7e-171:
		tmp = z + (a * ((t + y) / x))
	elif y <= 1.95e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(Float64(Float64(x + t) + y) / Float64(t + y)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.6e-66)
		tmp = t_2;
	elseif (y <= 3e-285)
		tmp = t_1;
	elseif (y <= 2.7e-171)
		tmp = Float64(z + Float64(a * Float64(Float64(t + y) / x)));
	elseif (y <= 1.95e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (((x + t) + y) / (t + y));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.6e-66)
		tmp = t_2;
	elseif (y <= 3e-285)
		tmp = t_1;
	elseif (y <= 2.7e-171)
		tmp = z + (a * ((t + y) / x));
	elseif (y <= 1.95e+39)
		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[(a / N[(N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.6e-66], t$95$2, If[LessEqual[y, 3e-285], t$95$1, If[LessEqual[y, 2.7e-171], N[(z + N[(a * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999991e-66 or 1.95e39 < y

   1. Initial program 46.0%

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

   2. Taylor expanded in y around inf 71.0%

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

   if -1.59999999999999991e-66 < y < 3.00000000000000003e-285 or 2.70000000000000014e-171 < y < 1.95e39

   1. Initial program 78.6%

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

   2. Taylor expanded in a around inf 38.3%

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

      1. +-commutative 38.3%

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

      2. +-commutative 38.3%

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

      3. associate-+r+ 38.3%

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

      4. associate-/l* 55.9%

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

      5. associate-+r+ 55.9%

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

      6. +-commutative 55.9%

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

      7. associate-+r+ 55.9%

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

      8. +-commutative 55.9%

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

   4. Simplified 55.9%

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

   if 3.00000000000000003e-285 < y < 2.70000000000000014e-171

   1. Initial program 82.9%

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

   2. Taylor expanded in x around inf 56.0%

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

      1. associate--l+ 56.0%

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

      2. +-commutative 56.0%

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

      3. associate-/l* 58.8%

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

      4. +-commutative 58.8%

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

      5. associate-/l* 58.8%

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

      6. associate-/l* 58.8%

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

      7. +-commutative 58.8%

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

      8. associate-/l* 61.6%

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

      9. +-commutative 61.6%

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

   4. Simplified 61.6%

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

   5. Taylor expanded in a around inf 61.8%

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

      1. distribute-lft-in 61.8%

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

      2. associate-*r/ 59.1%

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

      3. *-commutative 59.1%

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

      4. associate-*r/ 56.1%

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

      5. associate-*r/ 56.1%

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

      6. *-commutative 56.1%

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

      7. associate-*r/ 55.7%

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

      8. distribute-rgt-in 56.1%

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

      9. associate-*l/ 59.1%

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

      10. associate-*r/ 61.8%

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

      11. +-commutative 61.8%

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

   7. Simplified 61.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-66}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-285}:\\ \;\;\;\;\frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-171}:\\ \;\;\;\;z + a \cdot \frac{t + y}{x}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+39}:\\ \;\;\;\;\frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12: 68.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-46} \lor \neg \left(y \leq 3.5 \cdot 10^{-177}\right):\\ \;\;\;\;z + \left(\frac{a}{\frac{\left(x + t\right) + y}{t + y}} - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.6e-46) (not (<= y 3.5e-177)))
   (+ z (- (/ a (/ (+ (+ x t) y) (+ t y))) b))
   (/ (+ (* t a) (* z x)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.6e-46) || !(y <= 3.5e-177)) {
		tmp = z + ((a / (((x + t) + y) / (t + y))) - b);
	} else {
		tmp = ((t * a) + (z * x)) / (x + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8.6d-46)) .or. (.not. (y <= 3.5d-177))) then
        tmp = z + ((a / (((x + t) + y) / (t + y))) - b)
    else
        tmp = ((t * a) + (z * x)) / (x + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.6e-46) || !(y <= 3.5e-177)) {
		tmp = z + ((a / (((x + t) + y) / (t + y))) - b);
	} else {
		tmp = ((t * a) + (z * x)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.6e-46) or not (y <= 3.5e-177):
		tmp = z + ((a / (((x + t) + y) / (t + y))) - b)
	else:
		tmp = ((t * a) + (z * x)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.6e-46) || !(y <= 3.5e-177))
		tmp = Float64(z + Float64(Float64(a / Float64(Float64(Float64(x + t) + y) / Float64(t + y))) - b));
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.6e-46) || ~((y <= 3.5e-177)))
		tmp = z + ((a / (((x + t) + y) / (t + y))) - b);
	else
		tmp = ((t * a) + (z * x)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.6e-46], N[Not[LessEqual[y, 3.5e-177]], $MachinePrecision]], N[(z + N[(N[(a / N[(N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.6000000000000007e-46 or 3.5000000000000002e-177 < y

   1. Initial program 49.5%

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

   2. Taylor expanded in z around 0 60.8%

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

      1. associate--l+ 60.8%

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

      2. associate-+r+ 60.8%

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

      3. associate-+r+ 60.8%

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

      4. +-commutative 60.8%

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

      5. +-commutative 60.8%

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

      6. associate-+r+ 60.8%

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

      7. *-commutative 60.8%

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

      8. +-commutative 60.8%

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

      9. associate-+r+ 60.8%

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

      10. div-sub 60.8%

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

   4. Simplified 60.8%

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

      1. div-sub 60.8%

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

      2. associate-/l* 81.8%

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

      3. +-commutative 81.8%

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

      4. add-sqr-sqrt 43.1%

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

      5. sqrt-unprod 63.3%

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

      6. sqr-neg 63.3%

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

      7. *-commutative 63.3%

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

      8. distribute-lft-neg-out 63.3%

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

      9. *-commutative 63.3%

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

      10. distribute-lft-neg-out 63.3%

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

      11. sqrt-unprod 35.5%

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

      12. add-sqr-sqrt 71.0%

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

      13. div-inv 71.0%

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

      14. associate-*l* 78.1%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 87.2%

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

   8. Taylor expanded in y around inf 74.3%

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

   if -8.6000000000000007e-46 < y < 3.5000000000000002e-177

   1. Initial program 85.5%

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

   2. Taylor expanded in y around 0 69.8%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-46} \lor \neg \left(y \leq 3.5 \cdot 10^{-177}\right):\\ \;\;\;\;z + \left(\frac{a}{\frac{\left(x + t\right) + y}{t + y}} - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \end{array} \]

Alternative 13: 56.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{a}{\frac{t_1}{t + y}}\\ \mathbf{if}\;a \leq -5800:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-145}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y)) (t_2 (/ a (/ t_1 (+ t y)))))
   (if (<= a -5800.0)
     t_2
     (if (<= a -3.4e-145)
       (- (+ z a) b)
       (if (<= a 6.6e+16) (/ (+ x y) (/ t_1 z)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = a / (t_1 / (t + y));
	double tmp;
	if (a <= -5800.0) {
		tmp = t_2;
	} else if (a <= -3.4e-145) {
		tmp = (z + a) - b;
	} else if (a <= 6.6e+16) {
		tmp = (x + y) / (t_1 / z);
	} 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 = (x + t) + y
    t_2 = a / (t_1 / (t + y))
    if (a <= (-5800.0d0)) then
        tmp = t_2
    else if (a <= (-3.4d-145)) then
        tmp = (z + a) - b
    else if (a <= 6.6d+16) then
        tmp = (x + y) / (t_1 / z)
    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 = (x + t) + y;
	double t_2 = a / (t_1 / (t + y));
	double tmp;
	if (a <= -5800.0) {
		tmp = t_2;
	} else if (a <= -3.4e-145) {
		tmp = (z + a) - b;
	} else if (a <= 6.6e+16) {
		tmp = (x + y) / (t_1 / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = a / (t_1 / (t + y))
	tmp = 0
	if a <= -5800.0:
		tmp = t_2
	elif a <= -3.4e-145:
		tmp = (z + a) - b
	elif a <= 6.6e+16:
		tmp = (x + y) / (t_1 / z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(a / Float64(t_1 / Float64(t + y)))
	tmp = 0.0
	if (a <= -5800.0)
		tmp = t_2;
	elseif (a <= -3.4e-145)
		tmp = Float64(Float64(z + a) - b);
	elseif (a <= 6.6e+16)
		tmp = Float64(Float64(x + y) / Float64(t_1 / z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = a / (t_1 / (t + y));
	tmp = 0.0;
	if (a <= -5800.0)
		tmp = t_2;
	elseif (a <= -3.4e-145)
		tmp = (z + a) - b;
	elseif (a <= 6.6e+16)
		tmp = (x + y) / (t_1 / z);
	else
		tmp = t_2;
	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[(a / N[(t$95$1 / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5800.0], t$95$2, If[LessEqual[a, -3.4e-145], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, 6.6e+16], N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5800 or 6.6e16 < a

   1. Initial program 47.7%

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

   2. Taylor expanded in a around inf 34.5%

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

      1. +-commutative 34.5%

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

      2. +-commutative 34.5%

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

      3. associate-+r+ 34.5%

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

      4. associate-/l* 72.4%

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

      5. associate-+r+ 72.4%

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

      6. +-commutative 72.4%

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

      7. associate-+r+ 72.4%

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

      8. +-commutative 72.4%

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

   4. Simplified 72.4%

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

   if -5800 < a < -3.3999999999999999e-145

   1. Initial program 76.2%

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

   2. Taylor expanded in y around inf 63.2%

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

   if -3.3999999999999999e-145 < a < 6.6e16

   1. Initial program 74.6%

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

   2. Taylor expanded in z around inf 50.0%

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

      1. +-commutative 50.0%

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

      2. associate-+r+ 50.0%

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

      3. *-commutative 50.0%

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

      4. associate-/l* 56.6%

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

      5. +-commutative 56.6%

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

      6. +-commutative 56.6%

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

      7. associate-+l+ 56.6%

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

   4. Simplified 56.6%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5800:\\ \;\;\;\;\frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-145}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + y}{\frac{\left(x + t\right) + y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ \end{array} \]

Alternative 14: 63.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-170}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;\frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.55e-41)
     t_1
     (if (<= y 6e-170)
       (/ (+ (* t a) (* z x)) (+ x t))
       (if (<= y 2.6e+39) (/ a (/ (+ (+ x t) y) (+ t y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.55e-41) {
		tmp = t_1;
	} else if (y <= 6e-170) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (y <= 2.6e+39) {
		tmp = a / (((x + t) + y) / (t + y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.55d-41)) then
        tmp = t_1
    else if (y <= 6d-170) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if (y <= 2.6d+39) then
        tmp = a / (((x + t) + y) / (t + y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.55e-41) {
		tmp = t_1;
	} else if (y <= 6e-170) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (y <= 2.6e+39) {
		tmp = a / (((x + t) + y) / (t + y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.55e-41:
		tmp = t_1
	elif y <= 6e-170:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif y <= 2.6e+39:
		tmp = a / (((x + t) + y) / (t + y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.55e-41)
		tmp = t_1;
	elseif (y <= 6e-170)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif (y <= 2.6e+39)
		tmp = Float64(a / Float64(Float64(Float64(x + t) + y) / Float64(t + y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.55e-41)
		tmp = t_1;
	elseif (y <= 6e-170)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif (y <= 2.6e+39)
		tmp = a / (((x + t) + y) / (t + y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.55e-41], t$95$1, If[LessEqual[y, 6e-170], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+39], N[(a / N[(N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e-41 or 2.6e39 < y

   1. Initial program 44.3%

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

   2. Taylor expanded in y around inf 72.0%

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

   if -1.55e-41 < y < 6.00000000000000027e-170

   1. Initial program 83.7%

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

   2. Taylor expanded in y around 0 68.4%

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

   if 6.00000000000000027e-170 < y < 2.6e39

   1. Initial program 70.9%

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

   2. Taylor expanded in a around inf 33.7%

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

      1. +-commutative 33.7%

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

      2. +-commutative 33.7%

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

      3. associate-+r+ 33.7%

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

      4. associate-/l* 62.8%

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

      5. associate-+r+ 62.8%

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

      6. +-commutative 62.8%

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

      7. associate-+r+ 62.8%

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

      8. +-commutative 62.8%

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

   4. Simplified 62.8%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-41}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-170}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;\frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 15: 56.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-40} \lor \neg \left(y \leq 2.5 \cdot 10^{-170}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.6e-40) (not (<= y 2.5e-170)))
   (- (+ z a) b)
   (+ z (* y (/ a x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.6e-40) || !(y <= 2.5e-170)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (y * (a / 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 <= (-4.6d-40)) .or. (.not. (y <= 2.5d-170))) then
        tmp = (z + a) - b
    else
        tmp = z + (y * (a / 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 <= -4.6e-40) || !(y <= 2.5e-170)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (y * (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.6e-40) or not (y <= 2.5e-170):
		tmp = (z + a) - b
	else:
		tmp = z + (y * (a / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.6e-40) || !(y <= 2.5e-170))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(y * Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.6e-40) || ~((y <= 2.5e-170)))
		tmp = (z + a) - b;
	else
		tmp = z + (y * (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.6e-40], N[Not[LessEqual[y, 2.5e-170]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6e-40 or 2.50000000000000005e-170 < y

   1. Initial program 49.7%

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

   2. Taylor expanded in y around inf 65.2%

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

   if -4.6e-40 < y < 2.50000000000000005e-170

   1. Initial program 83.9%

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

   2. Taylor expanded in x around inf 48.9%

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

      1. associate--l+ 51.1%

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

      2. +-commutative 51.1%

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

      3. associate-/l* 53.5%

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

      4. +-commutative 53.5%

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

      5. associate-/l* 51.2%

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

      6. associate-/l* 51.1%

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

      7. +-commutative 51.1%

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

      8. associate-/l* 51.2%

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

      9. +-commutative 51.2%

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

   4. Simplified 51.2%

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

   5. Taylor expanded in a around -inf 48.3%

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

   6. Taylor expanded in t around 0 40.4%

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

      1. *-commutative 40.4%

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

      2. associate-*r/ 39.4%

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

   8. Simplified 39.4%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-40} \lor \neg \left(y \leq 2.5 \cdot 10^{-170}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \end{array} \]

Alternative 16: 58.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-40} \lor \neg \left(y \leq 3 \cdot 10^{-166}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + \frac{a}{\frac{x}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.8e-40) (not (<= y 3e-166)))
   (- (+ z a) b)
   (+ z (/ a (/ x t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.8e-40) || !(y <= 3e-166)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a / (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.8d-40)) .or. (.not. (y <= 3d-166))) then
        tmp = (z + a) - b
    else
        tmp = z + (a / (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.8e-40) || !(y <= 3e-166)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a / (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.8e-40) or not (y <= 3e-166):
		tmp = (z + a) - b
	else:
		tmp = z + (a / (x / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.8e-40) || !(y <= 3e-166))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(a / Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.8e-40) || ~((y <= 3e-166)))
		tmp = (z + a) - b;
	else
		tmp = z + (a / (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.8e-40], N[Not[LessEqual[y, 3e-166]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(a / N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999999e-40 or 3.0000000000000003e-166 < y

   1. Initial program 49.4%

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

   2. Taylor expanded in y around inf 65.5%

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

   if -3.7999999999999999e-40 < y < 3.0000000000000003e-166

   1. Initial program 84.0%

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

   2. Taylor expanded in x around inf 48.7%

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

      1. associate--l+ 50.8%

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

      2. +-commutative 50.8%

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

      3. associate-/l* 53.2%

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

      4. +-commutative 53.2%

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

      5. associate-/l* 51.0%

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

      6. associate-/l* 50.8%

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

      7. +-commutative 50.8%

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

      8. associate-/l* 50.9%

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

      9. +-commutative 50.9%

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

   4. Simplified 50.9%

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

   5. Taylor expanded in a around -inf 48.0%

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

   6. Taylor expanded in y around 0 44.2%

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

      1. +-commutative 44.2%

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

      2. associate-/l* 46.6%

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

   8. Simplified 46.6%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-40} \lor \neg \left(y \leq 3 \cdot 10^{-166}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + \frac{a}{\frac{x}{t}}\\ \end{array} \]

Alternative 17: 56.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-182} \lor \neg \left(y \leq 1.42 \cdot 10^{-168}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e-182) (not (<= y 1.42e-168))) (- (+ z a) b) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e-182) || !(y <= 1.42e-168)) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.15d-182)) .or. (.not. (y <= 1.42d-168))) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e-182) || !(y <= 1.42e-168)) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.15e-182) or not (y <= 1.42e-168):
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e-182) || !(y <= 1.42e-168))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.15e-182) || ~((y <= 1.42e-168)))
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e-182], N[Not[LessEqual[y, 1.42e-168]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-182 or 1.4199999999999999e-168 < y

   1. Initial program 56.3%

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

   2. Taylor expanded in y around inf 60.1%

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

   if -1.15e-182 < y < 1.4199999999999999e-168

   1. Initial program 79.9%

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

   2. Taylor expanded in x around inf 39.1%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-182} \lor \neg \left(y \leq 1.42 \cdot 10^{-168}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 18: 45.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-54}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.75e-54) a (if (<= a 1.35e+33) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.75e-54) {
		tmp = a;
	} else if (a <= 1.35e+33) {
		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 <= (-1.75d-54)) then
        tmp = a
    else if (a <= 1.35d+33) 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 <= -1.75e-54) {
		tmp = a;
	} else if (a <= 1.35e+33) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.75e-54:
		tmp = a
	elif a <= 1.35e+33:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.75e-54)
		tmp = a;
	elseif (a <= 1.35e+33)
		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 <= -1.75e-54)
		tmp = a;
	elseif (a <= 1.35e+33)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.75e-54], a, If[LessEqual[a, 1.35e+33], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -1.74999999999999991e-54 or 1.34999999999999996e33 < a

   1. Initial program 49.4%

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

   2. Taylor expanded in t around inf 53.1%

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

   if -1.74999999999999991e-54 < a < 1.34999999999999996e33

   1. Initial program 75.0%

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

   2. Taylor expanded in x around inf 41.7%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-54}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 19: 32.7% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.6%

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

2. Taylor expanded in t around inf 35.0%

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

3. Final simplification 35.0%

   \[\leadsto a \]

Developer target: 82.7% 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 2023301 
(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)))