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

Percentage Accurate: 59.7% → 99.5%

Time: 19.8s

Alternatives: 21

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: 59.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(x + y\right) + t\\ t_3 := a \cdot \left(\frac{t}{t_2} + \frac{y}{t_2}\right)\\ t_4 := \left(x + y\right) \cdot z\\ t_5 := \frac{\left(t_4 + \left(y + t\right) \cdot a\right) - y \cdot b}{t_1}\\ t_6 := t_3 + \left(x + y\right) \cdot \frac{z}{t_1}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_6 - \frac{y}{\frac{t_1}{b}}\\ \mathbf{elif}\;t_5 \leq 10^{+307}:\\ \;\;\;\;\left(t_3 + \frac{t_4}{t_2}\right) - \frac{y \cdot b}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_6 - b \cdot \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ (+ x y) t))
        (t_3 (* a (+ (/ t t_2) (/ y t_2))))
        (t_4 (* (+ x y) z))
        (t_5 (/ (- (+ t_4 (* (+ y t) a)) (* y b)) t_1))
        (t_6 (+ t_3 (* (+ x y) (/ z t_1)))))
   (if (<= t_5 (- INFINITY))
     (- t_6 (/ y (/ t_1 b)))
     (if (<= t_5 1e+307)
       (- (+ t_3 (/ t_4 t_2)) (/ (* y b) t_2))
       (- t_6 (* b (/ 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 t_2 = (x + y) + t;
	double t_3 = a * ((t / t_2) + (y / t_2));
	double t_4 = (x + y) * z;
	double t_5 = ((t_4 + ((y + t) * a)) - (y * b)) / t_1;
	double t_6 = t_3 + ((x + y) * (z / t_1));
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_6 - (y / (t_1 / b));
	} else if (t_5 <= 1e+307) {
		tmp = (t_3 + (t_4 / t_2)) - ((y * b) / t_2);
	} else {
		tmp = t_6 - (b * (y / t_1));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (x + y) + t;
	double t_3 = a * ((t / t_2) + (y / t_2));
	double t_4 = (x + y) * z;
	double t_5 = ((t_4 + ((y + t) * a)) - (y * b)) / t_1;
	double t_6 = t_3 + ((x + y) * (z / t_1));
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = t_6 - (y / (t_1 / b));
	} else if (t_5 <= 1e+307) {
		tmp = (t_3 + (t_4 / t_2)) - ((y * b) / t_2);
	} else {
		tmp = t_6 - (b * (y / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (x + y) + t
	t_3 = a * ((t / t_2) + (y / t_2))
	t_4 = (x + y) * z
	t_5 = ((t_4 + ((y + t) * a)) - (y * b)) / t_1
	t_6 = t_3 + ((x + y) * (z / t_1))
	tmp = 0
	if t_5 <= -math.inf:
		tmp = t_6 - (y / (t_1 / b))
	elif t_5 <= 1e+307:
		tmp = (t_3 + (t_4 / t_2)) - ((y * b) / t_2)
	else:
		tmp = t_6 - (b * (y / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(x + y) + t)
	t_3 = Float64(a * Float64(Float64(t / t_2) + Float64(y / t_2)))
	t_4 = Float64(Float64(x + y) * z)
	t_5 = Float64(Float64(Float64(t_4 + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	t_6 = Float64(t_3 + Float64(Float64(x + y) * Float64(z / t_1)))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(t_6 - Float64(y / Float64(t_1 / b)));
	elseif (t_5 <= 1e+307)
		tmp = Float64(Float64(t_3 + Float64(t_4 / t_2)) - Float64(Float64(y * b) / t_2));
	else
		tmp = Float64(t_6 - Float64(b * Float64(y / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (x + y) + t;
	t_3 = a * ((t / t_2) + (y / t_2));
	t_4 = (x + y) * z;
	t_5 = ((t_4 + ((y + t) * a)) - (y * b)) / t_1;
	t_6 = t_3 + ((x + y) * (z / t_1));
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = t_6 - (y / (t_1 / b));
	elseif (t_5 <= 1e+307)
		tmp = (t_3 + (t_4 / t_2)) - ((y * b) / t_2);
	else
		tmp = t_6 - (b * (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]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(t / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$3 + N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(t$95$6 - N[(y / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 1e+307], N[(N[(t$95$3 + N[(t$95$4 / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$6 - N[(b * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 5.5%

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

   3. Taylor expanded in a around 0 45.2%

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

      1. *-un-lft-identity 45.2%

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

      2. times-frac 58.5%

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

      3. associate-+r+ 58.5%

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

      4. +-commutative 58.5%

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

      5. +-commutative 58.5%

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

   5. Applied egg-rr 58.5%

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

      1. *-commutative 58.5%

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

      2. *-un-lft-identity 58.5%

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

      3. times-frac 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in b around 0 82.9%

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

      1. *-commutative 82.9%

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

      2. +-commutative 82.9%

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

      3. +-commutative 82.9%

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

      4. associate-+r+ 82.9%

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

      5. associate-/l* 99.9%

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

      6. +-commutative 99.9%

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

   10. Simplified 99.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999986e306

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0 99.0%

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

   if 9.99999999999999986e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.0%

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

   3. Taylor expanded in a around 0 38.9%

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

      1. *-un-lft-identity 38.9%

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

      2. times-frac 57.0%

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

      3. associate-+r+ 57.0%

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

      4. +-commutative 57.0%

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

      5. +-commutative 57.0%

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

   5. Applied egg-rr 57.0%

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

      1. *-commutative 57.0%

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

      2. *-un-lft-identity 57.0%

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

      3. times-frac 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 99.4%

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

Alternative 2: 96.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(x + y\right) \cdot z\\ t_3 := \frac{\left(t_2 + \left(y + t\right) \cdot a\right) - y \cdot b}{t_1}\\ t_4 := \left(x + y\right) + t\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 10^{+307}\right):\\ \;\;\;\;\left(a + \left(x + y\right) \cdot \frac{z}{t_1}\right) - b \cdot \frac{y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(\frac{t}{t_4} + \frac{y}{t_4}\right) + \frac{t_2}{t_4}\right) - \frac{y \cdot b}{t_4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (* (+ x y) z))
        (t_3 (/ (- (+ t_2 (* (+ y t) a)) (* y b)) t_1))
        (t_4 (+ (+ x y) t)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 1e+307)))
     (- (+ a (* (+ x y) (/ z t_1))) (* b (/ y t_1)))
     (- (+ (* a (+ (/ t t_4) (/ y t_4))) (/ t_2 t_4)) (/ (* y b) t_4)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (x + y) * z;
	double t_3 = ((t_2 + ((y + t) * a)) - (y * b)) / t_1;
	double t_4 = (x + y) + t;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 1e+307)) {
		tmp = (a + ((x + y) * (z / t_1))) - (b * (y / t_1));
	} else {
		tmp = ((a * ((t / t_4) + (y / t_4))) + (t_2 / t_4)) - ((y * b) / t_4);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (x + y) * z;
	double t_3 = ((t_2 + ((y + t) * a)) - (y * b)) / t_1;
	double t_4 = (x + y) + t;
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 1e+307)) {
		tmp = (a + ((x + y) * (z / t_1))) - (b * (y / t_1));
	} else {
		tmp = ((a * ((t / t_4) + (y / t_4))) + (t_2 / t_4)) - ((y * b) / t_4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (x + y) * z
	t_3 = ((t_2 + ((y + t) * a)) - (y * b)) / t_1
	t_4 = (x + y) + t
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 1e+307):
		tmp = (a + ((x + y) * (z / t_1))) - (b * (y / t_1))
	else:
		tmp = ((a * ((t / t_4) + (y / t_4))) + (t_2 / t_4)) - ((y * b) / t_4)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(x + y) * z)
	t_3 = Float64(Float64(Float64(t_2 + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	t_4 = Float64(Float64(x + y) + t)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 1e+307))
		tmp = Float64(Float64(a + Float64(Float64(x + y) * Float64(z / t_1))) - Float64(b * Float64(y / t_1)));
	else
		tmp = Float64(Float64(Float64(a * Float64(Float64(t / t_4) + Float64(y / t_4))) + Float64(t_2 / t_4)) - Float64(Float64(y * b) / t_4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (x + y) * z;
	t_3 = ((t_2 + ((y + t) * a)) - (y * b)) / t_1;
	t_4 = (x + y) + t;
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 1e+307)))
		tmp = (a + ((x + y) * (z / t_1))) - (b * (y / t_1));
	else
		tmp = ((a * ((t / t_4) + (y / t_4))) + (t_2 / t_4)) - ((y * b) / t_4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 1e+307]], $MachinePrecision]], N[(N[(a + N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * N[(N[(t / t$95$4), $MachinePrecision] + N[(y / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 / t$95$4), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 9.99999999999999986e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.2%

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

   3. Taylor expanded in a around 0 42.0%

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

      1. *-un-lft-identity 42.0%

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

      2. times-frac 57.7%

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

      3. associate-+r+ 57.7%

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

      4. +-commutative 57.7%

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

      5. +-commutative 57.7%

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

   5. Applied egg-rr 57.7%

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

      1. *-commutative 57.7%

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

      2. *-un-lft-identity 57.7%

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

      3. times-frac 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in t around inf 92.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999986e306

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0 99.0%

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

4. Final simplification 96.2%

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

Alternative 3: 99.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := a \cdot \left(\frac{t}{t_1} + \frac{y}{t_1}\right)\\ t_3 := y + \left(x + t\right)\\ t_4 := \left(x + y\right) \cdot z\\ t_5 := \frac{\left(t_4 + \left(y + t\right) \cdot a\right) - y \cdot b}{t_3}\\ \mathbf{if}\;t_5 \leq -\infty \lor \neg \left(t_5 \leq 10^{+307}\right):\\ \;\;\;\;\left(t_2 + \left(x + y\right) \cdot \frac{z}{t_3}\right) - \frac{y}{\frac{t_3}{b}}\\ \mathbf{else}:\\ \;\;\;\;\left(t_2 + \frac{t_4}{t_1}\right) - \frac{y \cdot b}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t))
        (t_2 (* a (+ (/ t t_1) (/ y t_1))))
        (t_3 (+ y (+ x t)))
        (t_4 (* (+ x y) z))
        (t_5 (/ (- (+ t_4 (* (+ y t) a)) (* y b)) t_3)))
   (if (or (<= t_5 (- INFINITY)) (not (<= t_5 1e+307)))
     (- (+ t_2 (* (+ x y) (/ z t_3))) (/ y (/ t_3 b)))
     (- (+ t_2 (/ t_4 t_1)) (/ (* y b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = a * ((t / t_1) + (y / t_1));
	double t_3 = y + (x + t);
	double t_4 = (x + y) * z;
	double t_5 = ((t_4 + ((y + t) * a)) - (y * b)) / t_3;
	double tmp;
	if ((t_5 <= -((double) INFINITY)) || !(t_5 <= 1e+307)) {
		tmp = (t_2 + ((x + y) * (z / t_3))) - (y / (t_3 / b));
	} else {
		tmp = (t_2 + (t_4 / t_1)) - ((y * b) / t_1);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = a * ((t / t_1) + (y / t_1));
	double t_3 = y + (x + t);
	double t_4 = (x + y) * z;
	double t_5 = ((t_4 + ((y + t) * a)) - (y * b)) / t_3;
	double tmp;
	if ((t_5 <= -Double.POSITIVE_INFINITY) || !(t_5 <= 1e+307)) {
		tmp = (t_2 + ((x + y) * (z / t_3))) - (y / (t_3 / b));
	} else {
		tmp = (t_2 + (t_4 / t_1)) - ((y * b) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + t
	t_2 = a * ((t / t_1) + (y / t_1))
	t_3 = y + (x + t)
	t_4 = (x + y) * z
	t_5 = ((t_4 + ((y + t) * a)) - (y * b)) / t_3
	tmp = 0
	if (t_5 <= -math.inf) or not (t_5 <= 1e+307):
		tmp = (t_2 + ((x + y) * (z / t_3))) - (y / (t_3 / b))
	else:
		tmp = (t_2 + (t_4 / t_1)) - ((y * b) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(a * Float64(Float64(t / t_1) + Float64(y / t_1)))
	t_3 = Float64(y + Float64(x + t))
	t_4 = Float64(Float64(x + y) * z)
	t_5 = Float64(Float64(Float64(t_4 + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_3)
	tmp = 0.0
	if ((t_5 <= Float64(-Inf)) || !(t_5 <= 1e+307))
		tmp = Float64(Float64(t_2 + Float64(Float64(x + y) * Float64(z / t_3))) - Float64(y / Float64(t_3 / b)));
	else
		tmp = Float64(Float64(t_2 + Float64(t_4 / t_1)) - Float64(Float64(y * b) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + t;
	t_2 = a * ((t / t_1) + (y / t_1));
	t_3 = y + (x + t);
	t_4 = (x + y) * z;
	t_5 = ((t_4 + ((y + t) * a)) - (y * b)) / t_3;
	tmp = 0.0;
	if ((t_5 <= -Inf) || ~((t_5 <= 1e+307)))
		tmp = (t_2 + ((x + y) * (z / t_3))) - (y / (t_3 / b));
	else
		tmp = (t_2 + (t_4 / t_1)) - ((y * b) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[Or[LessEqual[t$95$5, (-Infinity)], N[Not[LessEqual[t$95$5, 1e+307]], $MachinePrecision]], N[(N[(t$95$2 + N[(N[(x + y), $MachinePrecision] * N[(z / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$3 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 + N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 9.99999999999999986e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.2%

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

   3. Taylor expanded in a around 0 42.0%

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

      1. *-un-lft-identity 42.0%

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

      2. times-frac 57.7%

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

      3. associate-+r+ 57.7%

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

      4. +-commutative 57.7%

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

      5. +-commutative 57.7%

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

   5. Applied egg-rr 57.7%

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

      1. *-commutative 57.7%

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

      2. *-un-lft-identity 57.7%

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

      3. times-frac 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in b around 0 76.9%

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

      1. *-commutative 76.9%

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

      2. +-commutative 76.9%

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

      3. +-commutative 76.9%

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

      4. associate-+r+ 76.9%

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

      5. associate-/l* 99.9%

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

      6. +-commutative 99.9%

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

   10. Simplified 99.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999986e306

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0 99.0%

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

4. Final simplification 99.4%

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

Alternative 4: 90.9% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+307)))
     (+ (* a (/ (+ y t) t_1)) (* (+ x y) (/ z t_1)))
     t_2)))

C

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

Java

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

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+307):
		tmp = (a * ((y + t) / t_1)) + ((x + y) * (z / t_1))
	else:
		tmp = t_2
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 1e+307]], $MachinePrecision]], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 9.99999999999999986e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.2%

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

   3. Taylor expanded in b around 0 5.0%

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

   4. Taylor expanded in a around inf 5.0%

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

      1. associate-/l* 44.8%

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

      2. associate-+r+ 44.8%

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

      3. +-commutative 44.8%

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

      4. +-commutative 44.8%

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

      5. *-commutative 44.8%

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

      6. +-commutative 44.8%

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

      7. +-commutative 44.8%

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

      8. associate-+r+ 44.8%

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

      9. associate-*r/ 81.3%

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

      10. +-commutative 81.3%

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

      11. +-commutative 81.3%

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

   6. Simplified 81.3%

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

      1. div-inv 81.3%

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

      2. clear-num 81.3%

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

      3. +-commutative 81.3%

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

   8. Applied egg-rr 81.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999986e306

   1. Initial program 99.0%

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

4. Final simplification 91.9%

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

Alternative 5: 96.4% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+307)))
     (- (+ a (* (+ x y) (/ z t_1))) (* b (/ y t_1)))
     t_2)))

C

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

Java

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

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+307):
		tmp = (a + ((x + y) * (z / t_1))) - (b * (y / t_1))
	else:
		tmp = t_2
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 1e+307]], $MachinePrecision]], N[(N[(a + N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 9.99999999999999986e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.2%

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

   3. Taylor expanded in a around 0 42.0%

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

      1. *-un-lft-identity 42.0%

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

      2. times-frac 57.7%

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

      3. associate-+r+ 57.7%

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

      4. +-commutative 57.7%

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

      5. +-commutative 57.7%

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

   5. Applied egg-rr 57.7%

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

      1. *-commutative 57.7%

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

      2. *-un-lft-identity 57.7%

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

      3. times-frac 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in t around inf 92.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999986e306

   1. Initial program 99.0%

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

4. Final simplification 96.2%

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

Alternative 6: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;a + \left(x + y\right) \cdot \frac{z}{t_1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+256}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) t_1)))
   (if (<= t_2 (- INFINITY))
     (+ a (* (+ x y) (/ z t_1)))
     (if (<= t_2 2e+256) t_2 (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = a + ((x + y) * (z / t_1));
	} else if (t_2 <= 2e+256) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = a + ((x + y) * (z / t_1));
	} else if (t_2 <= 2e+256) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = a + ((x + y) * (z / t_1))
	elif t_2 <= 2e+256:
		tmp = t_2
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(a + Float64(Float64(x + y) * Float64(z / t_1)));
	elseif (t_2 <= 2e+256)
		tmp = t_2;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = a + ((x + y) * (z / t_1));
	elseif (t_2 <= 2e+256)
		tmp = t_2;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(a + N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+256], t$95$2, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 5.5%

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

   3. Taylor expanded in b around 0 5.3%

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

   4. Taylor expanded in a around inf 5.3%

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

      1. associate-/l* 48.8%

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

      2. associate-+r+ 48.8%

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

      3. +-commutative 48.8%

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

      4. +-commutative 48.8%

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

      5. *-commutative 48.8%

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

      6. +-commutative 48.8%

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

      7. +-commutative 48.8%

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

      8. associate-+r+ 48.8%

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

      9. associate-*r/ 86.4%

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

      10. +-commutative 86.4%

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

      11. +-commutative 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in y around inf 80.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e256

   1. Initial program 99.0%

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

   if 2.0000000000000001e256 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.4%

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

   3. Taylor expanded in y around inf 70.0%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;a + \left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+256}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(x + y\right) \cdot \frac{z}{t_1} + \frac{a}{1 + \frac{x}{t}}\\ \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-195}:\\ \;\;\;\;z + \frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-246}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+33}:\\ \;\;\;\;z + a \cdot \frac{y + t}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ (* (+ x y) (/ z t_1)) (/ a (+ 1.0 (/ x t))))))
   (if (<= z -5200000000.0)
     t_2
     (if (<= z -3.5e-195)
       (+ z (/ a (/ t_1 (+ y t))))
       (if (<= z -2.1e-246)
         (- (+ z a) b)
         (if (<= z 6.4e+33) (+ z (* a (/ (+ y t) t_1))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((x + y) * (z / t_1)) + (a / (1.0 + (x / t)));
	double tmp;
	if (z <= -5200000000.0) {
		tmp = t_2;
	} else if (z <= -3.5e-195) {
		tmp = z + (a / (t_1 / (y + t)));
	} else if (z <= -2.1e-246) {
		tmp = (z + a) - b;
	} else if (z <= 6.4e+33) {
		tmp = z + (a * ((y + t) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = ((x + y) * (z / t_1)) + (a / (1.0d0 + (x / t)))
    if (z <= (-5200000000.0d0)) then
        tmp = t_2
    else if (z <= (-3.5d-195)) then
        tmp = z + (a / (t_1 / (y + t)))
    else if (z <= (-2.1d-246)) then
        tmp = (z + a) - b
    else if (z <= 6.4d+33) then
        tmp = z + (a * ((y + t) / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((x + y) * (z / t_1)) + (a / (1.0 + (x / t)));
	double tmp;
	if (z <= -5200000000.0) {
		tmp = t_2;
	} else if (z <= -3.5e-195) {
		tmp = z + (a / (t_1 / (y + t)));
	} else if (z <= -2.1e-246) {
		tmp = (z + a) - b;
	} else if (z <= 6.4e+33) {
		tmp = z + (a * ((y + t) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((x + y) * (z / t_1)) + (a / (1.0 + (x / t)))
	tmp = 0
	if z <= -5200000000.0:
		tmp = t_2
	elif z <= -3.5e-195:
		tmp = z + (a / (t_1 / (y + t)))
	elif z <= -2.1e-246:
		tmp = (z + a) - b
	elif z <= 6.4e+33:
		tmp = z + (a * ((y + t) / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(x + y) * Float64(z / t_1)) + Float64(a / Float64(1.0 + Float64(x / t))))
	tmp = 0.0
	if (z <= -5200000000.0)
		tmp = t_2;
	elseif (z <= -3.5e-195)
		tmp = Float64(z + Float64(a / Float64(t_1 / Float64(y + t))));
	elseif (z <= -2.1e-246)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= 6.4e+33)
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((x + y) * (z / t_1)) + (a / (1.0 + (x / t)));
	tmp = 0.0;
	if (z <= -5200000000.0)
		tmp = t_2;
	elseif (z <= -3.5e-195)
		tmp = z + (a / (t_1 / (y + t)));
	elseif (z <= -2.1e-246)
		tmp = (z + a) - b;
	elseif (z <= 6.4e+33)
		tmp = z + (a * ((y + t) / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5200000000.0], t$95$2, If[LessEqual[z, -3.5e-195], N[(z + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-246], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, 6.4e+33], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2e9 or 6.40000000000000034e33 < z

   1. Initial program 49.8%

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

   3. Taylor expanded in b around 0 38.6%

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

   4. Taylor expanded in a around inf 38.6%

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

      1. associate-/l* 50.5%

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

      2. associate-+r+ 50.5%

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

      3. +-commutative 50.5%

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

      4. +-commutative 50.5%

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

      5. *-commutative 50.5%

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

      6. +-commutative 50.5%

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

      7. +-commutative 50.5%

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

      8. associate-+r+ 50.5%

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

      9. associate-*r/ 82.6%

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

      10. +-commutative 82.6%

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

      11. +-commutative 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in t around inf 80.1%

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

   if -5.2e9 < z < -3.50000000000000014e-195

   1. Initial program 76.7%

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

   3. Taylor expanded in b around 0 57.6%

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

   4. Taylor expanded in a around inf 57.6%

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

      1. associate-/l* 69.0%

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

      2. associate-+r+ 69.0%

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

      3. +-commutative 69.0%

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

      4. +-commutative 69.0%

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

      5. *-commutative 69.0%

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

      6. +-commutative 69.0%

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

      7. +-commutative 69.0%

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

      8. associate-+r+ 69.0%

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

      9. associate-*r/ 55.1%

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

      10. +-commutative 55.1%

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

      11. +-commutative 55.1%

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

   6. Simplified 55.1%

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

   7. Taylor expanded in y around inf 66.8%

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

   if -3.50000000000000014e-195 < z < -2.09999999999999995e-246

   1. Initial program 41.7%

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

   3. Taylor expanded in y around inf 78.6%

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

   if -2.09999999999999995e-246 < z < 6.40000000000000034e33

   1. Initial program 73.1%

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

   3. Taylor expanded in b around 0 58.3%

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

   4. Taylor expanded in a around inf 58.3%

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

      1. associate-/l* 77.2%

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

      2. associate-+r+ 77.2%

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

      3. +-commutative 77.2%

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

      4. +-commutative 77.2%

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

      5. *-commutative 77.2%

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

      6. +-commutative 77.2%

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

      7. +-commutative 77.2%

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

      8. associate-+r+ 77.2%

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

      9. associate-*r/ 73.9%

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

      10. +-commutative 73.9%

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

      11. +-commutative 73.9%

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

   6. Simplified 73.9%

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

      1. div-inv 73.9%

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

      2. clear-num 74.0%

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

      3. +-commutative 74.0%

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

   8. Applied egg-rr 74.0%

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

   9. Taylor expanded in y around inf 75.1%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)} + \frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-195}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-246}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+33}:\\ \;\;\;\;z + a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)} + \frac{a}{1 + \frac{x}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := a + \left(x + y\right) \cdot \frac{z}{t_1}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-61}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (- (+ z a) b))
        (t_3 (+ a (* (+ x y) (/ z t_1)))))
   (if (<= z -2.05e-60)
     t_3
     (if (<= z -8.4e-253)
       t_2
       (if (<= z 1.8e-61) (/ a (/ t_1 (+ y t))) (if (<= z 4e+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 + a) - b;
	double t_3 = a + ((x + y) * (z / t_1));
	double tmp;
	if (z <= -2.05e-60) {
		tmp = t_3;
	} else if (z <= -8.4e-253) {
		tmp = t_2;
	} else if (z <= 1.8e-61) {
		tmp = a / (t_1 / (y + t));
	} else if (z <= 4e+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 + a) - b
    t_3 = a + ((x + y) * (z / t_1))
    if (z <= (-2.05d-60)) then
        tmp = t_3
    else if (z <= (-8.4d-253)) then
        tmp = t_2
    else if (z <= 1.8d-61) then
        tmp = a / (t_1 / (y + t))
    else if (z <= 4d+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 + a) - b;
	double t_3 = a + ((x + y) * (z / t_1));
	double tmp;
	if (z <= -2.05e-60) {
		tmp = t_3;
	} else if (z <= -8.4e-253) {
		tmp = t_2;
	} else if (z <= 1.8e-61) {
		tmp = a / (t_1 / (y + t));
	} else if (z <= 4e+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 + a) - b
	t_3 = a + ((x + y) * (z / t_1))
	tmp = 0
	if z <= -2.05e-60:
		tmp = t_3
	elif z <= -8.4e-253:
		tmp = t_2
	elif z <= 1.8e-61:
		tmp = a / (t_1 / (y + t))
	elif z <= 4e+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(Float64(z + a) - b)
	t_3 = Float64(a + Float64(Float64(x + y) * Float64(z / t_1)))
	tmp = 0.0
	if (z <= -2.05e-60)
		tmp = t_3;
	elseif (z <= -8.4e-253)
		tmp = t_2;
	elseif (z <= 1.8e-61)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (z <= 4e+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 + a) - b;
	t_3 = a + ((x + y) * (z / t_1));
	tmp = 0.0;
	if (z <= -2.05e-60)
		tmp = t_3;
	elseif (z <= -8.4e-253)
		tmp = t_2;
	elseif (z <= 1.8e-61)
		tmp = a / (t_1 / (y + t));
	elseif (z <= 4e+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[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e-60], t$95$3, If[LessEqual[z, -8.4e-253], t$95$2, If[LessEqual[z, 1.8e-61], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+88], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05000000000000006e-60 or 3.99999999999999984e88 < z

   1. Initial program 50.7%

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

   3. Taylor expanded in b around 0 42.5%

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

   4. Taylor expanded in a around inf 42.5%

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

      1. associate-/l* 54.2%

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

      2. associate-+r+ 54.2%

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

      3. +-commutative 54.2%

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

      4. +-commutative 54.2%

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

      5. *-commutative 54.2%

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

      6. +-commutative 54.2%

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

      7. +-commutative 54.2%

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

      8. associate-+r+ 54.2%

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

      9. associate-*r/ 84.9%

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

      10. +-commutative 84.9%

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

      11. +-commutative 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in y around inf 76.2%

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

   if -2.05000000000000006e-60 < z < -8.3999999999999996e-253 or 1.80000000000000007e-61 < z < 3.99999999999999984e88

   1. Initial program 65.7%

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

   3. Taylor expanded in y around inf 67.2%

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

   if -8.3999999999999996e-253 < z < 1.80000000000000007e-61

   1. Initial program 74.3%

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

   3. Taylor expanded in a around inf 50.0%

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

      1. associate-/l* 69.8%

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

      2. associate-+r+ 69.8%

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

   5. Simplified 69.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-60}:\\ \;\;\;\;a + \left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-253}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-61}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+88}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z + a \cdot \frac{y + t}{t_1}\\ t_3 := a + \left(x + y\right) \cdot \frac{z}{t_1}\\ \mathbf{if}\;z \leq -0.0007:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-246}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ z (* a (/ (+ y t) t_1))))
        (t_3 (+ a (* (+ x y) (/ z t_1)))))
   (if (<= z -0.0007)
     t_3
     (if (<= z -6.2e-197)
       t_2
       (if (<= z -2.1e-246) (- (+ z a) b) (if (<= z 3.5e+58) 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 + (a * ((y + t) / t_1));
	double t_3 = a + ((x + y) * (z / t_1));
	double tmp;
	if (z <= -0.0007) {
		tmp = t_3;
	} else if (z <= -6.2e-197) {
		tmp = t_2;
	} else if (z <= -2.1e-246) {
		tmp = (z + a) - b;
	} else if (z <= 3.5e+58) {
		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 + (a * ((y + t) / t_1))
    t_3 = a + ((x + y) * (z / t_1))
    if (z <= (-0.0007d0)) then
        tmp = t_3
    else if (z <= (-6.2d-197)) then
        tmp = t_2
    else if (z <= (-2.1d-246)) then
        tmp = (z + a) - b
    else if (z <= 3.5d+58) 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 + (a * ((y + t) / t_1));
	double t_3 = a + ((x + y) * (z / t_1));
	double tmp;
	if (z <= -0.0007) {
		tmp = t_3;
	} else if (z <= -6.2e-197) {
		tmp = t_2;
	} else if (z <= -2.1e-246) {
		tmp = (z + a) - b;
	} else if (z <= 3.5e+58) {
		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 + (a * ((y + t) / t_1))
	t_3 = a + ((x + y) * (z / t_1))
	tmp = 0
	if z <= -0.0007:
		tmp = t_3
	elif z <= -6.2e-197:
		tmp = t_2
	elif z <= -2.1e-246:
		tmp = (z + a) - b
	elif z <= 3.5e+58:
		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(a * Float64(Float64(y + t) / t_1)))
	t_3 = Float64(a + Float64(Float64(x + y) * Float64(z / t_1)))
	tmp = 0.0
	if (z <= -0.0007)
		tmp = t_3;
	elseif (z <= -6.2e-197)
		tmp = t_2;
	elseif (z <= -2.1e-246)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= 3.5e+58)
		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 + (a * ((y + t) / t_1));
	t_3 = a + ((x + y) * (z / t_1));
	tmp = 0.0;
	if (z <= -0.0007)
		tmp = t_3;
	elseif (z <= -6.2e-197)
		tmp = t_2;
	elseif (z <= -2.1e-246)
		tmp = (z + a) - b;
	elseif (z <= 3.5e+58)
		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[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0007], t$95$3, If[LessEqual[z, -6.2e-197], t$95$2, If[LessEqual[z, -2.1e-246], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, 3.5e+58], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999993e-4 or 3.4999999999999997e58 < z

   1. Initial program 49.8%

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

   3. Taylor expanded in b around 0 39.4%

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

   4. Taylor expanded in a around inf 39.4%

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

      1. associate-/l* 49.8%

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

      2. associate-+r+ 49.8%

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

      3. +-commutative 49.8%

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

      4. +-commutative 49.8%

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

      5. *-commutative 49.8%

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

      6. +-commutative 49.8%

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

      7. +-commutative 49.8%

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

      8. associate-+r+ 49.8%

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

      9. associate-*r/ 82.5%

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

      10. +-commutative 82.5%

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

      11. +-commutative 82.5%

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

   6. Simplified 82.5%

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

   7. Taylor expanded in y around inf 76.1%

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

   if -6.99999999999999993e-4 < z < -6.20000000000000057e-197 or -2.09999999999999995e-246 < z < 3.4999999999999997e58

   1. Initial program 73.9%

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

   3. Taylor expanded in b around 0 57.1%

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

   4. Taylor expanded in a around inf 57.1%

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

      1. associate-/l* 74.7%

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

      2. associate-+r+ 74.7%

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

      3. +-commutative 74.7%

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

      4. +-commutative 74.7%

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

      5. *-commutative 74.7%

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

      6. +-commutative 74.7%

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

      7. +-commutative 74.7%

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

      8. associate-+r+ 74.7%

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

      9. associate-*r/ 68.1%

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

      10. +-commutative 68.1%

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

      11. +-commutative 68.1%

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

   6. Simplified 68.1%

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

      1. div-inv 68.1%

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

      2. clear-num 68.1%

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

      3. +-commutative 68.1%

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

   8. Applied egg-rr 68.1%

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

   9. Taylor expanded in y around inf 72.4%

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

   if -6.20000000000000057e-197 < z < -2.09999999999999995e-246

   1. Initial program 41.7%

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

   3. Taylor expanded in y around inf 78.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0007:\\ \;\;\;\;a + \left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-197}:\\ \;\;\;\;z + a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-246}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+58}:\\ \;\;\;\;z + a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a + \left(x + y\right) \cdot \frac{z}{t_1}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-197}:\\ \;\;\;\;z + \frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-246}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+52}:\\ \;\;\;\;z + a \cdot \frac{y + t}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (+ a (* (+ x y) (/ z t_1)))))
   (if (<= z -2.6e-7)
     t_2
     (if (<= z -6.8e-197)
       (+ z (/ a (/ t_1 (+ y t))))
       (if (<= z -2.15e-246)
         (- (+ z a) b)
         (if (<= z 1.05e+52) (+ z (* a (/ (+ y t) t_1))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + ((x + y) * (z / t_1));
	double tmp;
	if (z <= -2.6e-7) {
		tmp = t_2;
	} else if (z <= -6.8e-197) {
		tmp = z + (a / (t_1 / (y + t)));
	} else if (z <= -2.15e-246) {
		tmp = (z + a) - b;
	} else if (z <= 1.05e+52) {
		tmp = z + (a * ((y + t) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a + ((x + y) * (z / t_1))
    if (z <= (-2.6d-7)) then
        tmp = t_2
    else if (z <= (-6.8d-197)) then
        tmp = z + (a / (t_1 / (y + t)))
    else if (z <= (-2.15d-246)) then
        tmp = (z + a) - b
    else if (z <= 1.05d+52) then
        tmp = z + (a * ((y + t) / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + ((x + y) * (z / t_1));
	double tmp;
	if (z <= -2.6e-7) {
		tmp = t_2;
	} else if (z <= -6.8e-197) {
		tmp = z + (a / (t_1 / (y + t)));
	} else if (z <= -2.15e-246) {
		tmp = (z + a) - b;
	} else if (z <= 1.05e+52) {
		tmp = z + (a * ((y + t) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a + ((x + y) * (z / t_1))
	tmp = 0
	if z <= -2.6e-7:
		tmp = t_2
	elif z <= -6.8e-197:
		tmp = z + (a / (t_1 / (y + t)))
	elif z <= -2.15e-246:
		tmp = (z + a) - b
	elif z <= 1.05e+52:
		tmp = z + (a * ((y + t) / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a + Float64(Float64(x + y) * Float64(z / t_1)))
	tmp = 0.0
	if (z <= -2.6e-7)
		tmp = t_2;
	elseif (z <= -6.8e-197)
		tmp = Float64(z + Float64(a / Float64(t_1 / Float64(y + t))));
	elseif (z <= -2.15e-246)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= 1.05e+52)
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a + ((x + y) * (z / t_1));
	tmp = 0.0;
	if (z <= -2.6e-7)
		tmp = t_2;
	elseif (z <= -6.8e-197)
		tmp = z + (a / (t_1 / (y + t)));
	elseif (z <= -2.15e-246)
		tmp = (z + a) - b;
	elseif (z <= 1.05e+52)
		tmp = z + (a * ((y + t) / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e-7], t$95$2, If[LessEqual[z, -6.8e-197], N[(z + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-246], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, 1.05e+52], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.59999999999999999e-7 or 1.05e52 < z

   1. Initial program 49.8%

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

   3. Taylor expanded in b around 0 39.4%

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

   4. Taylor expanded in a around inf 39.4%

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

      1. associate-/l* 49.8%

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

      2. associate-+r+ 49.8%

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

      3. +-commutative 49.8%

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

      4. +-commutative 49.8%

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

      5. *-commutative 49.8%

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

      6. +-commutative 49.8%

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

      7. +-commutative 49.8%

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

      8. associate-+r+ 49.8%

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

      9. associate-*r/ 82.5%

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

      10. +-commutative 82.5%

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

      11. +-commutative 82.5%

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

   6. Simplified 82.5%

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

   7. Taylor expanded in y around inf 76.1%

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

   if -2.59999999999999999e-7 < z < -6.7999999999999996e-197

   1. Initial program 81.9%

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

   3. Taylor expanded in b around 0 61.0%

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

   4. Taylor expanded in a around inf 60.9%

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

      1. associate-/l* 70.9%

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

      2. associate-+r+ 70.9%

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

      3. +-commutative 70.9%

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

      4. +-commutative 70.9%

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

      5. *-commutative 70.9%

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

      6. +-commutative 70.9%

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

      7. +-commutative 70.9%

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

      8. associate-+r+ 70.9%

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

      9. associate-*r/ 55.6%

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

      10. +-commutative 55.6%

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

      11. +-commutative 55.6%

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

   6. Simplified 55.6%

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

   7. Taylor expanded in y around inf 68.6%

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

   if -6.7999999999999996e-197 < z < -2.14999999999999996e-246

   1. Initial program 41.7%

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

   3. Taylor expanded in y around inf 78.6%

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

   if -2.14999999999999996e-246 < z < 1.05e52

   1. Initial program 70.6%

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

   3. Taylor expanded in b around 0 55.5%

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

   4. Taylor expanded in a around inf 55.5%

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

      1. associate-/l* 76.2%

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

      2. associate-+r+ 76.2%

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

      3. +-commutative 76.2%

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

      4. +-commutative 76.2%

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

      5. *-commutative 76.2%

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

      6. +-commutative 76.2%

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

      7. +-commutative 76.2%

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

      8. associate-+r+ 76.2%

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

      9. associate-*r/ 73.2%

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

      10. +-commutative 73.2%

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

      11. +-commutative 73.2%

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

   6. Simplified 73.2%

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

      1. div-inv 73.2%

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

      2. clear-num 73.2%

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

      3. +-commutative 73.2%

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

   8. Applied egg-rr 73.2%

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

   9. Taylor expanded in y around inf 74.0%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-7}:\\ \;\;\;\;a + \left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-197}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-246}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+52}:\\ \;\;\;\;z + a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+72}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-222}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -8.6e+72)
     (/ a (/ (+ x t) t))
     (if (<= t 1.25e-261)
       t_1
       (if (<= t 3.7e-222)
         z
         (if (<= t 6.6e+101) t_1 (+ a (/ (* x (- z a)) t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -8.6e+72) {
		tmp = a / ((x + t) / t);
	} else if (t <= 1.25e-261) {
		tmp = t_1;
	} else if (t <= 3.7e-222) {
		tmp = z;
	} else if (t <= 6.6e+101) {
		tmp = t_1;
	} else {
		tmp = a + ((x * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-8.6d+72)) then
        tmp = a / ((x + t) / t)
    else if (t <= 1.25d-261) then
        tmp = t_1
    else if (t <= 3.7d-222) then
        tmp = z
    else if (t <= 6.6d+101) then
        tmp = t_1
    else
        tmp = a + ((x * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -8.6e+72) {
		tmp = a / ((x + t) / t);
	} else if (t <= 1.25e-261) {
		tmp = t_1;
	} else if (t <= 3.7e-222) {
		tmp = z;
	} else if (t <= 6.6e+101) {
		tmp = t_1;
	} else {
		tmp = a + ((x * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -8.6e+72:
		tmp = a / ((x + t) / t)
	elif t <= 1.25e-261:
		tmp = t_1
	elif t <= 3.7e-222:
		tmp = z
	elif t <= 6.6e+101:
		tmp = t_1
	else:
		tmp = a + ((x * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -8.6e+72)
		tmp = Float64(a / Float64(Float64(x + t) / t));
	elseif (t <= 1.25e-261)
		tmp = t_1;
	elseif (t <= 3.7e-222)
		tmp = z;
	elseif (t <= 6.6e+101)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(Float64(x * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -8.6e+72)
		tmp = a / ((x + t) / t);
	elseif (t <= 1.25e-261)
		tmp = t_1;
	elseif (t <= 3.7e-222)
		tmp = z;
	elseif (t <= 6.6e+101)
		tmp = t_1;
	else
		tmp = a + ((x * (z - a)) / t);
	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[t, -8.6e+72], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-261], t$95$1, If[LessEqual[t, 3.7e-222], z, If[LessEqual[t, 6.6e+101], t$95$1, N[(a + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.6000000000000003e72

   1. Initial program 48.4%

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

   3. Taylor expanded in y around 0 36.2%

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

   4. Taylor expanded in a around inf 33.7%

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

      1. associate-/l* 65.5%

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

   6. Simplified 65.5%

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

   if -8.6000000000000003e72 < t < 1.24999999999999995e-261 or 3.6999999999999999e-222 < t < 6.60000000000000022e101

   1. Initial program 68.9%

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

   3. Taylor expanded in y around inf 62.1%

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

   if 1.24999999999999995e-261 < t < 3.6999999999999999e-222

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 59.0%

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

   if 6.60000000000000022e101 < t

   1. Initial program 39.1%

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

   3. Taylor expanded in y around 0 31.4%

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

   4. Taylor expanded in t around -inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. unsub-neg 59.4%

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

      3. distribute-lft-out-- 59.4%

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

      4. mul-1-neg 59.4%

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

      5. *-commutative 59.4%

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

      6. distribute-lft-out-- 59.5%

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

   6. Simplified 59.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+72}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-261}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-222}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+101}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;z \leq 2.6 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-146}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= z 2.6e-304)
     t_1
     (if (<= z 7.2e-146)
       (/ a (/ (+ x t) t))
       (if (<= z 5.5e+94) t_1 (* (+ x y) (/ z (+ y (+ x t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (z <= 2.6e-304) {
		tmp = t_1;
	} else if (z <= 7.2e-146) {
		tmp = a / ((x + t) / t);
	} else if (z <= 5.5e+94) {
		tmp = t_1;
	} else {
		tmp = (x + y) * (z / (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) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (z <= 2.6d-304) then
        tmp = t_1
    else if (z <= 7.2d-146) then
        tmp = a / ((x + t) / t)
    else if (z <= 5.5d+94) then
        tmp = t_1
    else
        tmp = (x + y) * (z / (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 t_1 = (z + a) - b;
	double tmp;
	if (z <= 2.6e-304) {
		tmp = t_1;
	} else if (z <= 7.2e-146) {
		tmp = a / ((x + t) / t);
	} else if (z <= 5.5e+94) {
		tmp = t_1;
	} else {
		tmp = (x + y) * (z / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if z <= 2.6e-304:
		tmp = t_1
	elif z <= 7.2e-146:
		tmp = a / ((x + t) / t)
	elif z <= 5.5e+94:
		tmp = t_1
	else:
		tmp = (x + y) * (z / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (z <= 2.6e-304)
		tmp = t_1;
	elseif (z <= 7.2e-146)
		tmp = Float64(a / Float64(Float64(x + t) / t));
	elseif (z <= 5.5e+94)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + y) * Float64(z / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (z <= 2.6e-304)
		tmp = t_1;
	elseif (z <= 7.2e-146)
		tmp = a / ((x + t) / t);
	elseif (z <= 5.5e+94)
		tmp = t_1;
	else
		tmp = (x + y) * (z / (y + (x + t)));
	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[z, 2.6e-304], t$95$1, If[LessEqual[z, 7.2e-146], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+94], t$95$1, N[(N[(x + y), $MachinePrecision] * N[(z / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < 2.59999999999999997e-304 or 7.19999999999999957e-146 < z < 5.4999999999999997e94

   1. Initial program 60.9%

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

   3. Taylor expanded in y around inf 59.2%

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

   if 2.59999999999999997e-304 < z < 7.19999999999999957e-146

   1. Initial program 74.6%

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

   3. Taylor expanded in y around 0 42.5%

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

   4. Taylor expanded in a around inf 42.0%

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

      1. associate-/l* 60.8%

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

   6. Simplified 60.8%

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

   if 5.4999999999999997e94 < z

   1. Initial program 53.7%

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

   3. Taylor expanded in b around 0 47.6%

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

   4. Taylor expanded in a around 0 41.0%

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

      1. *-commutative 41.0%

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

      2. +-commutative 41.0%

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

      3. +-commutative 41.0%

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

      4. associate-+r+ 41.0%

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

      5. associate-*r/ 73.9%

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

      6. +-commutative 73.9%

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

      7. +-commutative 73.9%

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

   6. Simplified 73.9%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.6 \cdot 10^{-304}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-146}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+94}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= z -5.1e-256)
     t_2
     (if (<= z 1.6e-61)
       (/ a (/ t_1 (+ y t)))
       (if (<= z 2.45e+94) t_2 (* (+ x y) (/ 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 t_2 = (z + a) - b;
	double tmp;
	if (z <= -5.1e-256) {
		tmp = t_2;
	} else if (z <= 1.6e-61) {
		tmp = a / (t_1 / (y + t));
	} else if (z <= 2.45e+94) {
		tmp = t_2;
	} else {
		tmp = (x + y) * (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) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - b
    if (z <= (-5.1d-256)) then
        tmp = t_2
    else if (z <= 1.6d-61) then
        tmp = a / (t_1 / (y + t))
    else if (z <= 2.45d+94) then
        tmp = t_2
    else
        tmp = (x + y) * (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 t_2 = (z + a) - b;
	double tmp;
	if (z <= -5.1e-256) {
		tmp = t_2;
	} else if (z <= 1.6e-61) {
		tmp = a / (t_1 / (y + t));
	} else if (z <= 2.45e+94) {
		tmp = t_2;
	} else {
		tmp = (x + y) * (z / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	tmp = 0
	if z <= -5.1e-256:
		tmp = t_2
	elif z <= 1.6e-61:
		tmp = a / (t_1 / (y + t))
	elif z <= 2.45e+94:
		tmp = t_2
	else:
		tmp = (x + y) * (z / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (z <= -5.1e-256)
		tmp = t_2;
	elseif (z <= 1.6e-61)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (z <= 2.45e+94)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + y) * Float64(z / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (z <= -5.1e-256)
		tmp = t_2;
	elseif (z <= 1.6e-61)
		tmp = a / (t_1 / (y + t));
	elseif (z <= 2.45e+94)
		tmp = t_2;
	else
		tmp = (x + y) * (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]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[z, -5.1e-256], t$95$2, If[LessEqual[z, 1.6e-61], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+94], t$95$2, N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.10000000000000011e-256 or 1.6000000000000001e-61 < z < 2.4499999999999999e94

   1. Initial program 57.5%

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

   3. Taylor expanded in y around inf 62.2%

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

   if -5.10000000000000011e-256 < z < 1.6000000000000001e-61

   1. Initial program 74.3%

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

   3. Taylor expanded in a around inf 50.0%

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

      1. associate-/l* 69.8%

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

      2. associate-+r+ 69.8%

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

   5. Simplified 69.8%

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

   if 2.4499999999999999e94 < z

   1. Initial program 53.7%

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

   3. Taylor expanded in b around 0 47.6%

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

   4. Taylor expanded in a around 0 41.0%

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

      1. *-commutative 41.0%

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

      2. +-commutative 41.0%

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

      3. +-commutative 41.0%

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

      4. associate-+r+ 41.0%

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

      5. associate-*r/ 73.9%

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

      6. +-commutative 73.9%

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

      7. +-commutative 73.9%

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

   6. Simplified 73.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-256}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+94}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-61}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= z -1.08e-246)
     t_2
     (if (<= z 2.55e-61)
       (/ a (/ t_1 (+ y t)))
       (if (<= z 7e+94) t_2 (/ z (/ t_1 (+ x y))))))))

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 + a) - b;
	double tmp;
	if (z <= -1.08e-246) {
		tmp = t_2;
	} else if (z <= 2.55e-61) {
		tmp = a / (t_1 / (y + t));
	} else if (z <= 7e+94) {
		tmp = t_2;
	} else {
		tmp = z / (t_1 / (x + 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) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - b
    if (z <= (-1.08d-246)) then
        tmp = t_2
    else if (z <= 2.55d-61) then
        tmp = a / (t_1 / (y + t))
    else if (z <= 7d+94) then
        tmp = t_2
    else
        tmp = z / (t_1 / (x + 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 t_2 = (z + a) - b;
	double tmp;
	if (z <= -1.08e-246) {
		tmp = t_2;
	} else if (z <= 2.55e-61) {
		tmp = a / (t_1 / (y + t));
	} else if (z <= 7e+94) {
		tmp = t_2;
	} else {
		tmp = z / (t_1 / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	tmp = 0
	if z <= -1.08e-246:
		tmp = t_2
	elif z <= 2.55e-61:
		tmp = a / (t_1 / (y + t))
	elif z <= 7e+94:
		tmp = t_2
	else:
		tmp = z / (t_1 / (x + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (z <= -1.08e-246)
		tmp = t_2;
	elseif (z <= 2.55e-61)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (z <= 7e+94)
		tmp = t_2;
	else
		tmp = Float64(z / Float64(t_1 / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (z <= -1.08e-246)
		tmp = t_2;
	elseif (z <= 2.55e-61)
		tmp = a / (t_1 / (y + t));
	elseif (z <= 7e+94)
		tmp = t_2;
	else
		tmp = z / (t_1 / (x + 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]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[z, -1.08e-246], t$95$2, If[LessEqual[z, 2.55e-61], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+94], t$95$2, N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08000000000000003e-246 or 2.54999999999999984e-61 < z < 6.9999999999999994e94

   1. Initial program 57.5%

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

   3. Taylor expanded in y around inf 62.2%

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

   if -1.08000000000000003e-246 < z < 2.54999999999999984e-61

   1. Initial program 74.3%

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

   3. Taylor expanded in a around inf 50.0%

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

      1. associate-/l* 69.8%

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

      2. associate-+r+ 69.8%

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

   5. Simplified 69.8%

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

   if 6.9999999999999994e94 < z

   1. Initial program 53.7%

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

   3. Taylor expanded in z around inf 41.0%

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

      1. associate-/l* 75.9%

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

      2. associate-+r+ 75.9%

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

      3. +-commutative 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-246}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-61}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+94}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+81} \lor \neg \left(x \leq 5.4 \cdot 10^{+144}\right):\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.9e+81) (not (<= x 5.4e+144)))
   (+ z (* t (- (/ a x) (/ z x))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.9e+81) || !(x <= 5.4e+144)) {
		tmp = z + (t * ((a / x) - (z / x)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.9d+81)) .or. (.not. (x <= 5.4d+144))) then
        tmp = z + (t * ((a / x) - (z / x)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.9e+81) || !(x <= 5.4e+144)) {
		tmp = z + (t * ((a / x) - (z / x)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.9e+81) or not (x <= 5.4e+144):
		tmp = z + (t * ((a / x) - (z / x)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.9e+81) || !(x <= 5.4e+144))
		tmp = Float64(z + Float64(t * Float64(Float64(a / x) - Float64(z / x))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.9e+81) || ~((x <= 5.4e+144)))
		tmp = z + (t * ((a / x) - (z / x)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.9e+81], N[Not[LessEqual[x, 5.4e+144]], $MachinePrecision]], N[(z + N[(t * N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e81 or 5.4000000000000003e144 < x

   1. Initial program 51.7%

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

   3. Taylor expanded in y around 0 34.6%

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

   4. Taylor expanded in t around 0 58.2%

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

   if -1.9e81 < x < 5.4000000000000003e144

   1. Initial program 66.7%

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

   3. Taylor expanded in y around inf 62.6%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+81} \lor \neg \left(x \leq 5.4 \cdot 10^{+144}\right):\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+143} \lor \neg \left(b \leq 5 \cdot 10^{+178}\right):\\ \;\;\;\;\frac{-b}{\frac{y + \left(x + t\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.2e+143) (not (<= b 5e+178)))
   (/ (- b) (/ (+ y (+ x t)) y))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.2e+143) || !(b <= 5e+178)) {
		tmp = -b / ((y + (x + t)) / y);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.2d+143)) .or. (.not. (b <= 5d+178))) then
        tmp = -b / ((y + (x + t)) / y)
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.2e+143) || !(b <= 5e+178)) {
		tmp = -b / ((y + (x + t)) / y);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.2e+143) or not (b <= 5e+178):
		tmp = -b / ((y + (x + t)) / y)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.2e+143) || !(b <= 5e+178))
		tmp = Float64(Float64(-b) / Float64(Float64(y + Float64(x + t)) / y));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.2e+143) || ~((b <= 5e+178)))
		tmp = -b / ((y + (x + t)) / y);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.2e+143], N[Not[LessEqual[b, 5e+178]], $MachinePrecision]], N[((-b) / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1999999999999999e143 or 4.9999999999999999e178 < b

   1. Initial program 64.9%

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

   3. Taylor expanded in b around inf 38.3%

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

      1. mul-1-neg 38.3%

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

      2. associate-/l* 53.1%

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

      3. distribute-neg-frac 53.1%

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

      4. associate-+r+ 53.1%

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

   5. Simplified 53.1%

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

   if -1.1999999999999999e143 < b < 4.9999999999999999e178

   1. Initial program 60.5%

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

   3. Taylor expanded in y around inf 61.2%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+143} \lor \neg \left(b \leq 5 \cdot 10^{+178}\right):\\ \;\;\;\;\frac{-b}{\frac{y + \left(x + t\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{-304} \lor \neg \left(z \leq 1.26 \cdot 10^{-146}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z 3e-304) (not (<= z 1.26e-146)))
   (- (+ z a) b)
   (/ a (/ (+ x t) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= 3e-304) || !(z <= 1.26e-146)) {
		tmp = (z + a) - b;
	} else {
		tmp = a / ((x + t) / 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 ((z <= 3d-304) .or. (.not. (z <= 1.26d-146))) then
        tmp = (z + a) - b
    else
        tmp = a / ((x + t) / 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 ((z <= 3e-304) || !(z <= 1.26e-146)) {
		tmp = (z + a) - b;
	} else {
		tmp = a / ((x + t) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= 3e-304) or not (z <= 1.26e-146):
		tmp = (z + a) - b
	else:
		tmp = a / ((x + t) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= 3e-304) || !(z <= 1.26e-146))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a / Float64(Float64(x + t) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= 3e-304) || ~((z <= 1.26e-146)))
		tmp = (z + a) - b;
	else
		tmp = a / ((x + t) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, 3e-304], N[Not[LessEqual[z, 1.26e-146]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.0000000000000001e-304 or 1.2599999999999999e-146 < z

   1. Initial program 59.5%

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

   3. Taylor expanded in y around inf 57.5%

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

   if 3.0000000000000001e-304 < z < 1.2599999999999999e-146

   1. Initial program 74.6%

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

   3. Taylor expanded in y around 0 42.5%

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

   4. Taylor expanded in a around inf 42.0%

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

      1. associate-/l* 60.8%

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

   6. Simplified 60.8%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{-304} \lor \neg \left(z \leq 1.26 \cdot 10^{-146}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 60.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-53} \lor \neg \left(y \leq 5.1 \cdot 10^{-17}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.4e-53) (not (<= y 5.1e-17))) (- (+ z a) b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4e-53) || !(y <= 5.1e-17)) {
		tmp = (z + a) - b;
	} 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 ((y <= (-1.4d-53)) .or. (.not. (y <= 5.1d-17))) then
        tmp = (z + a) - b
    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 ((y <= -1.4e-53) || !(y <= 5.1e-17)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.4e-53) or not (y <= 5.1e-17):
		tmp = (z + a) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.4e-53) || !(y <= 5.1e-17))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.4e-53) || ~((y <= 5.1e-17)))
		tmp = (z + a) - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.4e-53], N[Not[LessEqual[y, 5.1e-17]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999993e-53 or 5.1000000000000003e-17 < y

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 65.7%

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

   if -1.39999999999999993e-53 < y < 5.1000000000000003e-17

   1. Initial program 75.1%

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

   3. Taylor expanded in b around 0 64.5%

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

   4. Taylor expanded in y around inf 52.2%

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

      1. +-commutative 52.2%

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

   6. Simplified 52.2%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-53} \lor \neg \left(y \leq 5.1 \cdot 10^{-17}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 46.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-21}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3e-21) a (if (<= a 1.4e+35) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3e-21) {
		tmp = a;
	} else if (a <= 1.4e+35) {
		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 <= (-3d-21)) then
        tmp = a
    else if (a <= 1.4d+35) 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 <= -3e-21) {
		tmp = a;
	} else if (a <= 1.4e+35) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3e-21:
		tmp = a
	elif a <= 1.4e+35:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3e-21)
		tmp = a;
	elseif (a <= 1.4e+35)
		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 <= -3e-21)
		tmp = a;
	elseif (a <= 1.4e+35)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3e-21], a, If[LessEqual[a, 1.4e+35], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.99999999999999991e-21 or 1.39999999999999999e35 < a

   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. Add Preprocessing

   3. Taylor expanded in t around inf 51.9%

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

   if -2.99999999999999991e-21 < a < 1.39999999999999999e35

   1. Initial program 74.0%

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

   3. Taylor expanded in x around inf 42.2%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-21}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 54.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+183}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= t -9.6e+183) a (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.6e+183) {
		tmp = a;
	} 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 (t <= (-9.6d+183)) then
        tmp = a
    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 (t <= -9.6e+183) {
		tmp = a;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.6e+183:
		tmp = a
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.6e+183)
		tmp = a;
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.6e+183)
		tmp = a;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.6e+183], a, N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.6000000000000006e183

   1. Initial program 39.6%

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

   3. Taylor expanded in t around inf 77.9%

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

   if -9.6000000000000006e183 < t

   1. Initial program 63.0%

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

   3. Taylor expanded in b around 0 46.9%

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

   4. Taylor expanded in y around inf 51.1%

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

      1. +-commutative 51.1%

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

   6. Simplified 51.1%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+183}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.4% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.3%

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

3. Taylor expanded in t around inf 32.4%

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

4. Final simplification 32.4%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.8% 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 2024020 
(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)))