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

Percentage Accurate: 59.9% → 89.3%

Time: 13.0s

Alternatives: 16

Speedup: 1.4×

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: 59.9% 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: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+182}:\\ \;\;\;\;z + \left(\left(\frac{y}{\frac{x}{a + \left(z - b\right)}} + \frac{a}{\frac{x}{t}}\right) - \frac{z}{\frac{x}{y + t}}\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+257}:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(\frac{a}{\frac{t_1}{y + t}} + \frac{x \cdot z}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= x -2.8e+182)
     (+ z (- (+ (/ y (/ x (+ a (- z b)))) (/ a (/ x t))) (/ z (/ x (+ y t)))))
     (if (<= x 1.2e+257)
       (+ (/ (- z b) (/ t_1 y)) (+ (/ a (/ t_1 (+ y t))) (/ (* x z) t_1)))
       (* z (/ (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (x <= -2.8e+182) {
		tmp = z + (((y / (x / (a + (z - b)))) + (a / (x / t))) - (z / (x / (y + t))));
	} else if (x <= 1.2e+257) {
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	} else {
		tmp = z * ((x + y) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (x <= (-2.8d+182)) then
        tmp = z + (((y / (x / (a + (z - b)))) + (a / (x / t))) - (z / (x / (y + t))))
    else if (x <= 1.2d+257) then
        tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1))
    else
        tmp = z * ((x + y) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (x <= -2.8e+182) {
		tmp = z + (((y / (x / (a + (z - b)))) + (a / (x / t))) - (z / (x / (y + t))));
	} else if (x <= 1.2e+257) {
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	} else {
		tmp = z * ((x + y) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if x <= -2.8e+182:
		tmp = z + (((y / (x / (a + (z - b)))) + (a / (x / t))) - (z / (x / (y + t))))
	elif x <= 1.2e+257:
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1))
	else:
		tmp = z * ((x + y) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (x <= -2.8e+182)
		tmp = Float64(z + Float64(Float64(Float64(y / Float64(x / Float64(a + Float64(z - b)))) + Float64(a / Float64(x / t))) - Float64(z / Float64(x / Float64(y + t)))));
	elseif (x <= 1.2e+257)
		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(z * Float64(Float64(x + y) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (x <= -2.8e+182)
		tmp = z + (((y / (x / (a + (z - b)))) + (a / (x / t))) - (z / (x / (y + t))));
	elseif (x <= 1.2e+257)
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	else
		tmp = z * ((x + y) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+182], N[(z + N[(N[(N[(y / N[(x / N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(x / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+257], 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[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.80000000000000006e182

   1. Initial program 40.8%

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

   3. Simplified 41.0%

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

   4. Taylor expanded in x around inf 63.9%

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

      1. associate--l+ 63.9%

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

      2. associate-/l* 72.7%

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

      3. sub-neg 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-+r+ 72.7%

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

      6. sub-neg 72.7%

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

      7. +-commutative 72.7%

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

      8. associate-+l- 72.7%

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

      9. associate-/l* 77.0%

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

      10. associate-/l* 91.1%

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

   6. Simplified 91.1%

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

   if -2.80000000000000006e182 < x < 1.2e257

   1. Initial program 65.0%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in a around inf 65.0%

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

      1. associate-/l* 75.3%

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

      2. +-commutative 75.3%

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

      3. associate-/l* 92.9%

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

   6. Simplified 92.9%

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

   if 1.2e257 < x

   1. Initial program 28.3%

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

   2. Taylor expanded in z around inf 29.7%

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

      1. associate-/l* 81.3%

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

   4. Simplified 81.3%

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

      1. associate-/r/ 93.1%

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

      2. +-commutative 93.1%

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

      3. +-commutative 93.1%

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

   6. Applied egg-rr 93.1%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+182}:\\ \;\;\;\;z + \left(\left(\frac{y}{\frac{x}{a + \left(z - b\right)}} + \frac{a}{\frac{x}{t}}\right) - \frac{z}{\frac{x}{y + t}}\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+257}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{x \cdot z}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 2: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+247}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (<= t_1 (- INFINITY))
     (+ z a)
     (if (<= t_1 2e+247) t_1 (+ a (/ (- z b) (/ (+ y t) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z + a;
	} else if (t_1 <= 2e+247) {
		tmp = t_1;
	} else {
		tmp = a + ((z - b) / ((y + t) / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z + a;
	} else if (t_1 <= 2e+247) {
		tmp = t_1;
	} else {
		tmp = a + ((z - b) / ((y + t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z + a
	elif t_1 <= 2e+247:
		tmp = t_1
	else:
		tmp = a + ((z - b) / ((y + t) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z + a);
	elseif (t_1 <= 2e+247)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z + a;
	elseif (t_1 <= 2e+247)
		tmp = t_1;
	else
		tmp = a + ((z - b) / ((y + t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z + a), $MachinePrecision], If[LessEqual[t$95$1, 2e+247], t$95$1, N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $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 7.4%

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

   3. Simplified 7.3%

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

   4. Taylor expanded in a around inf 7.4%

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

      1. associate-/l* 30.8%

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

      2. +-commutative 30.8%

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

      3. associate-/l* 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in y around inf 64.3%

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

   8. Taylor expanded in x around inf 70.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e247

   1. Initial program 99.1%

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

   if 1.9999999999999999e247 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.7%

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

   3. Simplified 7.3%

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

   4. Taylor expanded in a around inf 6.0%

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

      1. associate-/l* 29.7%

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

      2. +-commutative 29.7%

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

      3. associate-/l* 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in y around inf 63.6%

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

   8. Taylor expanded in x around 0 27.9%

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

      1. associate-/l* 77.2%

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

   10. Simplified 77.2%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;z + a\\ \mathbf{elif}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+247}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \end{array} \]

Alternative 3: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+90}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right) + \frac{a \cdot \left(y + t\right) - y \cdot b}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(a + \frac{x \cdot z}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= y -3.6e+90)
     (+ a (/ (- z b) (/ (+ y t) y)))
     (if (<= y 1.45e+30)
       (+ (* z (+ (/ x t_1) (/ y t_1))) (/ (- (* a (+ y t)) (* y b)) t_1))
       (+ (/ (- z b) (/ t_1 y)) (+ a (/ (* x z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -3.6e+90) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else if (y <= 1.45e+30) {
		tmp = (z * ((x / t_1) + (y / t_1))) + (((a * (y + t)) - (y * b)) / t_1);
	} else {
		tmp = ((z - b) / (t_1 / y)) + (a + ((x * z) / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (y <= (-3.6d+90)) then
        tmp = a + ((z - b) / ((y + t) / y))
    else if (y <= 1.45d+30) then
        tmp = (z * ((x / t_1) + (y / t_1))) + (((a * (y + t)) - (y * b)) / t_1)
    else
        tmp = ((z - b) / (t_1 / y)) + (a + ((x * z) / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -3.6e+90) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else if (y <= 1.45e+30) {
		tmp = (z * ((x / t_1) + (y / t_1))) + (((a * (y + t)) - (y * b)) / t_1);
	} else {
		tmp = ((z - b) / (t_1 / y)) + (a + ((x * z) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if y <= -3.6e+90:
		tmp = a + ((z - b) / ((y + t) / y))
	elif y <= 1.45e+30:
		tmp = (z * ((x / t_1) + (y / t_1))) + (((a * (y + t)) - (y * b)) / t_1)
	else:
		tmp = ((z - b) / (t_1 / y)) + (a + ((x * z) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -3.6e+90)
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	elseif (y <= 1.45e+30)
		tmp = Float64(Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))) + Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_1));
	else
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(a + Float64(Float64(x * z) / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (y <= -3.6e+90)
		tmp = a + ((z - b) / ((y + t) / y));
	elseif (y <= 1.45e+30)
		tmp = (z * ((x / t_1) + (y / t_1))) + (((a * (y + t)) - (y * b)) / t_1);
	else
		tmp = ((z - b) / (t_1 / y)) + (a + ((x * z) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+90], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+30], N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(a + N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e90

   1. Initial program 28.6%

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

   3. Simplified 29.5%

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

   4. Taylor expanded in a around inf 28.8%

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

      1. associate-/l* 54.2%

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

      2. +-commutative 54.2%

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

      3. associate-/l* 79.5%

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

   6. Simplified 79.5%

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

   7. Taylor expanded in y around inf 75.1%

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

   8. Taylor expanded in x around 0 40.6%

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

      1. associate-/l* 83.9%

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

   10. Simplified 83.9%

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

   if -3.6e90 < y < 1.4499999999999999e30

   1. Initial program 77.6%

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

   2. Taylor expanded in z around 0 92.6%

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

      1. associate--l+ 92.6%

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

      2. *-commutative 92.6%

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

      3. div-sub 92.6%

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

   4. Simplified 92.6%

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

   if 1.4499999999999999e30 < y

   1. Initial program 33.7%

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

   3. Simplified 34.8%

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

   4. Taylor expanded in a around inf 33.9%

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

      1. associate-/l* 55.2%

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

      2. +-commutative 55.2%

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

      3. associate-/l* 90.3%

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

   6. Simplified 90.3%

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

   7. Taylor expanded in y around inf 85.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+90}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)}\right) + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(a + \frac{x \cdot z}{y + \left(x + t\right)}\right)\\ \end{array} \]

Alternative 4: 57.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.25 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-272}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-260}:\\ \;\;\;\;\frac{x + y}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-229}:\\ \;\;\;\;\frac{a \cdot t}{t_1}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ (+ x y) t_1))) (t_3 (- (+ z a) b)))
   (if (<= y -1.9e-25)
     t_3
     (if (<= y -4.25e-240)
       t_2
       (if (<= y -2.9e-272)
         a
         (if (<= y 1.22e-260)
           (/ (+ x y) (/ (+ x t) z))
           (if (<= y 2.3e-229)
             (/ (* a t) t_1)
             (if (<= y 1.95e-88) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -1.9e-25) {
		tmp = t_3;
	} else if (y <= -4.25e-240) {
		tmp = t_2;
	} else if (y <= -2.9e-272) {
		tmp = a;
	} else if (y <= 1.22e-260) {
		tmp = (x + y) / ((x + t) / z);
	} else if (y <= 2.3e-229) {
		tmp = (a * t) / t_1;
	} else if (y <= 1.95e-88) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * ((x + y) / t_1)
    t_3 = (z + a) - b
    if (y <= (-1.9d-25)) then
        tmp = t_3
    else if (y <= (-4.25d-240)) then
        tmp = t_2
    else if (y <= (-2.9d-272)) then
        tmp = a
    else if (y <= 1.22d-260) then
        tmp = (x + y) / ((x + t) / z)
    else if (y <= 2.3d-229) then
        tmp = (a * t) / t_1
    else if (y <= 1.95d-88) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -1.9e-25) {
		tmp = t_3;
	} else if (y <= -4.25e-240) {
		tmp = t_2;
	} else if (y <= -2.9e-272) {
		tmp = a;
	} else if (y <= 1.22e-260) {
		tmp = (x + y) / ((x + t) / z);
	} else if (y <= 2.3e-229) {
		tmp = (a * t) / t_1;
	} else if (y <= 1.95e-88) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * ((x + y) / t_1)
	t_3 = (z + a) - b
	tmp = 0
	if y <= -1.9e-25:
		tmp = t_3
	elif y <= -4.25e-240:
		tmp = t_2
	elif y <= -2.9e-272:
		tmp = a
	elif y <= 1.22e-260:
		tmp = (x + y) / ((x + t) / z)
	elif y <= 2.3e-229:
		tmp = (a * t) / t_1
	elif y <= 1.95e-88:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.9e-25)
		tmp = t_3;
	elseif (y <= -4.25e-240)
		tmp = t_2;
	elseif (y <= -2.9e-272)
		tmp = a;
	elseif (y <= 1.22e-260)
		tmp = Float64(Float64(x + y) / Float64(Float64(x + t) / z));
	elseif (y <= 2.3e-229)
		tmp = Float64(Float64(a * t) / t_1);
	elseif (y <= 1.95e-88)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * ((x + y) / t_1);
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.9e-25)
		tmp = t_3;
	elseif (y <= -4.25e-240)
		tmp = t_2;
	elseif (y <= -2.9e-272)
		tmp = a;
	elseif (y <= 1.22e-260)
		tmp = (x + y) / ((x + t) / z);
	elseif (y <= 2.3e-229)
		tmp = (a * t) / t_1;
	elseif (y <= 1.95e-88)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.9e-25], t$95$3, If[LessEqual[y, -4.25e-240], t$95$2, If[LessEqual[y, -2.9e-272], a, If[LessEqual[y, 1.22e-260], N[(N[(x + y), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-229], N[(N[(a * t), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 1.95e-88], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.8999999999999999e-25 or 1.94999999999999996e-88 < y

   1. Initial program 45.6%

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

   2. Taylor expanded in y around inf 68.5%

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

      1. +-commutative 68.5%

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

   4. Simplified 68.5%

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

   if -1.8999999999999999e-25 < y < -4.25e-240 or 2.29999999999999996e-229 < y < 1.94999999999999996e-88

   1. Initial program 77.6%

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

   2. Taylor expanded in z around inf 49.2%

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

      1. associate-/l* 57.7%

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

   4. Simplified 57.7%

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

      1. associate-/r/ 65.6%

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

      2. +-commutative 65.6%

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

      3. +-commutative 65.6%

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

   6. Applied egg-rr 65.6%

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

   if -4.25e-240 < y < -2.89999999999999995e-272

   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 t around inf 100.0%

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

   if -2.89999999999999995e-272 < y < 1.22e-260

   1. Initial program 64.2%

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

   2. Taylor expanded in z around inf 39.9%

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

      1. associate-/l* 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in y around 0 60.3%

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

      1. +-commutative 60.3%

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

   7. Simplified 60.3%

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

   if 1.22e-260 < y < 2.29999999999999996e-229

   1. Initial program 99.6%

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

   2. Taylor expanded in t around inf 72.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -4.25 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-272}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-260}:\\ \;\;\;\;\frac{x + y}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-229}:\\ \;\;\;\;\frac{a \cdot t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 5: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+135}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;x \leq -0.0003:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-57}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{x} + \frac{t}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (/ (- z b) (/ (+ y t) y)))))
   (if (<= x -3.2e+135)
     (+ z (* y (- (/ a x) (/ b x))))
     (if (<= x -0.0003)
       t_1
       (if (<= x -8.6e-57)
         (/ (- (* z (+ x y)) (* y b)) (+ y (+ x t)))
         (if (<= x 1.4e+189) t_1 (+ z (* a (+ (/ y x) (/ t x))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + ((z - b) / ((y + t) / y));
	double tmp;
	if (x <= -3.2e+135) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (x <= -0.0003) {
		tmp = t_1;
	} else if (x <= -8.6e-57) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else if (x <= 1.4e+189) {
		tmp = t_1;
	} else {
		tmp = z + (a * ((y / x) + (t / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + ((z - b) / ((y + t) / y))
    if (x <= (-3.2d+135)) then
        tmp = z + (y * ((a / x) - (b / x)))
    else if (x <= (-0.0003d0)) then
        tmp = t_1
    else if (x <= (-8.6d-57)) then
        tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
    else if (x <= 1.4d+189) then
        tmp = t_1
    else
        tmp = z + (a * ((y / x) + (t / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + ((z - b) / ((y + t) / y));
	double tmp;
	if (x <= -3.2e+135) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (x <= -0.0003) {
		tmp = t_1;
	} else if (x <= -8.6e-57) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else if (x <= 1.4e+189) {
		tmp = t_1;
	} else {
		tmp = z + (a * ((y / x) + (t / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + ((z - b) / ((y + t) / y))
	tmp = 0
	if x <= -3.2e+135:
		tmp = z + (y * ((a / x) - (b / x)))
	elif x <= -0.0003:
		tmp = t_1
	elif x <= -8.6e-57:
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
	elif x <= 1.4e+189:
		tmp = t_1
	else:
		tmp = z + (a * ((y / x) + (t / x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)))
	tmp = 0.0
	if (x <= -3.2e+135)
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	elseif (x <= -0.0003)
		tmp = t_1;
	elseif (x <= -8.6e-57)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (x <= 1.4e+189)
		tmp = t_1;
	else
		tmp = Float64(z + Float64(a * Float64(Float64(y / x) + Float64(t / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + ((z - b) / ((y + t) / y));
	tmp = 0.0;
	if (x <= -3.2e+135)
		tmp = z + (y * ((a / x) - (b / x)));
	elseif (x <= -0.0003)
		tmp = t_1;
	elseif (x <= -8.6e-57)
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	elseif (x <= 1.4e+189)
		tmp = t_1;
	else
		tmp = z + (a * ((y / x) + (t / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+135], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -0.0003], t$95$1, If[LessEqual[x, -8.6e-57], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+189], t$95$1, N[(z + N[(a * N[(N[(y / x), $MachinePrecision] + N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.19999999999999975e135

   1. Initial program 47.5%

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

   3. Simplified 47.7%

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

   4. Taylor expanded in x around inf 61.9%

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

      1. associate--l+ 61.9%

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

      2. associate-/l* 70.4%

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

      3. sub-neg 70.4%

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

      4. +-commutative 70.4%

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

      5. associate-+r+ 70.4%

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

      6. sub-neg 70.4%

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

      7. +-commutative 70.4%

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

      8. associate-+l- 70.4%

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

      9. associate-/l* 73.6%

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

      10. associate-/l* 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in y around inf 75.3%

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

   if -3.19999999999999975e135 < x < -2.99999999999999974e-4 or -8.60000000000000043e-57 < x < 1.40000000000000003e189

   1. Initial program 62.2%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in a around inf 62.2%

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

      1. associate-/l* 74.6%

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

      2. +-commutative 74.6%

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

      3. associate-/l* 94.6%

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

   6. Simplified 94.6%

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

   7. Taylor expanded in y around inf 88.0%

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

   8. Taylor expanded in x around 0 54.3%

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

      1. associate-/l* 79.9%

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

   10. Simplified 79.9%

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

   if -2.99999999999999974e-4 < x < -8.60000000000000043e-57

   1. Initial program 92.1%

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

   2. Taylor expanded in a around 0 78.0%

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

   if 1.40000000000000003e189 < x

   1. Initial program 55.8%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in x around inf 55.8%

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

      1. associate--l+ 55.8%

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

      2. associate-/l* 55.5%

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

      3. sub-neg 55.5%

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

      4. +-commutative 55.5%

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

      5. associate-+r+ 55.5%

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

      6. sub-neg 55.5%

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

      7. +-commutative 55.5%

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

      8. associate-+l- 55.5%

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

      9. associate-/l* 59.3%

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

      10. associate-/l* 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in a around inf 63.8%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+135}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;x \leq -0.0003:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-57}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+189}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{x} + \frac{t}{x}\right)\\ \end{array} \]

Alternative 6: 57.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{x + t}{x}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-272}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-254}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-229}:\\ \;\;\;\;\frac{a \cdot t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ z (/ (+ x t) x))) (t_2 (- (+ z a) b)))
   (if (<= y -1.3e-25)
     t_2
     (if (<= y -1.75e-240)
       t_1
       (if (<= y -5.7e-272)
         a
         (if (<= y 4.2e-254)
           (* z (/ x (+ x t)))
           (if (<= y 1.7e-229)
             (/ (* a t) (+ y (+ x t)))
             (if (<= y 2e-90) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / ((x + t) / x);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.3e-25) {
		tmp = t_2;
	} else if (y <= -1.75e-240) {
		tmp = t_1;
	} else if (y <= -5.7e-272) {
		tmp = a;
	} else if (y <= 4.2e-254) {
		tmp = z * (x / (x + t));
	} else if (y <= 1.7e-229) {
		tmp = (a * t) / (y + (x + t));
	} else if (y <= 2e-90) {
		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 / ((x + t) / x)
    t_2 = (z + a) - b
    if (y <= (-1.3d-25)) then
        tmp = t_2
    else if (y <= (-1.75d-240)) then
        tmp = t_1
    else if (y <= (-5.7d-272)) then
        tmp = a
    else if (y <= 4.2d-254) then
        tmp = z * (x / (x + t))
    else if (y <= 1.7d-229) then
        tmp = (a * t) / (y + (x + t))
    else if (y <= 2d-90) 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 / ((x + t) / x);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.3e-25) {
		tmp = t_2;
	} else if (y <= -1.75e-240) {
		tmp = t_1;
	} else if (y <= -5.7e-272) {
		tmp = a;
	} else if (y <= 4.2e-254) {
		tmp = z * (x / (x + t));
	} else if (y <= 1.7e-229) {
		tmp = (a * t) / (y + (x + t));
	} else if (y <= 2e-90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z / ((x + t) / x)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -1.3e-25:
		tmp = t_2
	elif y <= -1.75e-240:
		tmp = t_1
	elif y <= -5.7e-272:
		tmp = a
	elif y <= 4.2e-254:
		tmp = z * (x / (x + t))
	elif y <= 1.7e-229:
		tmp = (a * t) / (y + (x + t))
	elif y <= 2e-90:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z / Float64(Float64(x + t) / x))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.3e-25)
		tmp = t_2;
	elseif (y <= -1.75e-240)
		tmp = t_1;
	elseif (y <= -5.7e-272)
		tmp = a;
	elseif (y <= 4.2e-254)
		tmp = Float64(z * Float64(x / Float64(x + t)));
	elseif (y <= 1.7e-229)
		tmp = Float64(Float64(a * t) / Float64(y + Float64(x + t)));
	elseif (y <= 2e-90)
		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 / ((x + t) / x);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.3e-25)
		tmp = t_2;
	elseif (y <= -1.75e-240)
		tmp = t_1;
	elseif (y <= -5.7e-272)
		tmp = a;
	elseif (y <= 4.2e-254)
		tmp = z * (x / (x + t));
	elseif (y <= 1.7e-229)
		tmp = (a * t) / (y + (x + t));
	elseif (y <= 2e-90)
		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[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.3e-25], t$95$2, If[LessEqual[y, -1.75e-240], t$95$1, If[LessEqual[y, -5.7e-272], a, If[LessEqual[y, 4.2e-254], N[(z * N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-229], N[(N[(a * t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-90], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.3e-25 or 1.99999999999999999e-90 < y

   1. Initial program 45.6%

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

   2. Taylor expanded in y around inf 68.5%

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

      1. +-commutative 68.5%

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

   4. Simplified 68.5%

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

   if -1.3e-25 < y < -1.75000000000000008e-240 or 1.7e-229 < y < 1.99999999999999999e-90

   1. Initial program 77.6%

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

   2. Taylor expanded in x around inf 46.5%

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

   3. Taylor expanded in y around 0 46.5%

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

      1. associate-/l* 63.0%

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

   5. Simplified 63.0%

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

   if -1.75000000000000008e-240 < y < -5.6999999999999999e-272

   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 t around inf 100.0%

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

   if -5.6999999999999999e-272 < y < 4.19999999999999993e-254

   1. Initial program 64.2%

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

   2. Taylor expanded in z around inf 39.9%

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

      1. associate-/l* 60.3%

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

   4. Simplified 60.3%

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

      1. associate-/r/ 60.3%

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

      2. +-commutative 60.3%

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

      3. +-commutative 60.3%

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

   6. Applied egg-rr 60.3%

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

   7. Taylor expanded in y around 0 60.3%

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

   if 4.19999999999999993e-254 < y < 1.7e-229

   1. Initial program 99.6%

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

   2. Taylor expanded in t around inf 72.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-25}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-240}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-272}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-254}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-229}:\\ \;\;\;\;\frac{a \cdot t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-90}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 7: 56.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{x + t}{x}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-273}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-255}:\\ \;\;\;\;\frac{x + y}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-229}:\\ \;\;\;\;\frac{a \cdot t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ z (/ (+ x t) x))) (t_2 (- (+ z a) b)))
   (if (<= y -2.3e-23)
     t_2
     (if (<= y -3.9e-240)
       t_1
       (if (<= y -6.5e-273)
         a
         (if (<= y 6.5e-255)
           (/ (+ x y) (/ (+ x t) z))
           (if (<= y 1.36e-229)
             (/ (* a t) (+ y (+ x t)))
             (if (<= y 1.7e-89) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / ((x + t) / x);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2.3e-23) {
		tmp = t_2;
	} else if (y <= -3.9e-240) {
		tmp = t_1;
	} else if (y <= -6.5e-273) {
		tmp = a;
	} else if (y <= 6.5e-255) {
		tmp = (x + y) / ((x + t) / z);
	} else if (y <= 1.36e-229) {
		tmp = (a * t) / (y + (x + t));
	} else if (y <= 1.7e-89) {
		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 / ((x + t) / x)
    t_2 = (z + a) - b
    if (y <= (-2.3d-23)) then
        tmp = t_2
    else if (y <= (-3.9d-240)) then
        tmp = t_1
    else if (y <= (-6.5d-273)) then
        tmp = a
    else if (y <= 6.5d-255) then
        tmp = (x + y) / ((x + t) / z)
    else if (y <= 1.36d-229) then
        tmp = (a * t) / (y + (x + t))
    else if (y <= 1.7d-89) 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 / ((x + t) / x);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2.3e-23) {
		tmp = t_2;
	} else if (y <= -3.9e-240) {
		tmp = t_1;
	} else if (y <= -6.5e-273) {
		tmp = a;
	} else if (y <= 6.5e-255) {
		tmp = (x + y) / ((x + t) / z);
	} else if (y <= 1.36e-229) {
		tmp = (a * t) / (y + (x + t));
	} else if (y <= 1.7e-89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z / ((x + t) / x)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -2.3e-23:
		tmp = t_2
	elif y <= -3.9e-240:
		tmp = t_1
	elif y <= -6.5e-273:
		tmp = a
	elif y <= 6.5e-255:
		tmp = (x + y) / ((x + t) / z)
	elif y <= 1.36e-229:
		tmp = (a * t) / (y + (x + t))
	elif y <= 1.7e-89:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z / Float64(Float64(x + t) / x))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.3e-23)
		tmp = t_2;
	elseif (y <= -3.9e-240)
		tmp = t_1;
	elseif (y <= -6.5e-273)
		tmp = a;
	elseif (y <= 6.5e-255)
		tmp = Float64(Float64(x + y) / Float64(Float64(x + t) / z));
	elseif (y <= 1.36e-229)
		tmp = Float64(Float64(a * t) / Float64(y + Float64(x + t)));
	elseif (y <= 1.7e-89)
		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 / ((x + t) / x);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.3e-23)
		tmp = t_2;
	elseif (y <= -3.9e-240)
		tmp = t_1;
	elseif (y <= -6.5e-273)
		tmp = a;
	elseif (y <= 6.5e-255)
		tmp = (x + y) / ((x + t) / z);
	elseif (y <= 1.36e-229)
		tmp = (a * t) / (y + (x + t));
	elseif (y <= 1.7e-89)
		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[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.3e-23], t$95$2, If[LessEqual[y, -3.9e-240], t$95$1, If[LessEqual[y, -6.5e-273], a, If[LessEqual[y, 6.5e-255], N[(N[(x + y), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.36e-229], N[(N[(a * t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-89], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.3000000000000001e-23 or 1.7e-89 < y

   1. Initial program 45.6%

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

   2. Taylor expanded in y around inf 68.5%

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

      1. +-commutative 68.5%

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

   4. Simplified 68.5%

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

   if -2.3000000000000001e-23 < y < -3.90000000000000015e-240 or 1.36e-229 < y < 1.7e-89

   1. Initial program 77.6%

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

   2. Taylor expanded in x around inf 46.5%

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

   3. Taylor expanded in y around 0 46.5%

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

      1. associate-/l* 63.0%

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

   5. Simplified 63.0%

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

   if -3.90000000000000015e-240 < y < -6.49999999999999979e-273

   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 t around inf 100.0%

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

   if -6.49999999999999979e-273 < y < 6.5e-255

   1. Initial program 64.2%

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

   2. Taylor expanded in z around inf 39.9%

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

      1. associate-/l* 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in y around 0 60.3%

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

      1. +-commutative 60.3%

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

   7. Simplified 60.3%

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

   if 6.5e-255 < y < 1.36e-229

   1. Initial program 99.6%

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

   2. Taylor expanded in t around inf 72.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-23}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-240}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-273}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-255}:\\ \;\;\;\;\frac{x + y}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-229}:\\ \;\;\;\;\frac{a \cdot t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-89}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 8: 71.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+195}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+143}:\\ \;\;\;\;\frac{-y}{\frac{t_1}{b}}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+106} \lor \neg \left(x \leq 2 \cdot 10^{+190}\right):\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= x -1.85e+195)
     (/ z (/ (+ x t) x))
     (if (<= x -1.5e+143)
       (/ (- y) (/ t_1 b))
       (if (or (<= x -3.5e+106) (not (<= x 2e+190)))
         (* z (/ (+ x y) t_1))
         (+ a (/ (- z b) (/ (+ y t) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (x <= -1.85e+195) {
		tmp = z / ((x + t) / x);
	} else if (x <= -1.5e+143) {
		tmp = -y / (t_1 / b);
	} else if ((x <= -3.5e+106) || !(x <= 2e+190)) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = a + ((z - b) / ((y + 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 = y + (x + t)
    if (x <= (-1.85d+195)) then
        tmp = z / ((x + t) / x)
    else if (x <= (-1.5d+143)) then
        tmp = -y / (t_1 / b)
    else if ((x <= (-3.5d+106)) .or. (.not. (x <= 2d+190))) then
        tmp = z * ((x + y) / t_1)
    else
        tmp = a + ((z - b) / ((y + 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 = y + (x + t);
	double tmp;
	if (x <= -1.85e+195) {
		tmp = z / ((x + t) / x);
	} else if (x <= -1.5e+143) {
		tmp = -y / (t_1 / b);
	} else if ((x <= -3.5e+106) || !(x <= 2e+190)) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = a + ((z - b) / ((y + t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if x <= -1.85e+195:
		tmp = z / ((x + t) / x)
	elif x <= -1.5e+143:
		tmp = -y / (t_1 / b)
	elif (x <= -3.5e+106) or not (x <= 2e+190):
		tmp = z * ((x + y) / t_1)
	else:
		tmp = a + ((z - b) / ((y + t) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (x <= -1.85e+195)
		tmp = Float64(z / Float64(Float64(x + t) / x));
	elseif (x <= -1.5e+143)
		tmp = Float64(Float64(-y) / Float64(t_1 / b));
	elseif ((x <= -3.5e+106) || !(x <= 2e+190))
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	else
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (x <= -1.85e+195)
		tmp = z / ((x + t) / x);
	elseif (x <= -1.5e+143)
		tmp = -y / (t_1 / b);
	elseif ((x <= -3.5e+106) || ~((x <= 2e+190)))
		tmp = z * ((x + y) / t_1);
	else
		tmp = a + ((z - b) / ((y + t) / y));
	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[x, -1.85e+195], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e+143], N[((-y) / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.5e+106], N[Not[LessEqual[x, 2e+190]], $MachinePrecision]], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.85e195

   1. Initial program 35.0%

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

   2. Taylor expanded in x around inf 25.4%

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

   3. Taylor expanded in y around 0 25.4%

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

      1. associate-/l* 72.4%

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

   5. Simplified 72.4%

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

   if -1.85e195 < x < -1.5e143

   1. Initial program 71.8%

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

   2. Taylor expanded in b around inf 40.1%

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

      1. mul-1-neg 40.1%

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

      2. associate-/l* 51.1%

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

      3. distribute-neg-frac 51.1%

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

   4. Simplified 51.1%

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

   if -1.5e143 < x < -3.49999999999999981e106 or 2.0000000000000001e190 < x

   1. Initial program 55.2%

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

   2. Taylor expanded in z around inf 34.2%

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

      1. associate-/l* 55.8%

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

   4. Simplified 55.8%

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

      1. associate-/r/ 63.6%

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

      2. +-commutative 63.6%

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

      3. +-commutative 63.6%

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

   6. Applied egg-rr 63.6%

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

   if -3.49999999999999981e106 < x < 2.0000000000000001e190

   1. Initial program 65.0%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in a around inf 65.0%

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

      1. associate-/l* 76.5%

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

      2. +-commutative 76.5%

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

      3. associate-/l* 96.4%

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

   6. Simplified 96.4%

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

   7. Taylor expanded in y around inf 90.6%

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

   8. Taylor expanded in x around 0 55.6%

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

      1. associate-/l* 78.3%

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

   10. Simplified 78.3%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+195}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+143}:\\ \;\;\;\;\frac{-y}{\frac{y + \left(x + t\right)}{b}}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+106} \lor \neg \left(x \leq 2 \cdot 10^{+190}\right):\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \end{array} \]

Alternative 9: 57.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{x + t}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.1 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.72 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-275}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ x (+ x t)))) (t_2 (- (+ z a) b)))
   (if (<= y -6.1e-27)
     t_2
     (if (<= y -1.72e-240)
       t_1
       (if (<= y -1.06e-275) a (if (<= y 2.3e-88) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x / (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.1e-27) {
		tmp = t_2;
	} else if (y <= -1.72e-240) {
		tmp = t_1;
	} else if (y <= -1.06e-275) {
		tmp = a;
	} else if (y <= 2.3e-88) {
		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 * (x / (x + t))
    t_2 = (z + a) - b
    if (y <= (-6.1d-27)) then
        tmp = t_2
    else if (y <= (-1.72d-240)) then
        tmp = t_1
    else if (y <= (-1.06d-275)) then
        tmp = a
    else if (y <= 2.3d-88) 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 * (x / (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.1e-27) {
		tmp = t_2;
	} else if (y <= -1.72e-240) {
		tmp = t_1;
	} else if (y <= -1.06e-275) {
		tmp = a;
	} else if (y <= 2.3e-88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (x / (x + t))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -6.1e-27:
		tmp = t_2
	elif y <= -1.72e-240:
		tmp = t_1
	elif y <= -1.06e-275:
		tmp = a
	elif y <= 2.3e-88:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x / Float64(x + t)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6.1e-27)
		tmp = t_2;
	elseif (y <= -1.72e-240)
		tmp = t_1;
	elseif (y <= -1.06e-275)
		tmp = a;
	elseif (y <= 2.3e-88)
		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 * (x / (x + t));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.1e-27)
		tmp = t_2;
	elseif (y <= -1.72e-240)
		tmp = t_1;
	elseif (y <= -1.06e-275)
		tmp = a;
	elseif (y <= 2.3e-88)
		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[(z * N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.1e-27], t$95$2, If[LessEqual[y, -1.72e-240], t$95$1, If[LessEqual[y, -1.06e-275], a, If[LessEqual[y, 2.3e-88], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.0999999999999999e-27 or 2.29999999999999986e-88 < y

   1. Initial program 45.6%

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

   2. Taylor expanded in y around inf 68.5%

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

      1. +-commutative 68.5%

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

   4. Simplified 68.5%

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

   if -6.0999999999999999e-27 < y < -1.7199999999999999e-240 or -1.05999999999999994e-275 < y < 2.29999999999999986e-88

   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 z around inf 44.7%

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

      1. associate-/l* 54.5%

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

   4. Simplified 54.5%

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

      1. associate-/r/ 60.6%

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

      2. +-commutative 60.6%

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

      3. +-commutative 60.6%

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

   6. Applied egg-rr 60.6%

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

   7. Taylor expanded in y around 0 58.6%

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

   if -1.7199999999999999e-240 < y < -1.05999999999999994e-275

   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 t around inf 100.0%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-27}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.72 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-275}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 57.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-240}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-274}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.3e-23)
     t_1
     (if (<= y -1.75e-240)
       (/ z (/ (+ x t) x))
       (if (<= y -7e-274) a (if (<= y 1.05e-88) (* z (/ x (+ x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.3e-23) {
		tmp = t_1;
	} else if (y <= -1.75e-240) {
		tmp = z / ((x + t) / x);
	} else if (y <= -7e-274) {
		tmp = a;
	} else if (y <= 1.05e-88) {
		tmp = z * (x / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.3d-23)) then
        tmp = t_1
    else if (y <= (-1.75d-240)) then
        tmp = z / ((x + t) / x)
    else if (y <= (-7d-274)) then
        tmp = a
    else if (y <= 1.05d-88) then
        tmp = z * (x / (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.3e-23) {
		tmp = t_1;
	} else if (y <= -1.75e-240) {
		tmp = z / ((x + t) / x);
	} else if (y <= -7e-274) {
		tmp = a;
	} else if (y <= 1.05e-88) {
		tmp = z * (x / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.3e-23:
		tmp = t_1
	elif y <= -1.75e-240:
		tmp = z / ((x + t) / x)
	elif y <= -7e-274:
		tmp = a
	elif y <= 1.05e-88:
		tmp = z * (x / (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.3e-23)
		tmp = t_1;
	elseif (y <= -1.75e-240)
		tmp = Float64(z / Float64(Float64(x + t) / x));
	elseif (y <= -7e-274)
		tmp = a;
	elseif (y <= 1.05e-88)
		tmp = Float64(z * Float64(x / Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.3e-23)
		tmp = t_1;
	elseif (y <= -1.75e-240)
		tmp = z / ((x + t) / x);
	elseif (y <= -7e-274)
		tmp = a;
	elseif (y <= 1.05e-88)
		tmp = z * (x / (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.3e-23], t$95$1, If[LessEqual[y, -1.75e-240], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-274], a, If[LessEqual[y, 1.05e-88], N[(z * N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e-23 or 1.05e-88 < y

   1. Initial program 45.6%

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

   2. Taylor expanded in y around inf 68.5%

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

      1. +-commutative 68.5%

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

   4. Simplified 68.5%

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

   if -1.3e-23 < y < -1.75000000000000008e-240

   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 x around inf 45.6%

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

   3. Taylor expanded in y around 0 45.7%

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

      1. associate-/l* 64.4%

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

   5. Simplified 64.4%

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

   if -1.75000000000000008e-240 < y < -6.99999999999999963e-274

   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 t around inf 100.0%

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

   if -6.99999999999999963e-274 < y < 1.05e-88

   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 z around inf 41.8%

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

      1. associate-/l* 47.9%

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

   4. Simplified 47.9%

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

      1. associate-/r/ 55.5%

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

      2. +-commutative 55.5%

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

      3. +-commutative 55.5%

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

   6. Applied egg-rr 55.5%

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

   7. Taylor expanded in y around 0 54.0%

      \[\leadsto \color{blue}{\frac{x}{t + x}} \cdot z \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-23}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-240}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-274}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 74.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+135}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+188}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.3e+135)
   (+ z (* y (- (/ a x) (/ b x))))
   (if (<= x 1.45e+188)
     (+ a (/ (- z b) (/ (+ y t) y)))
     (* z (/ (+ x y) (+ y (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.3e+135) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (x <= 1.45e+188) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else {
		tmp = z * ((x + y) / (y + (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 (x <= (-4.3d+135)) then
        tmp = z + (y * ((a / x) - (b / x)))
    else if (x <= 1.45d+188) then
        tmp = a + ((z - b) / ((y + t) / y))
    else
        tmp = z * ((x + y) / (y + (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 (x <= -4.3e+135) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (x <= 1.45e+188) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.3e+135:
		tmp = z + (y * ((a / x) - (b / x)))
	elif x <= 1.45e+188:
		tmp = a + ((z - b) / ((y + t) / y))
	else:
		tmp = z * ((x + y) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.3e+135)
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	elseif (x <= 1.45e+188)
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.3e+135)
		tmp = z + (y * ((a / x) - (b / x)));
	elseif (x <= 1.45e+188)
		tmp = a + ((z - b) / ((y + t) / y));
	else
		tmp = z * ((x + y) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.3e+135], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e+188], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.29999999999999972e135

   1. Initial program 47.5%

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

   3. Simplified 47.7%

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

   4. Taylor expanded in x around inf 61.9%

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

      1. associate--l+ 61.9%

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

      2. associate-/l* 70.4%

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

      3. sub-neg 70.4%

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

      4. +-commutative 70.4%

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

      5. associate-+r+ 70.4%

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

      6. sub-neg 70.4%

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

      7. +-commutative 70.4%

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

      8. associate-+l- 70.4%

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

      9. associate-/l* 73.6%

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

      10. associate-/l* 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in y around inf 75.3%

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

   if -4.29999999999999972e135 < x < 1.45e188

   1. Initial program 64.3%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in a around inf 64.3%

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

      1. associate-/l* 75.3%

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

      2. +-commutative 75.3%

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

      3. associate-/l* 94.4%

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

   6. Simplified 94.4%

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

   7. Taylor expanded in y around inf 87.8%

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

   8. Taylor expanded in x around 0 53.7%

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

      1. associate-/l* 77.0%

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

   10. Simplified 77.0%

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

   if 1.45e188 < x

   1. Initial program 55.8%

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

   2. Taylor expanded in z around inf 33.7%

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

      1. associate-/l* 46.2%

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

   4. Simplified 46.2%

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

      1. associate-/r/ 57.1%

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

      2. +-commutative 57.1%

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

      3. +-commutative 57.1%

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

   6. Applied egg-rr 57.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+135}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+188}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 12: 75.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+136}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+189}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{x} + \frac{t}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5e+136)
   (+ z (* y (- (/ a x) (/ b x))))
   (if (<= x 1.15e+189)
     (+ a (/ (- z b) (/ (+ y t) y)))
     (+ z (* a (+ (/ y x) (/ t x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5e+136) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (x <= 1.15e+189) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else {
		tmp = z + (a * ((y / x) + (t / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-5d+136)) then
        tmp = z + (y * ((a / x) - (b / x)))
    else if (x <= 1.15d+189) then
        tmp = a + ((z - b) / ((y + t) / y))
    else
        tmp = z + (a * ((y / x) + (t / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5e+136) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (x <= 1.15e+189) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else {
		tmp = z + (a * ((y / x) + (t / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5e+136:
		tmp = z + (y * ((a / x) - (b / x)))
	elif x <= 1.15e+189:
		tmp = a + ((z - b) / ((y + t) / y))
	else:
		tmp = z + (a * ((y / x) + (t / x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5e+136)
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	elseif (x <= 1.15e+189)
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	else
		tmp = Float64(z + Float64(a * Float64(Float64(y / x) + Float64(t / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5e+136)
		tmp = z + (y * ((a / x) - (b / x)));
	elseif (x <= 1.15e+189)
		tmp = a + ((z - b) / ((y + t) / y));
	else
		tmp = z + (a * ((y / x) + (t / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5e+136], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+189], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(a * N[(N[(y / x), $MachinePrecision] + N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.0000000000000002e136

   1. Initial program 47.5%

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

   3. Simplified 47.7%

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

   4. Taylor expanded in x around inf 61.9%

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

      1. associate--l+ 61.9%

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

      2. associate-/l* 70.4%

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

      3. sub-neg 70.4%

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

      4. +-commutative 70.4%

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

      5. associate-+r+ 70.4%

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

      6. sub-neg 70.4%

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

      7. +-commutative 70.4%

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

      8. associate-+l- 70.4%

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

      9. associate-/l* 73.6%

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

      10. associate-/l* 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in y around inf 75.3%

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

   if -5.0000000000000002e136 < x < 1.15e189

   1. Initial program 64.3%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in a around inf 64.3%

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

      1. associate-/l* 75.3%

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

      2. +-commutative 75.3%

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

      3. associate-/l* 94.4%

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

   6. Simplified 94.4%

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

   7. Taylor expanded in y around inf 87.8%

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

   8. Taylor expanded in x around 0 53.7%

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

      1. associate-/l* 77.0%

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

   10. Simplified 77.0%

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

   if 1.15e189 < x

   1. Initial program 55.8%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in x around inf 55.8%

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

      1. associate--l+ 55.8%

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

      2. associate-/l* 55.5%

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

      3. sub-neg 55.5%

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

      4. +-commutative 55.5%

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

      5. associate-+r+ 55.5%

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

      6. sub-neg 55.5%

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

      7. +-commutative 55.5%

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

      8. associate-+l- 55.5%

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

      9. associate-/l* 59.3%

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

      10. associate-/l* 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in a around inf 63.8%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+136}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+189}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{x} + \frac{t}{x}\right)\\ \end{array} \]

Alternative 13: 56.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-240}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-279}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+78}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.1e-27)
     t_1
     (if (<= y -3.2e-240)
       z
       (if (<= y -1.8e-279) a (if (<= y 3.1e+78) (+ z a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.1e-27) {
		tmp = t_1;
	} else if (y <= -3.2e-240) {
		tmp = z;
	} else if (y <= -1.8e-279) {
		tmp = a;
	} else if (y <= 3.1e+78) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.1d-27)) then
        tmp = t_1
    else if (y <= (-3.2d-240)) then
        tmp = z
    else if (y <= (-1.8d-279)) then
        tmp = a
    else if (y <= 3.1d+78) then
        tmp = z + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.1e-27) {
		tmp = t_1;
	} else if (y <= -3.2e-240) {
		tmp = z;
	} else if (y <= -1.8e-279) {
		tmp = a;
	} else if (y <= 3.1e+78) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.1e-27:
		tmp = t_1
	elif y <= -3.2e-240:
		tmp = z
	elif y <= -1.8e-279:
		tmp = a
	elif y <= 3.1e+78:
		tmp = z + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.1e-27)
		tmp = t_1;
	elseif (y <= -3.2e-240)
		tmp = z;
	elseif (y <= -1.8e-279)
		tmp = a;
	elseif (y <= 3.1e+78)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.1e-27)
		tmp = t_1;
	elseif (y <= -3.2e-240)
		tmp = z;
	elseif (y <= -1.8e-279)
		tmp = a;
	elseif (y <= 3.1e+78)
		tmp = z + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.1e-27], t$95$1, If[LessEqual[y, -3.2e-240], z, If[LessEqual[y, -1.8e-279], a, If[LessEqual[y, 3.1e+78], N[(z + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.10000000000000015e-27 or 3.1e78 < y

   1. Initial program 40.3%

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

   2. Taylor expanded in y around inf 72.1%

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

      1. +-commutative 72.1%

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

   4. Simplified 72.1%

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

   if -2.10000000000000015e-27 < y < -3.1999999999999999e-240

   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 x around inf 53.5%

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

   if -3.1999999999999999e-240 < y < -1.7999999999999998e-279

   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 t around inf 100.0%

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

   if -1.7999999999999998e-279 < y < 3.1e78

   1. Initial program 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in a around inf 73.2%

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

      1. associate-/l* 71.0%

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

      2. +-commutative 71.0%

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

      3. associate-/l* 79.6%

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

   6. Simplified 79.6%

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

   7. Taylor expanded in y around inf 61.1%

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

   8. Taylor expanded in x around inf 48.0%

      \[\leadsto \color{blue}{a + z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-27}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-240}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-279}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+78}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 14: 44.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+64}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+142}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.3e+64) a (if (<= a 4e+142) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.3e+64) {
		tmp = a;
	} else if (a <= 4e+142) {
		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 <= (-4.3d+64)) then
        tmp = a
    else if (a <= 4d+142) 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 <= -4.3e+64) {
		tmp = a;
	} else if (a <= 4e+142) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.3e+64:
		tmp = a
	elif a <= 4e+142:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.3e+64)
		tmp = a;
	elseif (a <= 4e+142)
		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 <= -4.3e+64)
		tmp = a;
	elseif (a <= 4e+142)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.3e+64], a, If[LessEqual[a, 4e+142], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -4.2999999999999998e64 or 4.0000000000000002e142 < a

   1. Initial program 42.7%

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

   2. Taylor expanded in t around inf 51.8%

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

   if -4.2999999999999998e64 < a < 4.0000000000000002e142

   1. Initial program 67.2%

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

   2. Taylor expanded in x around inf 44.3%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+64}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+142}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 15: 52.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+202}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -2.5e+202) z (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+202) {
		tmp = z;
	} else {
		tmp = z + 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 (x <= (-2.5d+202)) then
        tmp = z
    else
        tmp = z + 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 (x <= -2.5e+202) {
		tmp = z;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.5e+202:
		tmp = z
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.5e+202)
		tmp = z;
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.5e+202)
		tmp = z;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.5e+202], z, N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5e202

   1. Initial program 34.7%

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

   2. Taylor expanded in x around inf 74.5%

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

   if -2.5e202 < x

   1. Initial program 63.6%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in a around inf 63.6%

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

      1. associate-/l* 72.2%

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

      2. +-commutative 72.2%

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

      3. associate-/l* 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in y around inf 77.5%

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

   8. Taylor expanded in x around inf 48.3%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+202}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 16: 32.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.6%

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

2. Taylor expanded in t around inf 26.9%

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

3. Final simplification 26.9%

   \[\leadsto a \]

Developer target: 82.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t_2}{t_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t_1}{t_2}}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
        (t_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2023229 
(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)))