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

Percentage Accurate: 59.7% → 92.2%

Time: 14.6s

Alternatives: 16

Speedup: 1.1×

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: 92.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+196} \lor \neg \left(y \leq 4 \cdot 10^{+190}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right) + a \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y + t}{y + \left(x + t\right)}\right)\right)\right) - \frac{y \cdot b}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x))))
   (if (or (<= y -1.9e+196) (not (<= y 4e+190)))
     (- (+ a z) b)
     (-
      (+
       (* z (+ (/ x t_1) (/ y t_1)))
       (* a (expm1 (log1p (/ (+ y t) (+ y (+ x t)))))))
      (/ (* y b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double tmp;
	if ((y <= -1.9e+196) || !(y <= 4e+190)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((z * ((x / t_1) + (y / t_1))) + (a * expm1(log1p(((y + t) / (y + (x + t))))))) - ((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 = t + (y + x);
	double tmp;
	if ((y <= -1.9e+196) || !(y <= 4e+190)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((z * ((x / t_1) + (y / t_1))) + (a * Math.expm1(Math.log1p(((y + t) / (y + (x + t))))))) - ((y * b) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	tmp = 0
	if (y <= -1.9e+196) or not (y <= 4e+190):
		tmp = (a + z) - b
	else:
		tmp = ((z * ((x / t_1) + (y / t_1))) + (a * math.expm1(math.log1p(((y + t) / (y + (x + t))))))) - ((y * b) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	tmp = 0.0
	if ((y <= -1.9e+196) || !(y <= 4e+190))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))) + Float64(a * expm1(log1p(Float64(Float64(y + t) / Float64(y + Float64(x + t))))))) - Float64(Float64(y * b) / t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -1.9e+196], N[Not[LessEqual[y, 4e+190]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(Exp[N[Log[1 + N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000001e196 or 4.0000000000000003e190 < y

   1. Initial program 13.8%

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

   2. Taylor expanded in y around inf 95.7%

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

   if -1.9000000000000001e196 < y < 4.0000000000000003e190

   1. Initial program 67.5%

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

   2. Taylor expanded in z around 0 78.7%

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

      1. div-inv 78.6%

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

      2. +-commutative 78.6%

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

   4. Applied egg-rr 78.6%

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

      1. associate-*l* 94.5%

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

      2. +-commutative 94.5%

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

      3. +-commutative 94.5%

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

      4. +-commutative 94.5%

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

      5. +-commutative 94.5%

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

   6. Simplified 94.5%

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

      1. expm1-log1p-u 94.5%

         \[\leadsto \left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(y + t\right) \cdot \frac{1}{\left(y + x\right) + t}\right)\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]

      2. un-div-inv 94.6%

         \[\leadsto \left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + a \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{\frac{y + t}{\left(y + x\right) + t}}\right)\right)\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]

      3. associate-+l+ 94.6%

         \[\leadsto \left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + a \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y + t}{\color{blue}{y + \left(x + t\right)}}\right)\right)\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]

   8. Applied egg-rr 94.6%

      \[\leadsto \left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y + t}{y + \left(x + t\right)}\right)\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+196} \lor \neg \left(y \leq 4 \cdot 10^{+190}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t + \left(y + x\right)} + \frac{y}{t + \left(y + x\right)}\right) + a \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y + t}{y + \left(x + t\right)}\right)\right)\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \end{array} \]

Alternative 2: 89.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := t + \left(y + x\right)\\ t_3 := \left(z \cdot \left(\frac{x}{t_2} + \frac{y}{t_2}\right) + \left(y + t\right) \cdot \frac{a}{t_2}\right) - \frac{y \cdot b}{t_2}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) (+ y (+ x t))))
        (t_2 (+ t (+ y x)))
        (t_3
         (-
          (+ (* z (+ (/ x t_2) (/ y t_2))) (* (+ y t) (/ a t_2)))
          (/ (* y b) t_2))))
   (if (<= t_1 (- INFINITY))
     t_3
     (if (<= t_1 2e+83) t_1 (if (<= t_1 INFINITY) t_3 (- (+ a z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = t + (y + x);
	double t_3 = ((z * ((x / t_2) + (y / t_2))) + ((y + t) * (a / t_2))) - ((y * b) / t_2);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_1 <= 2e+83) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = t + (y + x);
	double t_3 = ((z * ((x / t_2) + (y / t_2))) + ((y + t) * (a / t_2))) - ((y * b) / t_2);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_1 <= 2e+83) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	t_2 = t + (y + x)
	t_3 = ((z * ((x / t_2) + (y / t_2))) + ((y + t) * (a / t_2))) - ((y * b) / t_2)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_3
	elif t_1 <= 2e+83:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_3
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(t + Float64(y + x))
	t_3 = Float64(Float64(Float64(z * Float64(Float64(x / t_2) + Float64(y / t_2))) + Float64(Float64(y + t) * Float64(a / t_2))) - Float64(Float64(y * b) / t_2))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_1 <= 2e+83)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	t_2 = t + (y + x);
	t_3 = ((z * ((x / t_2) + (y / t_2))) + ((y + t) * (a / t_2))) - ((y * b) / t_2);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_3;
	elseif (t_1 <= 2e+83)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_3;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * N[(a / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$3, If[LessEqual[t$95$1, 2e+83], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$3, N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000006e83 < (/.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 25.6%

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

   2. Taylor expanded in z around 0 48.9%

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

      1. expm1-log1p-u 41.5%

         \[\leadsto \left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)}\right)\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]

      2. expm1-udef 41.5%

         \[\leadsto \left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)}\right)} - 1\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]

      3. associate-/l* 58.4%

         \[\leadsto \left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{a}{\frac{t + \left(x + y\right)}{t + y}}}\right)} - 1\right)\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]

      4. +-commutative 58.4%

         \[\leadsto \left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \left(e^{\mathsf{log1p}\left(\frac{a}{\frac{t + \color{blue}{\left(y + x\right)}}{t + y}}\right)} - 1\right)\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]

   4. Applied egg-rr 58.4%

      \[\leadsto \left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a}{\frac{t + \left(y + x\right)}{t + y}}\right)} - 1\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]
   5. Step-by-step derivation

      1. expm1-def 58.4%

         \[\leadsto \left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a}{\frac{t + \left(y + x\right)}{t + y}}\right)\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]

      2. expm1-log1p 86.9%

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

      3. associate-/r/ 86.9%

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

      4. +-commutative 86.9%

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

      5. +-commutative 86.9%

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

      6. +-commutative 86.9%

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

      7. +-commutative 86.9%

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

   6. Simplified 86.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000006e83

   1. Initial program 99.8%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 82.9%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t + \left(y + x\right)} + \frac{y}{t + \left(y + x\right)}\right) + \left(y + t\right) \cdot \frac{a}{t + \left(y + x\right)}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+83}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq \infty:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t + \left(y + x\right)} + \frac{y}{t + \left(y + x\right)}\right) + \left(y + t\right) \cdot \frac{a}{t + \left(y + x\right)}\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 3: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+282}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+282))) (- (+ a z) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+282)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+282)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+282):
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+282))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+282)))
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+282]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

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 2.00000000000000007e282 < (/.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. Taylor expanded in y around inf 74.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000007e282

   1. Initial program 99.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+282}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 4: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\left(z + a \cdot \left(\left(y + t\right) \cdot \frac{1}{t_1}\right)\right) - \frac{y \cdot b}{t_1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x)))
        (t_2 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (<= t_2 (- INFINITY))
     (- (+ z (* a (* (+ y t) (/ 1.0 t_1)))) (/ (* y b) t_1))
     (if (<= t_2 2e+282) t_2 (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z + (a * ((y + t) * (1.0 / t_1)))) - ((y * b) / t_1);
	} else if (t_2 <= 2e+282) {
		tmp = t_2;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (z + (a * ((y + t) * (1.0 / t_1)))) - ((y * b) / t_1);
	} else if (t_2 <= 2e+282) {
		tmp = t_2;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (z + (a * ((y + t) * (1.0 / t_1)))) - ((y * b) / t_1)
	elif t_2 <= 2e+282:
		tmp = t_2
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z + Float64(a * Float64(Float64(y + t) * Float64(1.0 / t_1)))) - Float64(Float64(y * b) / t_1));
	elseif (t_2 <= 2e+282)
		tmp = t_2;
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (z + (a * ((y + t) * (1.0 / t_1)))) - ((y * b) / t_1);
	elseif (t_2 <= 2e+282)
		tmp = t_2;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z + N[(a * N[(N[(y + t), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+282], t$95$2, N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.4%

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

   2. Taylor expanded in z around 0 35.3%

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

      1. div-inv 35.3%

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

      2. +-commutative 35.3%

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

   4. Applied egg-rr 35.3%

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

      1. associate-*l* 85.2%

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

      2. +-commutative 85.2%

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

      3. +-commutative 85.2%

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

      4. +-commutative 85.2%

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

      5. +-commutative 85.2%

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

   6. Simplified 85.2%

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

   7. Taylor expanded in x around inf 83.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000007e282

   1. Initial program 99.8%

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

   if 2.00000000000000007e282 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.1%

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

   2. Taylor expanded in y around inf 69.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a \cdot \left(\left(y + t\right) \cdot \frac{1}{t + \left(y + x\right)}\right)\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 5: 92.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+185} \lor \neg \left(y \leq 3.45 \cdot 10^{+190}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right) + a \cdot \left(\left(y + t\right) \cdot \frac{1}{t_1}\right)\right) - \frac{y \cdot b}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x))))
   (if (or (<= y -3.8e+185) (not (<= y 3.45e+190)))
     (- (+ a z) b)
     (-
      (+ (* z (+ (/ x t_1) (/ y t_1))) (* a (* (+ y t) (/ 1.0 t_1))))
      (/ (* y b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double tmp;
	if ((y <= -3.8e+185) || !(y <= 3.45e+190)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((z * ((x / t_1) + (y / t_1))) + (a * ((y + t) * (1.0 / t_1)))) - ((y * b) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y + x)
    if ((y <= (-3.8d+185)) .or. (.not. (y <= 3.45d+190))) then
        tmp = (a + z) - b
    else
        tmp = ((z * ((x / t_1) + (y / t_1))) + (a * ((y + t) * (1.0d0 / t_1)))) - ((y * b) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double tmp;
	if ((y <= -3.8e+185) || !(y <= 3.45e+190)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((z * ((x / t_1) + (y / t_1))) + (a * ((y + t) * (1.0 / t_1)))) - ((y * b) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	tmp = 0
	if (y <= -3.8e+185) or not (y <= 3.45e+190):
		tmp = (a + z) - b
	else:
		tmp = ((z * ((x / t_1) + (y / t_1))) + (a * ((y + t) * (1.0 / t_1)))) - ((y * b) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	tmp = 0.0
	if ((y <= -3.8e+185) || !(y <= 3.45e+190))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))) + Float64(a * Float64(Float64(y + t) * Float64(1.0 / 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 = t + (y + x);
	tmp = 0.0;
	if ((y <= -3.8e+185) || ~((y <= 3.45e+190)))
		tmp = (a + z) - b;
	else
		tmp = ((z * ((x / t_1) + (y / t_1))) + (a * ((y + t) * (1.0 / t_1)))) - ((y * b) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -3.8e+185], N[Not[LessEqual[y, 3.45e+190]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(y + t), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999998e185 or 3.45e190 < y

   1. Initial program 15.1%

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

   2. Taylor expanded in y around inf 95.9%

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

   if -3.7999999999999998e185 < y < 3.45e190

   1. Initial program 68.0%

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

   2. Taylor expanded in z around 0 78.8%

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

      1. div-inv 78.7%

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

      2. +-commutative 78.7%

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

   4. Applied egg-rr 78.7%

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

      1. associate-*l* 94.4%

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

      2. +-commutative 94.4%

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

      3. +-commutative 94.4%

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

      4. +-commutative 94.4%

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

      5. +-commutative 94.4%

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

   6. Simplified 94.4%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+185} \lor \neg \left(y \leq 3.45 \cdot 10^{+190}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t + \left(y + x\right)} + \frac{y}{t + \left(y + x\right)}\right) + a \cdot \left(\left(y + t\right) \cdot \frac{1}{t + \left(y + x\right)}\right)\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \end{array} \]

Alternative 6: 56.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \frac{y}{t_1} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-175}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+20}:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x))) (t_2 (* (/ y t_1) (+ a (- z b)))))
   (if (<= b -1e+123)
     t_2
     (if (<= b -2.6e-43)
       (/ a (/ t_1 (+ y t)))
       (if (<= b 2.15e-175)
         (- (+ a z) b)
         (if (<= b 2.7e+20) (/ (+ (* a t) (* z x)) (+ x t)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (y / t_1) * (a + (z - b));
	double tmp;
	if (b <= -1e+123) {
		tmp = t_2;
	} else if (b <= -2.6e-43) {
		tmp = a / (t_1 / (y + t));
	} else if (b <= 2.15e-175) {
		tmp = (a + z) - b;
	} else if (b <= 2.7e+20) {
		tmp = ((a * t) + (z * x)) / (x + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y + x)
    t_2 = (y / t_1) * (a + (z - b))
    if (b <= (-1d+123)) then
        tmp = t_2
    else if (b <= (-2.6d-43)) then
        tmp = a / (t_1 / (y + t))
    else if (b <= 2.15d-175) then
        tmp = (a + z) - b
    else if (b <= 2.7d+20) then
        tmp = ((a * t) + (z * x)) / (x + t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (y / t_1) * (a + (z - b));
	double tmp;
	if (b <= -1e+123) {
		tmp = t_2;
	} else if (b <= -2.6e-43) {
		tmp = a / (t_1 / (y + t));
	} else if (b <= 2.15e-175) {
		tmp = (a + z) - b;
	} else if (b <= 2.7e+20) {
		tmp = ((a * t) + (z * x)) / (x + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	t_2 = (y / t_1) * (a + (z - b))
	tmp = 0
	if b <= -1e+123:
		tmp = t_2
	elif b <= -2.6e-43:
		tmp = a / (t_1 / (y + t))
	elif b <= 2.15e-175:
		tmp = (a + z) - b
	elif b <= 2.7e+20:
		tmp = ((a * t) + (z * x)) / (x + t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(Float64(y / t_1) * Float64(a + Float64(z - b)))
	tmp = 0.0
	if (b <= -1e+123)
		tmp = t_2;
	elseif (b <= -2.6e-43)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (b <= 2.15e-175)
		tmp = Float64(Float64(a + z) - b);
	elseif (b <= 2.7e+20)
		tmp = Float64(Float64(Float64(a * t) + Float64(z * x)) / Float64(x + t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	t_2 = (y / t_1) * (a + (z - b));
	tmp = 0.0;
	if (b <= -1e+123)
		tmp = t_2;
	elseif (b <= -2.6e-43)
		tmp = a / (t_1 / (y + t));
	elseif (b <= 2.15e-175)
		tmp = (a + z) - b;
	elseif (b <= 2.7e+20)
		tmp = ((a * t) + (z * x)) / (x + t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / t$95$1), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+123], t$95$2, If[LessEqual[b, -2.6e-43], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e-175], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[b, 2.7e+20], N[(N[(N[(a * t), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.99999999999999978e122 or 2.7e20 < b

   1. Initial program 48.2%

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

   2. Taylor expanded in y around inf 36.4%

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

      1. expm1-log1p-u 22.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)\right)} \]

      2. expm1-udef 13.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)} - 1} \]

      3. associate-/l* 25.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{\left(a + z\right) - b}}}\right)} - 1 \]

      4. +-commutative 25.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{\left(t + x\right)} + y}{\left(a + z\right) - b}}\right)} - 1 \]

      5. associate-+r+ 25.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{t + \left(x + y\right)}}{\left(a + z\right) - b}}\right)} - 1 \]

      6. +-commutative 25.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \color{blue}{\left(y + x\right)}}{\left(a + z\right) - b}}\right)} - 1 \]

      7. associate--l+ 25.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(y + x\right)}{\color{blue}{a + \left(z - b\right)}}}\right)} - 1 \]

   4. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(y + x\right)}{a + \left(z - b\right)}}\right)} - 1} \]
   5. Step-by-step derivation

      1. expm1-def 34.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t + \left(y + x\right)}{a + \left(z - b\right)}}\right)\right)} \]

      2. expm1-log1p 62.2%

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

      3. associate-/r/ 62.6%

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

      4. +-commutative 62.6%

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

      5. +-commutative 62.6%

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

      6. +-commutative 62.6%

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

   6. Simplified 62.6%

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

   if -9.99999999999999978e122 < b < -2.6e-43

   1. Initial program 53.8%

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

   2. Taylor expanded in a around inf 32.1%

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

      1. associate-/l* 65.7%

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

      2. +-commutative 65.7%

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

   4. Simplified 65.7%

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

   if -2.6e-43 < b < 2.14999999999999999e-175

   1. Initial program 58.9%

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

   2. Taylor expanded in y around inf 69.9%

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

   if 2.14999999999999999e-175 < b < 2.7e20

   1. Initial program 75.7%

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

   2. Taylor expanded in y around 0 73.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+123}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-175}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+20}:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]

Alternative 7: 56.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-215}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-304}:\\ \;\;\;\;\frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-300}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-169}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -1.05e-32)
     t_1
     (if (<= y -1.14e-215)
       (/ z (/ (+ x t) x))
       (if (<= y -4.4e-304)
         (/ a (/ (+ t (+ y x)) (+ y t)))
         (if (<= y 1.9e-300)
           z
           (if (<= y 6.5e-169) (+ a (/ (* y (- z b)) t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -1.05e-32) {
		tmp = t_1;
	} else if (y <= -1.14e-215) {
		tmp = z / ((x + t) / x);
	} else if (y <= -4.4e-304) {
		tmp = a / ((t + (y + x)) / (y + t));
	} else if (y <= 1.9e-300) {
		tmp = z;
	} else if (y <= 6.5e-169) {
		tmp = a + ((y * (z - b)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-1.05d-32)) then
        tmp = t_1
    else if (y <= (-1.14d-215)) then
        tmp = z / ((x + t) / x)
    else if (y <= (-4.4d-304)) then
        tmp = a / ((t + (y + x)) / (y + t))
    else if (y <= 1.9d-300) then
        tmp = z
    else if (y <= 6.5d-169) then
        tmp = a + ((y * (z - b)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -1.05e-32) {
		tmp = t_1;
	} else if (y <= -1.14e-215) {
		tmp = z / ((x + t) / x);
	} else if (y <= -4.4e-304) {
		tmp = a / ((t + (y + x)) / (y + t));
	} else if (y <= 1.9e-300) {
		tmp = z;
	} else if (y <= 6.5e-169) {
		tmp = a + ((y * (z - b)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -1.05e-32:
		tmp = t_1
	elif y <= -1.14e-215:
		tmp = z / ((x + t) / x)
	elif y <= -4.4e-304:
		tmp = a / ((t + (y + x)) / (y + t))
	elif y <= 1.9e-300:
		tmp = z
	elif y <= 6.5e-169:
		tmp = a + ((y * (z - b)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -1.05e-32)
		tmp = t_1;
	elseif (y <= -1.14e-215)
		tmp = Float64(z / Float64(Float64(x + t) / x));
	elseif (y <= -4.4e-304)
		tmp = Float64(a / Float64(Float64(t + Float64(y + x)) / Float64(y + t)));
	elseif (y <= 1.9e-300)
		tmp = z;
	elseif (y <= 6.5e-169)
		tmp = Float64(a + Float64(Float64(y * Float64(z - b)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -1.05e-32)
		tmp = t_1;
	elseif (y <= -1.14e-215)
		tmp = z / ((x + t) / x);
	elseif (y <= -4.4e-304)
		tmp = a / ((t + (y + x)) / (y + t));
	elseif (y <= 1.9e-300)
		tmp = z;
	elseif (y <= 6.5e-169)
		tmp = a + ((y * (z - b)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.05e-32], t$95$1, If[LessEqual[y, -1.14e-215], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.4e-304], N[(a / N[(N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-300], z, If[LessEqual[y, 6.5e-169], N[(a + N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.05e-32 or 6.5000000000000002e-169 < y

   1. Initial program 47.3%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -1.05e-32 < y < -1.14000000000000001e-215

   1. Initial program 77.7%

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

   2. Taylor expanded in z around inf 47.4%

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

      1. associate-/l* 64.5%

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

      2. +-commutative 64.5%

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

      3. +-commutative 64.5%

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

   4. Simplified 64.5%

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

   5. Taylor expanded in y around 0 61.8%

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

   if -1.14000000000000001e-215 < y < -4.4e-304

   1. Initial program 52.0%

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

   2. Taylor expanded in a around inf 31.3%

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

      1. associate-/l* 67.7%

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

      2. +-commutative 67.7%

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

   4. Simplified 67.7%

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

   if -4.4e-304 < y < 1.90000000000000006e-300

   1. Initial program 61.9%

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

   2. Taylor expanded in x around inf 80.8%

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

   if 1.90000000000000006e-300 < y < 6.5000000000000002e-169

   1. Initial program 81.5%

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

   2. Taylor expanded in x around 0 50.7%

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

      1. associate--l+ 50.7%

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

      2. *-commutative 50.7%

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

      3. distribute-lft-out-- 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in t around inf 58.4%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-32}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-215}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-304}:\\ \;\;\;\;\frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-300}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-169}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 8: 57.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-215}:\\ \;\;\;\;\frac{z}{\frac{t_1}{y + x}}\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-299}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-301}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-169}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x))) (t_2 (- (+ a z) b)))
   (if (<= y -1.6e-31)
     t_2
     (if (<= y -1.08e-215)
       (/ z (/ t_1 (+ y x)))
       (if (<= y -9.6e-299)
         (/ a (/ t_1 (+ y t)))
         (if (<= y 4.5e-301)
           z
           (if (<= y 3.2e-169) (+ a (/ (* y (- z b)) t)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -1.6e-31) {
		tmp = t_2;
	} else if (y <= -1.08e-215) {
		tmp = z / (t_1 / (y + x));
	} else if (y <= -9.6e-299) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 4.5e-301) {
		tmp = z;
	} else if (y <= 3.2e-169) {
		tmp = a + ((y * (z - b)) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y + x)
    t_2 = (a + z) - b
    if (y <= (-1.6d-31)) then
        tmp = t_2
    else if (y <= (-1.08d-215)) then
        tmp = z / (t_1 / (y + x))
    else if (y <= (-9.6d-299)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 4.5d-301) then
        tmp = z
    else if (y <= 3.2d-169) then
        tmp = a + ((y * (z - b)) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -1.6e-31) {
		tmp = t_2;
	} else if (y <= -1.08e-215) {
		tmp = z / (t_1 / (y + x));
	} else if (y <= -9.6e-299) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 4.5e-301) {
		tmp = z;
	} else if (y <= 3.2e-169) {
		tmp = a + ((y * (z - b)) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	t_2 = (a + z) - b
	tmp = 0
	if y <= -1.6e-31:
		tmp = t_2
	elif y <= -1.08e-215:
		tmp = z / (t_1 / (y + x))
	elif y <= -9.6e-299:
		tmp = a / (t_1 / (y + t))
	elif y <= 4.5e-301:
		tmp = z
	elif y <= 3.2e-169:
		tmp = a + ((y * (z - b)) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -1.6e-31)
		tmp = t_2;
	elseif (y <= -1.08e-215)
		tmp = Float64(z / Float64(t_1 / Float64(y + x)));
	elseif (y <= -9.6e-299)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 4.5e-301)
		tmp = z;
	elseif (y <= 3.2e-169)
		tmp = Float64(a + Float64(Float64(y * Float64(z - b)) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (y <= -1.6e-31)
		tmp = t_2;
	elseif (y <= -1.08e-215)
		tmp = z / (t_1 / (y + x));
	elseif (y <= -9.6e-299)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 4.5e-301)
		tmp = z;
	elseif (y <= 3.2e-169)
		tmp = a + ((y * (z - b)) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.6e-31], t$95$2, If[LessEqual[y, -1.08e-215], N[(z / N[(t$95$1 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.6e-299], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-301], z, If[LessEqual[y, 3.2e-169], N[(a + N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.60000000000000009e-31 or 3.19999999999999995e-169 < y

   1. Initial program 47.3%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -1.60000000000000009e-31 < y < -1.08e-215

   1. Initial program 77.7%

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

   2. Taylor expanded in z around inf 47.4%

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

      1. associate-/l* 64.5%

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

      2. +-commutative 64.5%

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

      3. +-commutative 64.5%

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

   4. Simplified 64.5%

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

   if -1.08e-215 < y < -9.60000000000000077e-299

   1. Initial program 52.0%

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

   2. Taylor expanded in a around inf 31.3%

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

      1. associate-/l* 67.7%

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

      2. +-commutative 67.7%

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

   4. Simplified 67.7%

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

   if -9.60000000000000077e-299 < y < 4.5000000000000002e-301

   1. Initial program 61.9%

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

   2. Taylor expanded in x around inf 80.8%

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

   if 4.5000000000000002e-301 < y < 3.19999999999999995e-169

   1. Initial program 81.5%

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

   2. Taylor expanded in x around 0 50.7%

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

      1. associate--l+ 50.7%

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

      2. *-commutative 50.7%

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

      3. distribute-lft-out-- 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in t around inf 58.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-31}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-215}:\\ \;\;\;\;\frac{z}{\frac{t + \left(y + x\right)}{y + x}}\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-299}:\\ \;\;\;\;\frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-301}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-169}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 9: 60.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-215}:\\ \;\;\;\;\frac{z}{\frac{t_1}{y + x}}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-291}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x))) (t_2 (- (+ a z) b)))
   (if (<= y -1.9e-26)
     t_2
     (if (<= y -1.14e-215)
       (/ z (/ t_1 (+ y x)))
       (if (<= y -1.9e-291)
         (/ a (/ t_1 (+ y t)))
         (if (<= y 1.5e-164) (/ (+ (* a t) (* z x)) (+ x t)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -1.9e-26) {
		tmp = t_2;
	} else if (y <= -1.14e-215) {
		tmp = z / (t_1 / (y + x));
	} else if (y <= -1.9e-291) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 1.5e-164) {
		tmp = ((a * t) + (z * x)) / (x + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y + x)
    t_2 = (a + z) - b
    if (y <= (-1.9d-26)) then
        tmp = t_2
    else if (y <= (-1.14d-215)) then
        tmp = z / (t_1 / (y + x))
    else if (y <= (-1.9d-291)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 1.5d-164) then
        tmp = ((a * t) + (z * x)) / (x + t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -1.9e-26) {
		tmp = t_2;
	} else if (y <= -1.14e-215) {
		tmp = z / (t_1 / (y + x));
	} else if (y <= -1.9e-291) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 1.5e-164) {
		tmp = ((a * t) + (z * x)) / (x + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	t_2 = (a + z) - b
	tmp = 0
	if y <= -1.9e-26:
		tmp = t_2
	elif y <= -1.14e-215:
		tmp = z / (t_1 / (y + x))
	elif y <= -1.9e-291:
		tmp = a / (t_1 / (y + t))
	elif y <= 1.5e-164:
		tmp = ((a * t) + (z * x)) / (x + t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -1.9e-26)
		tmp = t_2;
	elseif (y <= -1.14e-215)
		tmp = Float64(z / Float64(t_1 / Float64(y + x)));
	elseif (y <= -1.9e-291)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 1.5e-164)
		tmp = Float64(Float64(Float64(a * t) + Float64(z * x)) / Float64(x + t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (y <= -1.9e-26)
		tmp = t_2;
	elseif (y <= -1.14e-215)
		tmp = z / (t_1 / (y + x));
	elseif (y <= -1.9e-291)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 1.5e-164)
		tmp = ((a * t) + (z * x)) / (x + t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.9e-26], t$95$2, If[LessEqual[y, -1.14e-215], N[(z / N[(t$95$1 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-291], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-164], N[(N[(N[(a * t), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.90000000000000007e-26 or 1.5e-164 < y

   1. Initial program 47.3%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -1.90000000000000007e-26 < y < -1.14000000000000001e-215

   1. Initial program 77.7%

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

   2. Taylor expanded in z around inf 47.4%

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

      1. associate-/l* 64.5%

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

      2. +-commutative 64.5%

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

      3. +-commutative 64.5%

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

   4. Simplified 64.5%

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

   if -1.14000000000000001e-215 < y < -1.8999999999999999e-291

   1. Initial program 52.0%

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

   2. Taylor expanded in a around inf 31.3%

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

      1. associate-/l* 67.7%

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

      2. +-commutative 67.7%

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

   4. Simplified 67.7%

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

   if -1.8999999999999999e-291 < y < 1.5e-164

   1. Initial program 79.1%

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

   2. Taylor expanded in y around 0 55.5%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-26}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-215}:\\ \;\;\;\;\frac{z}{\frac{t + \left(y + x\right)}{y + x}}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-291}:\\ \;\;\;\;\frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 10: 56.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-293}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-168}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -4.4e-28)
     t_1
     (if (<= y 3.7e-293)
       (/ z (/ (+ x t) x))
       (if (<= y 6.4e-168) (+ a (/ (* y (- z b)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -4.4e-28) {
		tmp = t_1;
	} else if (y <= 3.7e-293) {
		tmp = z / ((x + t) / x);
	} else if (y <= 6.4e-168) {
		tmp = a + ((y * (z - b)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-4.4d-28)) then
        tmp = t_1
    else if (y <= 3.7d-293) then
        tmp = z / ((x + t) / x)
    else if (y <= 6.4d-168) then
        tmp = a + ((y * (z - b)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -4.4e-28) {
		tmp = t_1;
	} else if (y <= 3.7e-293) {
		tmp = z / ((x + t) / x);
	} else if (y <= 6.4e-168) {
		tmp = a + ((y * (z - b)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -4.4e-28:
		tmp = t_1
	elif y <= 3.7e-293:
		tmp = z / ((x + t) / x)
	elif y <= 6.4e-168:
		tmp = a + ((y * (z - b)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -4.4e-28)
		tmp = t_1;
	elseif (y <= 3.7e-293)
		tmp = Float64(z / Float64(Float64(x + t) / x));
	elseif (y <= 6.4e-168)
		tmp = Float64(a + Float64(Float64(y * Float64(z - b)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -4.4e-28)
		tmp = t_1;
	elseif (y <= 3.7e-293)
		tmp = z / ((x + t) / x);
	elseif (y <= 6.4e-168)
		tmp = a + ((y * (z - b)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.4e-28], t$95$1, If[LessEqual[y, 3.7e-293], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-168], N[(a + N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.39999999999999992e-28 or 6.40000000000000013e-168 < y

   1. Initial program 47.3%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -4.39999999999999992e-28 < y < 3.70000000000000008e-293

   1. Initial program 68.8%

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

   2. Taylor expanded in z around inf 38.7%

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

      1. associate-/l* 55.6%

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

      2. +-commutative 55.6%

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

      3. +-commutative 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in y around 0 53.8%

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

   if 3.70000000000000008e-293 < y < 6.40000000000000013e-168

   1. Initial program 81.5%

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

   2. Taylor expanded in x around 0 50.7%

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

      1. associate--l+ 50.7%

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

      2. *-commutative 50.7%

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

      3. distribute-lft-out-- 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in t around inf 58.4%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-28}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-293}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-168}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 11: 55.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-215}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-168}:\\ \;\;\;\;a + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -1.05e-84)
     t_1
     (if (<= y -1.14e-215) z (if (<= y 5.5e-168) (+ a (/ (* y z) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -1.05e-84) {
		tmp = t_1;
	} else if (y <= -1.14e-215) {
		tmp = z;
	} else if (y <= 5.5e-168) {
		tmp = a + ((y * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-1.05d-84)) then
        tmp = t_1
    else if (y <= (-1.14d-215)) then
        tmp = z
    else if (y <= 5.5d-168) then
        tmp = a + ((y * z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -1.05e-84) {
		tmp = t_1;
	} else if (y <= -1.14e-215) {
		tmp = z;
	} else if (y <= 5.5e-168) {
		tmp = a + ((y * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -1.05e-84:
		tmp = t_1
	elif y <= -1.14e-215:
		tmp = z
	elif y <= 5.5e-168:
		tmp = a + ((y * z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -1.05e-84)
		tmp = t_1;
	elseif (y <= -1.14e-215)
		tmp = z;
	elseif (y <= 5.5e-168)
		tmp = Float64(a + Float64(Float64(y * z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -1.05e-84)
		tmp = t_1;
	elseif (y <= -1.14e-215)
		tmp = z;
	elseif (y <= 5.5e-168)
		tmp = a + ((y * z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.05e-84], t$95$1, If[LessEqual[y, -1.14e-215], z, If[LessEqual[y, 5.5e-168], N[(a + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999999e-84 or 5.4999999999999999e-168 < y

   1. Initial program 50.4%

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

   2. Taylor expanded in y around inf 69.3%

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

   if -1.04999999999999999e-84 < y < -1.14000000000000001e-215

   1. Initial program 71.3%

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

   2. Taylor expanded in x around inf 52.1%

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

   if -1.14000000000000001e-215 < y < 5.4999999999999999e-168

   1. Initial program 70.9%

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

   2. Taylor expanded in x around 0 39.2%

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

      1. associate--l+ 39.2%

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

      2. *-commutative 39.2%

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

      3. distribute-lft-out-- 39.2%

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

   4. Simplified 39.2%

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

   5. Taylor expanded in t around inf 50.7%

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

   6. Taylor expanded in z around inf 44.9%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-84}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-215}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-168}:\\ \;\;\;\;a + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 12: 56.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-299}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-167}:\\ \;\;\;\;a + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -3.6e-30)
     t_1
     (if (<= y 3.7e-299)
       (/ z (/ (+ x t) x))
       (if (<= y 4.6e-167) (+ a (/ (* y z) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -3.6e-30) {
		tmp = t_1;
	} else if (y <= 3.7e-299) {
		tmp = z / ((x + t) / x);
	} else if (y <= 4.6e-167) {
		tmp = a + ((y * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-3.6d-30)) then
        tmp = t_1
    else if (y <= 3.7d-299) then
        tmp = z / ((x + t) / x)
    else if (y <= 4.6d-167) then
        tmp = a + ((y * z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -3.6e-30) {
		tmp = t_1;
	} else if (y <= 3.7e-299) {
		tmp = z / ((x + t) / x);
	} else if (y <= 4.6e-167) {
		tmp = a + ((y * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -3.6e-30:
		tmp = t_1
	elif y <= 3.7e-299:
		tmp = z / ((x + t) / x)
	elif y <= 4.6e-167:
		tmp = a + ((y * z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -3.6e-30)
		tmp = t_1;
	elseif (y <= 3.7e-299)
		tmp = Float64(z / Float64(Float64(x + t) / x));
	elseif (y <= 4.6e-167)
		tmp = Float64(a + Float64(Float64(y * z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -3.6e-30)
		tmp = t_1;
	elseif (y <= 3.7e-299)
		tmp = z / ((x + t) / x);
	elseif (y <= 4.6e-167)
		tmp = a + ((y * z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.6e-30], t$95$1, If[LessEqual[y, 3.7e-299], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-167], N[(a + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000003e-30 or 4.6000000000000003e-167 < y

   1. Initial program 47.3%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -3.6000000000000003e-30 < y < 3.70000000000000014e-299

   1. Initial program 68.8%

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

   2. Taylor expanded in z around inf 38.7%

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

      1. associate-/l* 55.6%

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

      2. +-commutative 55.6%

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

      3. +-commutative 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in y around 0 53.8%

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

   if 3.70000000000000014e-299 < y < 4.6000000000000003e-167

   1. Initial program 81.5%

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

   2. Taylor expanded in x around 0 50.7%

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

      1. associate--l+ 50.7%

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

      2. *-commutative 50.7%

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

      3. distribute-lft-out-- 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in t around inf 58.4%

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

   6. Taylor expanded in z around inf 48.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-299}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-167}:\\ \;\;\;\;a + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 13: 56.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-296}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-170}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -3.1e-32)
     t_1
     (if (<= y 9.5e-296)
       (/ z (/ (+ x t) x))
       (if (<= y 2.3e-170) (- a (/ (* y b) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -3.1e-32) {
		tmp = t_1;
	} else if (y <= 9.5e-296) {
		tmp = z / ((x + t) / x);
	} else if (y <= 2.3e-170) {
		tmp = a - ((y * b) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-3.1d-32)) then
        tmp = t_1
    else if (y <= 9.5d-296) then
        tmp = z / ((x + t) / x)
    else if (y <= 2.3d-170) then
        tmp = a - ((y * b) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -3.1e-32) {
		tmp = t_1;
	} else if (y <= 9.5e-296) {
		tmp = z / ((x + t) / x);
	} else if (y <= 2.3e-170) {
		tmp = a - ((y * b) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -3.1e-32:
		tmp = t_1
	elif y <= 9.5e-296:
		tmp = z / ((x + t) / x)
	elif y <= 2.3e-170:
		tmp = a - ((y * b) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -3.1e-32)
		tmp = t_1;
	elseif (y <= 9.5e-296)
		tmp = Float64(z / Float64(Float64(x + t) / x));
	elseif (y <= 2.3e-170)
		tmp = Float64(a - Float64(Float64(y * b) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -3.1e-32)
		tmp = t_1;
	elseif (y <= 9.5e-296)
		tmp = z / ((x + t) / x);
	elseif (y <= 2.3e-170)
		tmp = a - ((y * b) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.1e-32], t$95$1, If[LessEqual[y, 9.5e-296], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-170], N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.10000000000000011e-32 or 2.29999999999999987e-170 < y

   1. Initial program 47.3%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -3.10000000000000011e-32 < y < 9.50000000000000046e-296

   1. Initial program 68.8%

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

   2. Taylor expanded in z around inf 38.7%

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

      1. associate-/l* 55.6%

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

      2. +-commutative 55.6%

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

      3. +-commutative 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in y around 0 53.8%

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

   if 9.50000000000000046e-296 < y < 2.29999999999999987e-170

   1. Initial program 81.5%

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

   2. Taylor expanded in x around 0 50.7%

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

      1. associate--l+ 50.7%

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

      2. *-commutative 50.7%

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

      3. distribute-lft-out-- 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in t around inf 58.4%

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

   6. Taylor expanded in z around 0 53.8%

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

      1. associate-*r/ 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-*r* 53.8%

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

      4. mul-1-neg 53.8%

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

   8. Simplified 53.8%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-32}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-296}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-170}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 14: 55.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-215}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-165}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -7.5e-84)
     t_1
     (if (<= y -1.08e-215) z (if (<= y 4.3e-165) a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -7.5e-84) {
		tmp = t_1;
	} else if (y <= -1.08e-215) {
		tmp = z;
	} else if (y <= 4.3e-165) {
		tmp = a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-7.5d-84)) then
        tmp = t_1
    else if (y <= (-1.08d-215)) then
        tmp = z
    else if (y <= 4.3d-165) then
        tmp = a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -7.5e-84) {
		tmp = t_1;
	} else if (y <= -1.08e-215) {
		tmp = z;
	} else if (y <= 4.3e-165) {
		tmp = a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -7.5e-84:
		tmp = t_1
	elif y <= -1.08e-215:
		tmp = z
	elif y <= 4.3e-165:
		tmp = a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -7.5e-84)
		tmp = t_1;
	elseif (y <= -1.08e-215)
		tmp = z;
	elseif (y <= 4.3e-165)
		tmp = a;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -7.5e-84)
		tmp = t_1;
	elseif (y <= -1.08e-215)
		tmp = z;
	elseif (y <= 4.3e-165)
		tmp = a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -7.5e-84], t$95$1, If[LessEqual[y, -1.08e-215], z, If[LessEqual[y, 4.3e-165], a, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000026e-84 or 4.30000000000000007e-165 < y

   1. Initial program 50.4%

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

   2. Taylor expanded in y around inf 69.3%

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

   if -7.50000000000000026e-84 < y < -1.08e-215

   1. Initial program 71.3%

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

   2. Taylor expanded in x around inf 52.1%

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

   if -1.08e-215 < y < 4.30000000000000007e-165

   1. Initial program 70.9%

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

   2. Taylor expanded in t around inf 42.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-84}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-215}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-165}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]

Alternative 15: 44.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+24}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+154}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.8e+24) z (if (<= x 6.5e+154) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+24) {
		tmp = z;
	} else if (x <= 6.5e+154) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.8d+24)) then
        tmp = z
    else if (x <= 6.5d+154) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+24) {
		tmp = z;
	} else if (x <= 6.5e+154) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.8e+24:
		tmp = z
	elif x <= 6.5e+154:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.8e+24)
		tmp = z;
	elseif (x <= 6.5e+154)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.8e+24)
		tmp = z;
	elseif (x <= 6.5e+154)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.8e+24], z, If[LessEqual[x, 6.5e+154], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -8.80000000000000007e24 or 6.5000000000000005e154 < x

   1. Initial program 47.3%

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

   2. Taylor expanded in x around inf 48.6%

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

   if -8.80000000000000007e24 < x < 6.5000000000000005e154

   1. Initial program 63.2%

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

   2. Taylor expanded in t around inf 49.8%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+24}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+154}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 16: 33.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.2%

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

2. Taylor expanded in t around inf 37.8%

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

3. Final simplification 37.8%

   \[\leadsto a \]

Developer target: 81.8% 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 2023302 
(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)))