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

Percentage Accurate: 63.3% → 99.2%

Time: 24.3s

Alternatives: 12

Speedup: 1.2×

• could not determine a ground truth

  1. x = 1.0184332847130283e+212
  2. y = -2.1981725969532847e+89
  3. z = 7.527053569241403e-282
  4. t = -4.460256471056316e+265
  5. a = -1.0853599185564055e-52
  6. b = 1.1502825561124828e+154

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: 63.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+306} \lor \neg \left(t_2 \leq 5 \cdot 10^{+233}\right):\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(\frac{z}{\frac{t_1}{x}} + \frac{y + t}{\frac{t_1}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 -2e+306) (not (<= t_2 5e+233)))
     (+ (/ (- z b) (/ t_1 y)) (+ (/ z (/ t_1 x)) (/ (+ y t) (/ t_1 a))))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -2e+306) || !(t_2 <= 5e+233)) {
		tmp = ((z - b) / (t_1 / y)) + ((z / (t_1 / x)) + ((y + t) / (t_1 / a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
    if ((t_2 <= (-2d+306)) .or. (.not. (t_2 <= 5d+233))) then
        tmp = ((z - b) / (t_1 / y)) + ((z / (t_1 / x)) + ((y + t) / (t_1 / a)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -2e+306) || !(t_2 <= 5e+233)) {
		tmp = ((z - b) / (t_1 / y)) + ((z / (t_1 / x)) + ((y + t) / (t_1 / a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -2e+306) or not (t_2 <= 5e+233):
		tmp = ((z - b) / (t_1 / y)) + ((z / (t_1 / x)) + ((y + t) / (t_1 / a)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= -2e+306) || !(t_2 <= 5e+233))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(Float64(z / Float64(t_1 / x)) + Float64(Float64(y + t) / Float64(t_1 / a))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -2e+306) || ~((t_2 <= 5e+233)))
		tmp = ((z - b) / (t_1 / y)) + ((z / (t_1 / x)) + ((y + t) / (t_1 / a)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e+306], N[Not[LessEqual[t$95$2, 5e+233]], $MachinePrecision]], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] / N[(t$95$1 / a), $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)) < -2.00000000000000003e306 or 5.00000000000000009e233 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.8%

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

   3. Simplified 11.1%

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

   4. Taylor expanded in a around -inf 10.0%

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

      1. associate-/l* 32.8%

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

      2. mul-1-neg 32.8%

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

      3. unsub-neg 32.8%

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

      4. associate-/l* 51.0%

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

      5. associate-/l* 99.8%

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

      6. +-commutative 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. neg-mul-1 99.8%

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

   6. Simplified 99.8%

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

   if -2.00000000000000003e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000009e233

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+306} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+233}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(\frac{z}{\frac{y + \left(x + t\right)}{x}} + \frac{y + t}{\frac{y + \left(x + t\right)}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 2: 90.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+306}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (<= t_1 -2e+306)
     (+ a (/ (- z b) (/ (+ y t) y)))
     (if (<= t_1 5e+274) t_1 (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_1 <= -2e+306) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else if (t_1 <= 5e+274) {
		tmp = t_1;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t))
    if (t_1 <= (-2d+306)) then
        tmp = a + ((z - b) / ((y + t) / y))
    else if (t_1 <= 5d+274) then
        tmp = t_1
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_1 <= -2e+306) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else if (t_1 <= 5e+274) {
		tmp = t_1;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if t_1 <= -2e+306:
		tmp = a + ((z - b) / ((y + t) / y))
	elif t_1 <= 5e+274:
		tmp = t_1
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (t_1 <= -2e+306)
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	elseif (t_1 <= 5e+274)
		tmp = t_1;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if (t_1 <= -2e+306)
		tmp = a + ((z - b) / ((y + t) / y));
	elseif (t_1 <= 5e+274)
		tmp = t_1;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+306], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+274], t$95$1, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2.00000000000000003e306

   1. Initial program 9.1%

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

   3. Simplified 8.9%

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

   4. Taylor expanded in a around -inf 9.1%

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

      1. associate-/l* 25.3%

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

      2. mul-1-neg 25.3%

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

      3. unsub-neg 25.3%

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

      4. associate-/l* 53.0%

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

      5. associate-/l* 99.9%

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

      6. +-commutative 99.9%

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

      7. mul-1-neg 99.9%

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

      8. unsub-neg 99.9%

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

      9. neg-mul-1 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in x around 0 53.0%

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

      1. sub-neg 53.0%

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

      2. associate-/l* 77.5%

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

      3. +-commutative 77.5%

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

      4. mul-1-neg 77.5%

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

      5. remove-double-neg 77.5%

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

   9. Simplified 77.5%

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

   if -2.00000000000000003e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999998e274

   1. Initial program 99.8%

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

   if 4.9999999999999998e274 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.2%

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

   2. Taylor expanded in y around inf 82.3%

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

      1. +-commutative 82.3%

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

   4. Simplified 82.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+306}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 3: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq 6.2 \cdot 10^{+171}:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(\frac{a}{\frac{t_1}{y + t}} + \frac{x \cdot z}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= z 6.2e+171)
     (+ (/ (- z b) (/ t_1 y)) (+ (/ a (/ t_1 (+ y t))) (/ (* x z) t_1)))
     (/ (+ x y) (/ t_1 z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (z <= 6.2e+171) {
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	} else {
		tmp = (x + y) / (t_1 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (z <= 6.2d+171) then
        tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1))
    else
        tmp = (x + y) / (t_1 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (z <= 6.2e+171) {
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	} else {
		tmp = (x + y) / (t_1 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if z <= 6.2e+171:
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1))
	else:
		tmp = (x + y) / (t_1 / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (z <= 6.2e+171)
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(Float64(x * z) / t_1)));
	else
		tmp = Float64(Float64(x + y) / Float64(t_1 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (z <= 6.2e+171)
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	else
		tmp = (x + y) / (t_1 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 6.2e+171], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 6.1999999999999998e171

   1. Initial program 71.2%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in a around inf 71.3%

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

      1. associate-/l* 76.9%

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

      2. +-commutative 76.9%

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

      3. associate-/l* 94.0%

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

   6. Simplified 94.0%

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

   if 6.1999999999999998e171 < z

   1. Initial program 21.4%

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

   2. Taylor expanded in z around inf 16.3%

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

      1. associate-/l* 85.1%

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

   4. Simplified 85.1%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.2 \cdot 10^{+171}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{x \cdot z}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \end{array} \]

Alternative 4: 73.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+189}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+163}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.55e+189)
   z
   (if (<= x -3.5e+92)
     (* a (/ (+ y t) (+ y (+ x t))))
     (if (<= x 2.45e+163) (+ a (/ (- z b) (/ (+ y t) y))) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.55e+189) {
		tmp = z;
	} else if (x <= -3.5e+92) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (x <= 2.45e+163) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.55d+189)) then
        tmp = z
    else if (x <= (-3.5d+92)) then
        tmp = a * ((y + t) / (y + (x + t)))
    else if (x <= 2.45d+163) then
        tmp = a + ((z - b) / ((y + t) / y))
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.55e+189) {
		tmp = z;
	} else if (x <= -3.5e+92) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (x <= 2.45e+163) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.55e+189:
		tmp = z
	elif x <= -3.5e+92:
		tmp = a * ((y + t) / (y + (x + t)))
	elif x <= 2.45e+163:
		tmp = a + ((z - b) / ((y + t) / y))
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.55e+189)
		tmp = z;
	elseif (x <= -3.5e+92)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	elseif (x <= 2.45e+163)
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.55e+189)
		tmp = z;
	elseif (x <= -3.5e+92)
		tmp = a * ((y + t) / (y + (x + t)));
	elseif (x <= 2.45e+163)
		tmp = a + ((z - b) / ((y + t) / y));
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.55e+189], z, If[LessEqual[x, -3.5e+92], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.45e+163], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], z]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e189 or 2.45e163 < x

   1. Initial program 51.8%

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

   2. Taylor expanded in x around inf 67.5%

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

   if -1.55e189 < x < -3.49999999999999986e92

   1. Initial program 77.0%

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

   2. Taylor expanded in a around inf 49.9%

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

   3. Taylor expanded in a around 0 49.9%

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

      1. +-commutative 49.9%

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

      2. associate-*r/ 63.3%

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

      3. +-commutative 63.3%

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

   5. Simplified 63.3%

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

   if -3.49999999999999986e92 < x < 2.45e163

   1. Initial program 66.6%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in a around -inf 66.7%

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

      1. associate-/l* 76.6%

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

      2. mul-1-neg 76.6%

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

      3. unsub-neg 76.6%

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

      4. associate-/l* 79.4%

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

      5. associate-/l* 93.8%

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

      6. +-commutative 93.8%

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

      7. mul-1-neg 93.8%

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

      8. unsub-neg 93.8%

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

      9. neg-mul-1 93.8%

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

   6. Simplified 93.8%

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

   7. Taylor expanded in x around 0 63.9%

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

      1. sub-neg 63.9%

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

      2. associate-/l* 84.9%

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

      3. +-commutative 84.9%

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

      4. mul-1-neg 84.9%

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

      5. remove-double-neg 84.9%

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

   9. Simplified 84.9%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+189}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+163}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 63.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+131} \lor \neg \left(t \leq 3.8 \cdot 10^{+69}\right):\\ \;\;\;\;a + \frac{z - b}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.75e+131) (not (<= t 3.8e+69)))
   (+ a (/ (- z b) (/ t y)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.75e+131) || !(t <= 3.8e+69)) {
		tmp = a + ((z - b) / (t / y));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.75d+131)) .or. (.not. (t <= 3.8d+69))) then
        tmp = a + ((z - b) / (t / y))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.75e+131) || !(t <= 3.8e+69)) {
		tmp = a + ((z - b) / (t / y));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.75e+131) or not (t <= 3.8e+69):
		tmp = a + ((z - b) / (t / y))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.75e+131) || !(t <= 3.8e+69))
		tmp = Float64(a + Float64(Float64(z - b) / Float64(t / y)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.75e+131) || ~((t <= 3.8e+69)))
		tmp = a + ((z - b) / (t / y));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.75e+131], N[Not[LessEqual[t, 3.8e+69]], $MachinePrecision]], N[(a + N[(N[(z - b), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7499999999999999e131 or 3.80000000000000028e69 < t

   1. Initial program 60.2%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in a around -inf 60.4%

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

      1. associate-/l* 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. associate-/l* 73.6%

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

      5. associate-/l* 89.0%

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

      6. +-commutative 89.0%

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

      7. mul-1-neg 89.0%

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

      8. unsub-neg 89.0%

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

      9. neg-mul-1 89.0%

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

   6. Simplified 89.0%

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

   7. Taylor expanded in x around 0 67.8%

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

      1. sub-neg 67.8%

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

      2. associate-/l* 78.5%

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

      3. +-commutative 78.5%

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

      4. mul-1-neg 78.5%

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

      5. remove-double-neg 78.5%

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

   9. Simplified 78.5%

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

   10. Taylor expanded in t around inf 65.1%

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

       1. associate-/l* 68.8%

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

   12. Simplified 68.8%

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

   if -1.7499999999999999e131 < t < 3.80000000000000028e69

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf 63.8%

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

      1. +-commutative 63.8%

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

   4. Simplified 63.8%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+131} \lor \neg \left(t \leq 3.8 \cdot 10^{+69}\right):\\ \;\;\;\;a + \frac{z - b}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 6: 63.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+48}:\\ \;\;\;\;a - b \cdot \frac{y}{y + t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+68}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.1e+48)
   (- a (* b (/ y (+ y t))))
   (if (<= t 7e+68) (- (+ z a) b) (+ a (/ (- z b) (/ t y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.1e+48) {
		tmp = a - (b * (y / (y + t)));
	} else if (t <= 7e+68) {
		tmp = (z + a) - b;
	} else {
		tmp = a + ((z - b) / (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) :: tmp
    if (t <= (-1.1d+48)) then
        tmp = a - (b * (y / (y + t)))
    else if (t <= 7d+68) then
        tmp = (z + a) - b
    else
        tmp = a + ((z - b) / (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 tmp;
	if (t <= -1.1e+48) {
		tmp = a - (b * (y / (y + t)));
	} else if (t <= 7e+68) {
		tmp = (z + a) - b;
	} else {
		tmp = a + ((z - b) / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.1e+48:
		tmp = a - (b * (y / (y + t)))
	elif t <= 7e+68:
		tmp = (z + a) - b
	else:
		tmp = a + ((z - b) / (t / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.1e+48)
		tmp = Float64(a - Float64(b * Float64(y / Float64(y + t))));
	elseif (t <= 7e+68)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(Float64(z - b) / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.1e+48)
		tmp = a - (b * (y / (y + t)));
	elseif (t <= 7e+68)
		tmp = (z + a) - b;
	else
		tmp = a + ((z - b) / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.1e+48], N[(a - N[(b * N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+68], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(N[(z - b), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e48

   1. Initial program 60.8%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in a around -inf 60.9%

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

      1. associate-/l* 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. associate-/l* 68.2%

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

      5. associate-/l* 89.3%

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

      6. +-commutative 89.3%

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

      7. mul-1-neg 89.3%

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

      8. unsub-neg 89.3%

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

      9. neg-mul-1 89.3%

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

   6. Simplified 89.3%

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

   7. Taylor expanded in x around 0 57.5%

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

      1. sub-neg 57.5%

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

      2. associate-/l* 68.2%

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

      3. +-commutative 68.2%

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

      4. mul-1-neg 68.2%

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

      5. remove-double-neg 68.2%

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

   9. Simplified 68.2%

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

   10. Taylor expanded in z around 0 55.7%

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

       1. mul-1-neg 55.7%

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

       2. *-commutative 55.7%

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

       3. +-commutative 55.7%

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

       4. associate-*r/ 62.8%

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

       5. distribute-lft-neg-in 62.8%

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

       6. +-commutative 62.8%

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

   12. Simplified 62.8%

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

   13. Taylor expanded in b around 0 55.7%

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

       1. mul-1-neg 55.7%

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

       2. *-commutative 55.7%

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

       3. associate-*r/ 62.8%

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

       4. sub-neg 62.8%

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

   15. Simplified 62.8%

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

   if -1.1e48 < t < 6.99999999999999955e68

   1. Initial program 67.8%

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

   2. Taylor expanded in y around inf 66.3%

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

      1. +-commutative 66.3%

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

   4. Simplified 66.3%

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

   if 6.99999999999999955e68 < t

   1. Initial program 62.1%

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

   3. Simplified 62.1%

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

   4. Taylor expanded in a around -inf 62.3%

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

      1. associate-/l* 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. associate-/l* 81.1%

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

      5. associate-/l* 93.5%

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

      6. +-commutative 93.5%

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

      7. mul-1-neg 93.5%

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

      8. unsub-neg 93.5%

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

      9. neg-mul-1 93.5%

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

   6. Simplified 93.5%

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

   7. Taylor expanded in x around 0 71.2%

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

      1. sub-neg 71.2%

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

      2. associate-/l* 83.7%

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

      3. +-commutative 83.7%

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

      4. mul-1-neg 83.7%

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

      5. remove-double-neg 83.7%

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

   9. Simplified 83.7%

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

   10. Taylor expanded in t around inf 66.6%

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

       1. associate-/l* 70.8%

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

   12. Simplified 70.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+48}:\\ \;\;\;\;a - b \cdot \frac{y}{y + t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+68}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{t}{y}}\\ \end{array} \]

Alternative 7: 49.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-9}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+55}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+123}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+134}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.8e-9)
   z
   (if (<= x 1.9e+55)
     (- a b)
     (if (<= x 2e+123) z (if (<= x 1.25e+134) (- a b) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.8e-9) {
		tmp = z;
	} else if (x <= 1.9e+55) {
		tmp = a - b;
	} else if (x <= 2e+123) {
		tmp = z;
	} else if (x <= 1.25e+134) {
		tmp = 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 (x <= (-6.8d-9)) then
        tmp = z
    else if (x <= 1.9d+55) then
        tmp = a - b
    else if (x <= 2d+123) then
        tmp = z
    else if (x <= 1.25d+134) then
        tmp = 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 (x <= -6.8e-9) {
		tmp = z;
	} else if (x <= 1.9e+55) {
		tmp = a - b;
	} else if (x <= 2e+123) {
		tmp = z;
	} else if (x <= 1.25e+134) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.8e-9:
		tmp = z
	elif x <= 1.9e+55:
		tmp = a - b
	elif x <= 2e+123:
		tmp = z
	elif x <= 1.25e+134:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.8e-9)
		tmp = z;
	elseif (x <= 1.9e+55)
		tmp = Float64(a - b);
	elseif (x <= 2e+123)
		tmp = z;
	elseif (x <= 1.25e+134)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.8e-9)
		tmp = z;
	elseif (x <= 1.9e+55)
		tmp = a - b;
	elseif (x <= 2e+123)
		tmp = z;
	elseif (x <= 1.25e+134)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.8e-9], z, If[LessEqual[x, 1.9e+55], N[(a - b), $MachinePrecision], If[LessEqual[x, 2e+123], z, If[LessEqual[x, 1.25e+134], N[(a - b), $MachinePrecision], z]]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7999999999999997e-9 or 1.9e55 < x < 1.99999999999999996e123 or 1.24999999999999995e134 < x

   1. Initial program 58.8%

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

   2. Taylor expanded in x around inf 53.5%

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

   if -6.7999999999999997e-9 < x < 1.9e55 or 1.99999999999999996e123 < x < 1.24999999999999995e134

   1. Initial program 69.1%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in a around -inf 69.3%

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

      1. associate-/l* 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. associate-/l* 79.0%

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

      5. associate-/l* 92.5%

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

      6. +-commutative 92.5%

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

      7. mul-1-neg 92.5%

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

      8. unsub-neg 92.5%

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

      9. neg-mul-1 92.5%

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

   6. Simplified 92.5%

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

   7. Taylor expanded in x around 0 70.9%

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

      1. sub-neg 70.9%

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

      2. associate-/l* 90.3%

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

      3. +-commutative 90.3%

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

      4. mul-1-neg 90.3%

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

      5. remove-double-neg 90.3%

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

   9. Simplified 90.3%

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

   10. Taylor expanded in z around 0 60.4%

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

       1. mul-1-neg 60.4%

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

       2. *-commutative 60.4%

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

       3. +-commutative 60.4%

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

       4. associate-*r/ 71.0%

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

       5. distribute-lft-neg-in 71.0%

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

       6. +-commutative 71.0%

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

   12. Simplified 71.0%

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

   13. Taylor expanded in y around inf 53.1%

       \[\leadsto \color{blue}{a + -1 \cdot b} \]
   14. Step-by-step derivation

       1. mul-1-neg 53.1%

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

       2. unsub-neg 53.1%

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

   15. Simplified 53.1%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-9}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+55}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+123}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+134}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 8: 62.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+137} \lor \neg \left(t \leq 2.52 \cdot 10^{+70}\right):\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.2e+137) (not (<= t 2.52e+70)))
   (- a (* y (/ b t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e+137) || !(t <= 2.52e+70)) {
		tmp = a - (y * (b / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.2d+137)) .or. (.not. (t <= 2.52d+70))) then
        tmp = a - (y * (b / t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e+137) || !(t <= 2.52e+70)) {
		tmp = a - (y * (b / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.2e+137) or not (t <= 2.52e+70):
		tmp = a - (y * (b / t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.2e+137) || !(t <= 2.52e+70))
		tmp = Float64(a - Float64(y * Float64(b / t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.2e+137) || ~((t <= 2.52e+70)))
		tmp = a - (y * (b / t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.2e+137], N[Not[LessEqual[t, 2.52e+70]], $MachinePrecision]], N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.20000000000000015e137 or 2.52000000000000003e70 < t

   1. Initial program 59.7%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in a around -inf 59.9%

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

      1. associate-/l* 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. associate-/l* 73.3%

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

      5. associate-/l* 88.8%

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

      6. +-commutative 88.8%

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

      7. mul-1-neg 88.8%

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

      8. unsub-neg 88.8%

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

      9. neg-mul-1 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in x around 0 67.3%

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

      1. sub-neg 67.3%

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

      2. associate-/l* 78.3%

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

      3. +-commutative 78.3%

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

      4. mul-1-neg 78.3%

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

      5. remove-double-neg 78.3%

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

   9. Simplified 78.3%

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

   10. Taylor expanded in z around 0 62.0%

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

       1. mul-1-neg 62.0%

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

       2. *-commutative 62.0%

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

       3. +-commutative 62.0%

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

       4. associate-*r/ 65.7%

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

       5. distribute-lft-neg-in 65.7%

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

       6. +-commutative 65.7%

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

   12. Simplified 65.7%

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

   13. Taylor expanded in y around 0 60.9%

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

       1. mul-1-neg 60.9%

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

       2. associate-/l* 63.5%

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

       3. unsub-neg 63.5%

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

       4. associate-/l* 60.9%

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

       5. associate-*r/ 63.5%

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

   15. Simplified 63.5%

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

   if -2.20000000000000015e137 < t < 2.52000000000000003e70

   1. Initial program 67.8%

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

   2. Taylor expanded in y around inf 63.5%

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

      1. +-commutative 63.5%

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

   4. Simplified 63.5%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+137} \lor \neg \left(t \leq 2.52 \cdot 10^{+70}\right):\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 9: 60.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{+184}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+144}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - \frac{x}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.9e+184)
   a
   (if (<= t 2.9e+144) (- (+ z a) b) (* a (- 1.0 (/ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.9e+184) {
		tmp = a;
	} else if (t <= 2.9e+144) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (1.0 - (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.9d+184)) then
        tmp = a
    else if (t <= 2.9d+144) then
        tmp = (z + a) - b
    else
        tmp = a * (1.0d0 - (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.9e+184) {
		tmp = a;
	} else if (t <= 2.9e+144) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (1.0 - (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.9e+184:
		tmp = a
	elif t <= 2.9e+144:
		tmp = (z + a) - b
	else:
		tmp = a * (1.0 - (x / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.9e+184)
		tmp = a;
	elseif (t <= 2.9e+144)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(1.0 - Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.9e+184)
		tmp = a;
	elseif (t <= 2.9e+144)
		tmp = (z + a) - b;
	else
		tmp = a * (1.0 - (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.9e+184], a, If[LessEqual[t, 2.9e+144], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(1.0 - N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.9000000000000001e184

   1. Initial program 56.2%

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

   2. Taylor expanded in t around inf 61.7%

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

   if -5.9000000000000001e184 < t < 2.89999999999999998e144

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf 61.3%

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

      1. +-commutative 61.3%

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

   4. Simplified 61.3%

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

   if 2.89999999999999998e144 < t

   1. Initial program 57.1%

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

   3. Simplified 57.3%

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

   4. Taylor expanded in t around inf 74.1%

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

      1. associate--l+ 74.1%

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

      2. associate-/l* 80.5%

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

      3. +-commutative 80.5%

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

      4. associate-/l* 89.6%

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

      5. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in a around inf 64.4%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{+184}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+144}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - \frac{x}{t}\right)\\ \end{array} \]

Alternative 10: 46.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-9}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+122}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+140}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7e-9)
   z
   (if (<= x 1.45e+68) a (if (<= x 7.4e+122) z (if (<= x 1.15e+140) a z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7e-9) {
		tmp = z;
	} else if (x <= 1.45e+68) {
		tmp = a;
	} else if (x <= 7.4e+122) {
		tmp = z;
	} else if (x <= 1.15e+140) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-7d-9)) then
        tmp = z
    else if (x <= 1.45d+68) then
        tmp = a
    else if (x <= 7.4d+122) then
        tmp = z
    else if (x <= 1.15d+140) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7e-9) {
		tmp = z;
	} else if (x <= 1.45e+68) {
		tmp = a;
	} else if (x <= 7.4e+122) {
		tmp = z;
	} else if (x <= 1.15e+140) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7e-9:
		tmp = z
	elif x <= 1.45e+68:
		tmp = a
	elif x <= 7.4e+122:
		tmp = z
	elif x <= 1.15e+140:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7e-9)
		tmp = z;
	elseif (x <= 1.45e+68)
		tmp = a;
	elseif (x <= 7.4e+122)
		tmp = z;
	elseif (x <= 1.15e+140)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7e-9)
		tmp = z;
	elseif (x <= 1.45e+68)
		tmp = a;
	elseif (x <= 7.4e+122)
		tmp = z;
	elseif (x <= 1.15e+140)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7e-9], z, If[LessEqual[x, 1.45e+68], a, If[LessEqual[x, 7.4e+122], z, If[LessEqual[x, 1.15e+140], a, z]]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.9999999999999998e-9 or 1.45000000000000006e68 < x < 7.3999999999999993e122 or 1.14999999999999995e140 < x

   1. Initial program 58.9%

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

   2. Taylor expanded in x around inf 54.6%

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

   if -6.9999999999999998e-9 < x < 1.45000000000000006e68 or 7.3999999999999993e122 < x < 1.14999999999999995e140

   1. Initial program 68.9%

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

   2. Taylor expanded in t around inf 48.5%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-9}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+122}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+140}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 11: 60.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+187}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+145}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.55e+187) a (if (<= t 2.35e+145) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.55e+187) {
		tmp = a;
	} else if (t <= 2.35e+145) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.55d+187)) then
        tmp = a
    else if (t <= 2.35d+145) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.55e+187) {
		tmp = a;
	} else if (t <= 2.35e+145) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.55e+187:
		tmp = a
	elif t <= 2.35e+145:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.55e+187)
		tmp = a;
	elseif (t <= 2.35e+145)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.55e+187)
		tmp = a;
	elseif (t <= 2.35e+145)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.55e+187], a, If[LessEqual[t, 2.35e+145], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -2.55e187 or 2.3500000000000001e145 < t

   1. Initial program 56.7%

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

   2. Taylor expanded in t around inf 62.9%

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

   if -2.55e187 < t < 2.3500000000000001e145

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf 61.3%

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

      1. +-commutative 61.3%

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

   4. Simplified 61.3%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+187}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+145}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 12: 33.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.3%

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

2. Taylor expanded in t around inf 36.3%

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

3. Final simplification 36.3%

   \[\leadsto a \]

Developer target: 83.7% 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 2023278 
(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)))