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

Percentage Accurate: 59.6% → 93.0%

Time: 12.4s

Alternatives: 15

Speedup: 1.0×

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: 59.6% 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: 93.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{y}{t\_1}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-103} \lor \neg \left(z \leq 1.6 \cdot 10^{-29}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\left(t\_3 + \frac{a}{z} \cdot \frac{y + t}{t\_1}\right) - t\_3 \cdot \frac{b}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{\mathsf{fma}\left(z, \frac{x + y}{t\_2}, a \cdot \frac{y + t}{t\_2}\right)}{b} - \frac{y}{t\_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t)) (t_2 (+ y (+ x t))) (t_3 (/ y t_1)))
   (if (or (<= z -2.2e-103) (not (<= z 1.6e-29)))
     (*
      z
      (+ (/ x t_1) (- (+ t_3 (* (/ a z) (/ (+ y t) t_1))) (* t_3 (/ b z)))))
     (* b (- (/ (fma z (/ (+ x y) t_2) (* a (/ (+ y t) t_2))) b) (/ y t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = y + (x + t);
	double t_3 = y / t_1;
	double tmp;
	if ((z <= -2.2e-103) || !(z <= 1.6e-29)) {
		tmp = z * ((x / t_1) + ((t_3 + ((a / z) * ((y + t) / t_1))) - (t_3 * (b / z))));
	} else {
		tmp = b * ((fma(z, ((x + y) / t_2), (a * ((y + t) / t_2))) / b) - (y / t_2));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(y / t_1)
	tmp = 0.0
	if ((z <= -2.2e-103) || !(z <= 1.6e-29))
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(Float64(t_3 + Float64(Float64(a / z) * Float64(Float64(y + t) / t_1))) - Float64(t_3 * Float64(b / z)))));
	else
		tmp = Float64(b * Float64(Float64(fma(z, Float64(Float64(x + y) / t_2), Float64(a * Float64(Float64(y + t) / t_2))) / b) - Float64(y / t_2)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$1), $MachinePrecision]}, If[Or[LessEqual[z, -2.2e-103], N[Not[LessEqual[z, 1.6e-29]], $MachinePrecision]], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(t$95$3 + N[(N[(a / z), $MachinePrecision] * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$3 * N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e-103 or 1.6e-29 < z

   1. Initial program 48.7%

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

   3. Taylor expanded in z around inf 63.3%

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

      1. associate--l+ 63.3%

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

      2. +-commutative 63.3%

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

      3. +-commutative 63.3%

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

      4. times-frac 88.6%

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

      5. +-commutative 88.6%

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

      6. times-frac 99.2%

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

      7. +-commutative 99.2%

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

   5. Simplified 99.2%

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

   if -2.1999999999999999e-103 < z < 1.6e-29

   1. Initial program 74.8%

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

   3. Taylor expanded in b around -inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. distribute-rgt-neg-in 74.2%

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

      3. +-commutative 74.2%

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

      4. mul-1-neg 74.2%

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

      5. unsub-neg 74.2%

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

   5. Simplified 87.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-103} \lor \neg \left(z \leq 1.6 \cdot 10^{-29}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{\left(x + y\right) + t} + \left(\left(\frac{y}{\left(x + y\right) + t} + \frac{a}{z} \cdot \frac{y + t}{\left(x + y\right) + t}\right) - \frac{y}{\left(x + y\right) + t} \cdot \frac{b}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{\mathsf{fma}\left(z, \frac{x + y}{y + \left(x + t\right)}, a \cdot \frac{y + t}{y + \left(x + t\right)}\right)}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 10^{+268}\right):\\ \;\;\;\;a \cdot \frac{y + t}{t\_1} + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+268)))
     (+ (* a (/ (+ y t) t_1)) (- z b))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+268)) {
		tmp = (a * ((y + t) / t_1)) + (z - b);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 1e+268)) {
		tmp = (a * ((y + t) / t_1)) + (z - b);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+268):
		tmp = (a * ((y + t) / t_1)) + (z - b)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+268))
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_1)) + Float64(z - b));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 1e+268)))
		tmp = (a * ((y + t) / t_1)) + (z - b);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 1e+268]], $MachinePrecision]], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z - b), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 9.9999999999999997e267 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.8%

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

   3. Taylor expanded in b around 0 5.8%

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

      1. mul-1-neg 5.8%

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

      2. +-commutative 5.8%

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

      3. associate-+l+ 5.8%

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

      4. associate-/l* 35.5%

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

      5. +-commutative 35.5%

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

      6. associate-+r+ 35.5%

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

      7. +-commutative 35.5%

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

      8. associate-+l+ 35.5%

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

      9. sub-neg 35.5%

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

      10. div-sub 35.5%

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

      11. +-commutative 35.5%

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

      12. *-commutative 35.5%

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

      13. +-commutative 35.5%

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

      14. associate-+r+ 35.5%

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

      15. +-commutative 35.5%

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

      16. associate-+l+ 35.5%

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

   5. Simplified 35.5%

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

   6. Taylor expanded in y around inf 77.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999997e267

   1. Initial program 99.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+268}\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{y}{t\_1}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-136} \lor \neg \left(z \leq 4 \cdot 10^{-28}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\left(t\_3 + \frac{a}{z} \cdot \frac{y + t}{t\_1}\right) - t\_3 \cdot \frac{b}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_2} + \frac{z \cdot \left(x + y\right) - y \cdot b}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t)) (t_2 (+ y (+ x t))) (t_3 (/ y t_1)))
   (if (or (<= z -2.2e-136) (not (<= z 4e-28)))
     (*
      z
      (+ (/ x t_1) (- (+ t_3 (* (/ a z) (/ (+ y t) t_1))) (* t_3 (/ b z)))))
     (+ (* a (/ (+ y t) t_2)) (/ (- (* z (+ x y)) (* y b)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = y + (x + t);
	double t_3 = y / t_1;
	double tmp;
	if ((z <= -2.2e-136) || !(z <= 4e-28)) {
		tmp = z * ((x / t_1) + ((t_3 + ((a / z) * ((y + t) / t_1))) - (t_3 * (b / z))));
	} else {
		tmp = (a * ((y + t) / t_2)) + (((z * (x + y)) - (y * b)) / t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x + y) + t
    t_2 = y + (x + t)
    t_3 = y / t_1
    if ((z <= (-2.2d-136)) .or. (.not. (z <= 4d-28))) then
        tmp = z * ((x / t_1) + ((t_3 + ((a / z) * ((y + t) / t_1))) - (t_3 * (b / z))))
    else
        tmp = (a * ((y + t) / t_2)) + (((z * (x + y)) - (y * b)) / t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = y + (x + t);
	double t_3 = y / t_1;
	double tmp;
	if ((z <= -2.2e-136) || !(z <= 4e-28)) {
		tmp = z * ((x / t_1) + ((t_3 + ((a / z) * ((y + t) / t_1))) - (t_3 * (b / z))));
	} else {
		tmp = (a * ((y + t) / t_2)) + (((z * (x + y)) - (y * b)) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + t
	t_2 = y + (x + t)
	t_3 = y / t_1
	tmp = 0
	if (z <= -2.2e-136) or not (z <= 4e-28):
		tmp = z * ((x / t_1) + ((t_3 + ((a / z) * ((y + t) / t_1))) - (t_3 * (b / z))))
	else:
		tmp = (a * ((y + t) / t_2)) + (((z * (x + y)) - (y * b)) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(y / t_1)
	tmp = 0.0
	if ((z <= -2.2e-136) || !(z <= 4e-28))
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(Float64(t_3 + Float64(Float64(a / z) * Float64(Float64(y + t) / t_1))) - Float64(t_3 * Float64(b / z)))));
	else
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_2)) + Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + t;
	t_2 = y + (x + t);
	t_3 = y / t_1;
	tmp = 0.0;
	if ((z <= -2.2e-136) || ~((z <= 4e-28)))
		tmp = z * ((x / t_1) + ((t_3 + ((a / z) * ((y + t) / t_1))) - (t_3 * (b / z))));
	else
		tmp = (a * ((y + t) / t_2)) + (((z * (x + y)) - (y * b)) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$1), $MachinePrecision]}, If[Or[LessEqual[z, -2.2e-136], N[Not[LessEqual[z, 4e-28]], $MachinePrecision]], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(t$95$3 + N[(N[(a / z), $MachinePrecision] * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$3 * N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e-136 or 3.99999999999999988e-28 < z

   1. Initial program 48.3%

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

   3. Taylor expanded in z around inf 62.2%

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

      1. associate--l+ 62.2%

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

      2. +-commutative 62.2%

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

      3. +-commutative 62.2%

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

      4. times-frac 86.3%

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

      5. +-commutative 86.3%

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

      6. times-frac 97.5%

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

      7. +-commutative 97.5%

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

   5. Simplified 97.5%

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

   if -2.2000000000000001e-136 < z < 3.99999999999999988e-28

   1. Initial program 77.8%

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

   3. Taylor expanded in b around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. +-commutative 77.9%

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

      3. associate-+l+ 77.9%

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

      4. associate-/l* 87.2%

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

      5. +-commutative 87.2%

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

      6. associate-+r+ 87.2%

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

      7. +-commutative 87.2%

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

      8. associate-+l+ 87.2%

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

      9. sub-neg 87.2%

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

      10. div-sub 87.2%

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

      11. +-commutative 87.2%

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

      12. *-commutative 87.2%

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

      13. +-commutative 87.2%

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

      14. associate-+r+ 87.2%

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

      15. +-commutative 87.2%

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

      16. associate-+l+ 87.2%

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

   5. Simplified 87.2%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-136} \lor \neg \left(z \leq 4 \cdot 10^{-28}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{\left(x + y\right) + t} + \left(\left(\frac{y}{\left(x + y\right) + t} + \frac{a}{z} \cdot \frac{y + t}{\left(x + y\right) + t}\right) - \frac{y}{\left(x + y\right) + t} \cdot \frac{b}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} + \frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \frac{y \cdot b}{x}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-139}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-150}:\\ \;\;\;\;\left(z - b\right) + \frac{a \cdot \left(y + t\right)}{x}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-153}:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (/ (* y b) x))) (t_2 (- (+ z a) b)))
   (if (<= y -3.4e-88)
     t_2
     (if (<= y -3.2e-139)
       (- a (/ (* y b) t))
       (if (<= y -1.35e-150)
         (+ (- z b) (/ (* a (+ y t)) x))
         (if (<= y -3.1e-159)
           t_1
           (if (<= y 1.12e-153)
             (/ (+ (* a t) (* z x)) (+ x t))
             (if (<= y 1.12e-83)
               (* a (/ (+ y t) (+ y (+ x t))))
               (if (<= y 1.8e-18) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - ((y * b) / x);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -3.4e-88) {
		tmp = t_2;
	} else if (y <= -3.2e-139) {
		tmp = a - ((y * b) / t);
	} else if (y <= -1.35e-150) {
		tmp = (z - b) + ((a * (y + t)) / x);
	} else if (y <= -3.1e-159) {
		tmp = t_1;
	} else if (y <= 1.12e-153) {
		tmp = ((a * t) + (z * x)) / (x + t);
	} else if (y <= 1.12e-83) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (y <= 1.8e-18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z - ((y * b) / x)
    t_2 = (z + a) - b
    if (y <= (-3.4d-88)) then
        tmp = t_2
    else if (y <= (-3.2d-139)) then
        tmp = a - ((y * b) / t)
    else if (y <= (-1.35d-150)) then
        tmp = (z - b) + ((a * (y + t)) / x)
    else if (y <= (-3.1d-159)) then
        tmp = t_1
    else if (y <= 1.12d-153) then
        tmp = ((a * t) + (z * x)) / (x + t)
    else if (y <= 1.12d-83) then
        tmp = a * ((y + t) / (y + (x + t)))
    else if (y <= 1.8d-18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - ((y * b) / x);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -3.4e-88) {
		tmp = t_2;
	} else if (y <= -3.2e-139) {
		tmp = a - ((y * b) / t);
	} else if (y <= -1.35e-150) {
		tmp = (z - b) + ((a * (y + t)) / x);
	} else if (y <= -3.1e-159) {
		tmp = t_1;
	} else if (y <= 1.12e-153) {
		tmp = ((a * t) + (z * x)) / (x + t);
	} else if (y <= 1.12e-83) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (y <= 1.8e-18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - ((y * b) / x)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -3.4e-88:
		tmp = t_2
	elif y <= -3.2e-139:
		tmp = a - ((y * b) / t)
	elif y <= -1.35e-150:
		tmp = (z - b) + ((a * (y + t)) / x)
	elif y <= -3.1e-159:
		tmp = t_1
	elif y <= 1.12e-153:
		tmp = ((a * t) + (z * x)) / (x + t)
	elif y <= 1.12e-83:
		tmp = a * ((y + t) / (y + (x + t)))
	elif y <= 1.8e-18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(Float64(y * b) / x))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.4e-88)
		tmp = t_2;
	elseif (y <= -3.2e-139)
		tmp = Float64(a - Float64(Float64(y * b) / t));
	elseif (y <= -1.35e-150)
		tmp = Float64(Float64(z - b) + Float64(Float64(a * Float64(y + t)) / x));
	elseif (y <= -3.1e-159)
		tmp = t_1;
	elseif (y <= 1.12e-153)
		tmp = Float64(Float64(Float64(a * t) + Float64(z * x)) / Float64(x + t));
	elseif (y <= 1.12e-83)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	elseif (y <= 1.8e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - ((y * b) / x);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.4e-88)
		tmp = t_2;
	elseif (y <= -3.2e-139)
		tmp = a - ((y * b) / t);
	elseif (y <= -1.35e-150)
		tmp = (z - b) + ((a * (y + t)) / x);
	elseif (y <= -3.1e-159)
		tmp = t_1;
	elseif (y <= 1.12e-153)
		tmp = ((a * t) + (z * x)) / (x + t);
	elseif (y <= 1.12e-83)
		tmp = a * ((y + t) / (y + (x + t)));
	elseif (y <= 1.8e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.4e-88], t$95$2, If[LessEqual[y, -3.2e-139], N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-150], N[(N[(z - b), $MachinePrecision] + N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.1e-159], t$95$1, If[LessEqual[y, 1.12e-153], N[(N[(N[(a * t), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e-83], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-18], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.39999999999999975e-88 or 1.80000000000000005e-18 < y

   1. Initial program 47.9%

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

   3. Taylor expanded in y around inf 70.7%

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

   if -3.39999999999999975e-88 < y < -3.1999999999999999e-139

   1. Initial program 68.5%

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

   3. Taylor expanded in b around -inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. distribute-rgt-neg-in 47.2%

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

      3. +-commutative 47.2%

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

      4. mul-1-neg 47.2%

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

      5. unsub-neg 47.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in x around 0 57.3%

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

   7. Taylor expanded in z around 0 57.3%

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

   8. Taylor expanded in y around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. neg-mul-1 78.3%

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

      3. distribute-lft-neg-in 78.3%

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

   10. Simplified 78.3%

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

   if -3.1999999999999999e-139 < y < -1.3500000000000001e-150

   1. Initial program 83.8%

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

   3. Taylor expanded in b around 0 83.8%

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

      1. mul-1-neg 83.8%

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

      2. +-commutative 83.8%

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

      3. associate-+l+ 83.8%

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

      4. associate-/l* 68.3%

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

      5. +-commutative 68.3%

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

      6. associate-+r+ 68.3%

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

      7. +-commutative 68.3%

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

      8. associate-+l+ 68.3%

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

      9. sub-neg 68.3%

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

      10. div-sub 68.3%

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

      11. +-commutative 68.3%

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

      12. *-commutative 68.3%

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

      13. +-commutative 68.3%

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

      14. associate-+r+ 68.3%

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

      15. +-commutative 68.3%

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

      16. associate-+l+ 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in y around inf 68.8%

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

   7. Taylor expanded in x around inf 67.6%

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

   if -1.3500000000000001e-150 < y < -3.1e-159 or 1.11999999999999993e-83 < y < 1.80000000000000005e-18

   1. Initial program 83.9%

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

   3. Taylor expanded in b around -inf 77.9%

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

      1. mul-1-neg 77.9%

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

      2. distribute-rgt-neg-in 77.9%

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

      3. +-commutative 77.9%

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

      4. mul-1-neg 77.9%

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

      5. unsub-neg 77.9%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in x around inf 77.3%

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

   7. Taylor expanded in x around inf 77.3%

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

      1. associate-*r/ 77.3%

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

      2. neg-mul-1 77.3%

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

      3. distribute-lft-neg-in 77.3%

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

   9. Simplified 77.3%

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

   if -3.1e-159 < y < 1.12000000000000005e-153

   1. Initial program 74.8%

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

   3. Taylor expanded in y around 0 67.4%

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

   if 1.12000000000000005e-153 < y < 1.11999999999999993e-83

   1. Initial program 49.5%

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

   3. Taylor expanded in a around inf 42.6%

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

      1. associate-/l* 80.6%

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

      2. +-commutative 80.6%

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

      3. associate-+r+ 80.6%

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

      4. +-commutative 80.6%

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

      5. associate-+l+ 80.6%

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

   5. Simplified 80.6%

      \[\leadsto \color{blue}{a \cdot \frac{t + y}{y + \left(t + x\right)}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-88}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-139}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-150}:\\ \;\;\;\;\left(z - b\right) + \frac{a \cdot \left(y + t\right)}{x}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-159}:\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-153}:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-18}:\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \frac{y + t}{t\_1}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{x + y}\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-117}:\\ \;\;\;\;b \cdot \frac{y}{-\left(y + t\right)}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* a (/ (+ y t) t_1))))
   (if (<= a -1.8e+35)
     t_2
     (if (<= a -1.25e-292)
       (* b (- (/ z b) (/ y (+ x y))))
       (if (<= a 2.2e-127)
         (* z (/ (+ x y) t_1))
         (if (<= a 2.75e-117)
           (* b (/ y (- (+ y t))))
           (if (<= a 7.8e+153) (- (+ z a) b) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (a <= -1.8e+35) {
		tmp = t_2;
	} else if (a <= -1.25e-292) {
		tmp = b * ((z / b) - (y / (x + y)));
	} else if (a <= 2.2e-127) {
		tmp = z * ((x + y) / t_1);
	} else if (a <= 2.75e-117) {
		tmp = b * (y / -(y + t));
	} else if (a <= 7.8e+153) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a * ((y + t) / t_1)
    if (a <= (-1.8d+35)) then
        tmp = t_2
    else if (a <= (-1.25d-292)) then
        tmp = b * ((z / b) - (y / (x + y)))
    else if (a <= 2.2d-127) then
        tmp = z * ((x + y) / t_1)
    else if (a <= 2.75d-117) then
        tmp = b * (y / -(y + t))
    else if (a <= 7.8d+153) then
        tmp = (z + a) - b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (a <= -1.8e+35) {
		tmp = t_2;
	} else if (a <= -1.25e-292) {
		tmp = b * ((z / b) - (y / (x + y)));
	} else if (a <= 2.2e-127) {
		tmp = z * ((x + y) / t_1);
	} else if (a <= 2.75e-117) {
		tmp = b * (y / -(y + t));
	} else if (a <= 7.8e+153) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a * ((y + t) / t_1)
	tmp = 0
	if a <= -1.8e+35:
		tmp = t_2
	elif a <= -1.25e-292:
		tmp = b * ((z / b) - (y / (x + y)))
	elif a <= 2.2e-127:
		tmp = z * ((x + y) / t_1)
	elif a <= 2.75e-117:
		tmp = b * (y / -(y + t))
	elif a <= 7.8e+153:
		tmp = (z + a) - b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a * Float64(Float64(y + t) / t_1))
	tmp = 0.0
	if (a <= -1.8e+35)
		tmp = t_2;
	elseif (a <= -1.25e-292)
		tmp = Float64(b * Float64(Float64(z / b) - Float64(y / Float64(x + y))));
	elseif (a <= 2.2e-127)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	elseif (a <= 2.75e-117)
		tmp = Float64(b * Float64(y / Float64(-Float64(y + t))));
	elseif (a <= 7.8e+153)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a * ((y + t) / t_1);
	tmp = 0.0;
	if (a <= -1.8e+35)
		tmp = t_2;
	elseif (a <= -1.25e-292)
		tmp = b * ((z / b) - (y / (x + y)));
	elseif (a <= 2.2e-127)
		tmp = z * ((x + y) / t_1);
	elseif (a <= 2.75e-117)
		tmp = b * (y / -(y + t));
	elseif (a <= 7.8e+153)
		tmp = (z + a) - b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+35], t$95$2, If[LessEqual[a, -1.25e-292], N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-127], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.75e-117], N[(b * N[(y / (-N[(y + t), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e+153], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.8e35 or 7.79999999999999966e153 < a

   1. Initial program 43.4%

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

   3. Taylor expanded in a around inf 34.2%

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

      1. associate-/l* 72.7%

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

      2. +-commutative 72.7%

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

      3. associate-+r+ 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-+l+ 72.7%

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

   5. Simplified 72.7%

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

   if -1.8e35 < a < -1.24999999999999995e-292

   1. Initial program 67.8%

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

   3. Taylor expanded in b around -inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. distribute-rgt-neg-in 66.2%

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

      3. +-commutative 66.2%

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

      4. mul-1-neg 66.2%

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

      5. unsub-neg 66.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in x around inf 69.5%

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

   7. Taylor expanded in t around 0 65.1%

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

      1. +-commutative 65.1%

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

   9. Simplified 65.1%

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

   if -1.24999999999999995e-292 < a < 2.2000000000000001e-127

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf 46.7%

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

      1. associate-/l* 65.0%

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

      2. +-commutative 65.0%

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

      3. +-commutative 65.0%

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

      4. associate-+r+ 65.0%

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

      5. +-commutative 65.0%

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

      6. associate-+l+ 65.0%

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

   5. Simplified 65.0%

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

   if 2.2000000000000001e-127 < a < 2.75000000000000013e-117

   1. Initial program 100.0%

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

   3. Taylor expanded in b around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. +-commutative 100.0%

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

      4. mul-1-neg 100.0%

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

      5. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 100.0%

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

   7. Taylor expanded in b around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. +-commutative 100.0%

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

      6. mul-1-neg 100.0%

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

      7. associate-*r/ 100.0%

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

      8. mul-1-neg 100.0%

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

   9. Simplified 100.0%

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

   if 2.75000000000000013e-117 < a < 7.79999999999999966e153

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 62.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{x + y}\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-117}:\\ \;\;\;\;b \cdot \frac{y}{-\left(y + t\right)}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \frac{y + t}{t\_1}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{t\_1}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* a (/ (+ y t) t_1))))
   (if (<= a -5.5e+84)
     t_2
     (if (<= a -2.7e+35)
       (/ (+ (* a t) (* z x)) (+ x t))
       (if (<= a 1.8e-132)
         (* b (- (/ z b) (/ y t_1)))
         (if (<= a 1.2e+152) (- (+ z a) b) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (a <= -5.5e+84) {
		tmp = t_2;
	} else if (a <= -2.7e+35) {
		tmp = ((a * t) + (z * x)) / (x + t);
	} else if (a <= 1.8e-132) {
		tmp = b * ((z / b) - (y / t_1));
	} else if (a <= 1.2e+152) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a * ((y + t) / t_1)
    if (a <= (-5.5d+84)) then
        tmp = t_2
    else if (a <= (-2.7d+35)) then
        tmp = ((a * t) + (z * x)) / (x + t)
    else if (a <= 1.8d-132) then
        tmp = b * ((z / b) - (y / t_1))
    else if (a <= 1.2d+152) then
        tmp = (z + a) - b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (a <= -5.5e+84) {
		tmp = t_2;
	} else if (a <= -2.7e+35) {
		tmp = ((a * t) + (z * x)) / (x + t);
	} else if (a <= 1.8e-132) {
		tmp = b * ((z / b) - (y / t_1));
	} else if (a <= 1.2e+152) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a * ((y + t) / t_1)
	tmp = 0
	if a <= -5.5e+84:
		tmp = t_2
	elif a <= -2.7e+35:
		tmp = ((a * t) + (z * x)) / (x + t)
	elif a <= 1.8e-132:
		tmp = b * ((z / b) - (y / t_1))
	elif a <= 1.2e+152:
		tmp = (z + a) - b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a * Float64(Float64(y + t) / t_1))
	tmp = 0.0
	if (a <= -5.5e+84)
		tmp = t_2;
	elseif (a <= -2.7e+35)
		tmp = Float64(Float64(Float64(a * t) + Float64(z * x)) / Float64(x + t));
	elseif (a <= 1.8e-132)
		tmp = Float64(b * Float64(Float64(z / b) - Float64(y / t_1)));
	elseif (a <= 1.2e+152)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a * ((y + t) / t_1);
	tmp = 0.0;
	if (a <= -5.5e+84)
		tmp = t_2;
	elseif (a <= -2.7e+35)
		tmp = ((a * t) + (z * x)) / (x + t);
	elseif (a <= 1.8e-132)
		tmp = b * ((z / b) - (y / t_1));
	elseif (a <= 1.2e+152)
		tmp = (z + a) - b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e+84], t$95$2, If[LessEqual[a, -2.7e+35], N[(N[(N[(a * t), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-132], N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+152], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.5000000000000004e84 or 1.2e152 < a

   1. Initial program 39.3%

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

   3. Taylor expanded in a around inf 32.3%

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

      1. associate-/l* 75.1%

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

      2. +-commutative 75.1%

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

      3. associate-+r+ 75.1%

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

      4. +-commutative 75.1%

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

      5. associate-+l+ 75.1%

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

   5. Simplified 75.1%

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

   if -5.5000000000000004e84 < a < -2.70000000000000003e35

   1. Initial program 81.4%

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

   3. Taylor expanded in y around 0 90.9%

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

   if -2.70000000000000003e35 < a < 1.80000000000000004e-132

   1. Initial program 71.8%

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

   3. Taylor expanded in b around -inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. distribute-rgt-neg-in 68.0%

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

      3. +-commutative 68.0%

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

      4. mul-1-neg 68.0%

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

      5. unsub-neg 68.0%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in x around inf 66.0%

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

   if 1.80000000000000004e-132 < a < 1.2e152

   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. Add Preprocessing

   3. Taylor expanded in y around inf 62.1%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -0.95:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-113}:\\ \;\;\;\;z - \frac{y \cdot b}{x + \left(y + t\right)}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ (+ y t) (+ y (+ x t))))))
   (if (<= a -1.15e+84)
     t_1
     (if (<= a -0.95)
       (/ (+ (* a t) (* z x)) (+ x t))
       (if (<= a 3.4e-113)
         (- z (/ (* y b) (+ x (+ y t))))
         (if (<= a 2.15e+151) (- (+ z a) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * ((y + t) / (y + (x + t)));
	double tmp;
	if (a <= -1.15e+84) {
		tmp = t_1;
	} else if (a <= -0.95) {
		tmp = ((a * t) + (z * x)) / (x + t);
	} else if (a <= 3.4e-113) {
		tmp = z - ((y * b) / (x + (y + t)));
	} else if (a <= 2.15e+151) {
		tmp = (z + a) - b;
	} 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 * ((y + t) / (y + (x + t)))
    if (a <= (-1.15d+84)) then
        tmp = t_1
    else if (a <= (-0.95d0)) then
        tmp = ((a * t) + (z * x)) / (x + t)
    else if (a <= 3.4d-113) then
        tmp = z - ((y * b) / (x + (y + t)))
    else if (a <= 2.15d+151) then
        tmp = (z + a) - b
    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 * ((y + t) / (y + (x + t)));
	double tmp;
	if (a <= -1.15e+84) {
		tmp = t_1;
	} else if (a <= -0.95) {
		tmp = ((a * t) + (z * x)) / (x + t);
	} else if (a <= 3.4e-113) {
		tmp = z - ((y * b) / (x + (y + t)));
	} else if (a <= 2.15e+151) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * ((y + t) / (y + (x + t)))
	tmp = 0
	if a <= -1.15e+84:
		tmp = t_1
	elif a <= -0.95:
		tmp = ((a * t) + (z * x)) / (x + t)
	elif a <= 3.4e-113:
		tmp = z - ((y * b) / (x + (y + t)))
	elif a <= 2.15e+151:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (a <= -1.15e+84)
		tmp = t_1;
	elseif (a <= -0.95)
		tmp = Float64(Float64(Float64(a * t) + Float64(z * x)) / Float64(x + t));
	elseif (a <= 3.4e-113)
		tmp = Float64(z - Float64(Float64(y * b) / Float64(x + Float64(y + t))));
	elseif (a <= 2.15e+151)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * ((y + t) / (y + (x + t)));
	tmp = 0.0;
	if (a <= -1.15e+84)
		tmp = t_1;
	elseif (a <= -0.95)
		tmp = ((a * t) + (z * x)) / (x + t);
	elseif (a <= 3.4e-113)
		tmp = z - ((y * b) / (x + (y + t)));
	elseif (a <= 2.15e+151)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+84], t$95$1, If[LessEqual[a, -0.95], N[(N[(N[(a * t), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-113], N[(z - N[(N[(y * b), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e+151], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.1499999999999999e84 or 2.14999999999999991e151 < a

   1. Initial program 39.3%

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

   3. Taylor expanded in a around inf 32.3%

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

      1. associate-/l* 75.1%

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

      2. +-commutative 75.1%

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

      3. associate-+r+ 75.1%

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

      4. +-commutative 75.1%

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

      5. associate-+l+ 75.1%

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

   5. Simplified 75.1%

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

   if -1.1499999999999999e84 < a < -0.94999999999999996

   1. Initial program 60.7%

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

   3. Taylor expanded in y around 0 63.2%

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

   if -0.94999999999999996 < a < 3.4000000000000002e-113

   1. Initial program 74.8%

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

   3. Taylor expanded in b around -inf 69.1%

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

      1. mul-1-neg 69.1%

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

      2. distribute-rgt-neg-in 69.1%

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

      3. +-commutative 69.1%

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

      4. mul-1-neg 69.1%

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

      5. unsub-neg 69.1%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in x around inf 64.6%

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

   7. Taylor expanded in b around 0 66.2%

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

      1. associate-*r/ 66.2%

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

      2. neg-mul-1 66.2%

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

      3. distribute-lft-neg-in 66.2%

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

      4. +-commutative 66.2%

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

      5. associate-+r+ 66.2%

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

      6. +-commutative 66.2%

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

   9. Simplified 66.2%

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

   if 3.4000000000000002e-113 < a < 2.14999999999999991e151

   1. Initial program 61.7%

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

   3. Taylor expanded in y around inf 61.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -0.95:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-113}:\\ \;\;\;\;z - \frac{y \cdot b}{x + \left(y + t\right)}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-133}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{x + y}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ (+ y t) (+ y (+ x t))))))
   (if (<= a -3.1e+35)
     t_1
     (if (<= a 2.6e-133)
       (* b (- (/ z b) (/ y (+ x y))))
       (if (<= a 9.5e+152) (- (+ z a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * ((y + t) / (y + (x + t)));
	double tmp;
	if (a <= -3.1e+35) {
		tmp = t_1;
	} else if (a <= 2.6e-133) {
		tmp = b * ((z / b) - (y / (x + y)));
	} else if (a <= 9.5e+152) {
		tmp = (z + a) - b;
	} 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 * ((y + t) / (y + (x + t)))
    if (a <= (-3.1d+35)) then
        tmp = t_1
    else if (a <= 2.6d-133) then
        tmp = b * ((z / b) - (y / (x + y)))
    else if (a <= 9.5d+152) then
        tmp = (z + a) - b
    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 * ((y + t) / (y + (x + t)));
	double tmp;
	if (a <= -3.1e+35) {
		tmp = t_1;
	} else if (a <= 2.6e-133) {
		tmp = b * ((z / b) - (y / (x + y)));
	} else if (a <= 9.5e+152) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * ((y + t) / (y + (x + t)))
	tmp = 0
	if a <= -3.1e+35:
		tmp = t_1
	elif a <= 2.6e-133:
		tmp = b * ((z / b) - (y / (x + y)))
	elif a <= 9.5e+152:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (a <= -3.1e+35)
		tmp = t_1;
	elseif (a <= 2.6e-133)
		tmp = Float64(b * Float64(Float64(z / b) - Float64(y / Float64(x + y))));
	elseif (a <= 9.5e+152)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * ((y + t) / (y + (x + t)));
	tmp = 0.0;
	if (a <= -3.1e+35)
		tmp = t_1;
	elseif (a <= 2.6e-133)
		tmp = b * ((z / b) - (y / (x + y)));
	elseif (a <= 9.5e+152)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e+35], t$95$1, If[LessEqual[a, 2.6e-133], N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+152], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.09999999999999987e35 or 9.49999999999999916e152 < a

   1. Initial program 43.4%

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

   3. Taylor expanded in a around inf 34.2%

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

      1. associate-/l* 72.7%

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

      2. +-commutative 72.7%

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

      3. associate-+r+ 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-+l+ 72.7%

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

   5. Simplified 72.7%

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

   if -3.09999999999999987e35 < a < 2.5999999999999999e-133

   1. Initial program 71.8%

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

   3. Taylor expanded in b around -inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. distribute-rgt-neg-in 68.0%

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

      3. +-commutative 68.0%

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

      4. mul-1-neg 68.0%

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

      5. unsub-neg 68.0%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in x around inf 66.0%

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

   7. Taylor expanded in t around 0 61.2%

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

      1. +-commutative 61.2%

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

   9. Simplified 61.2%

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

   if 2.5999999999999999e-133 < a < 9.49999999999999916e152

   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. Add Preprocessing

   3. Taylor expanded in y around inf 62.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-133}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{x + y}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;b \leq -1.12 \cdot 10^{+178} \lor \neg \left(b \leq 1.7 \cdot 10^{+170}\right):\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1} + \left(z - b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (or (<= b -1.12e+178) (not (<= b 1.7e+170)))
     (* b (- (/ a b) (/ y t_1)))
     (+ (* a (/ (+ y t) t_1)) (- z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((b <= -1.12e+178) || !(b <= 1.7e+170)) {
		tmp = b * ((a / b) - (y / t_1));
	} else {
		tmp = (a * ((y + t) / t_1)) + (z - b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if ((b <= (-1.12d+178)) .or. (.not. (b <= 1.7d+170))) then
        tmp = b * ((a / b) - (y / t_1))
    else
        tmp = (a * ((y + t) / t_1)) + (z - b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((b <= -1.12e+178) || !(b <= 1.7e+170)) {
		tmp = b * ((a / b) - (y / t_1));
	} else {
		tmp = (a * ((y + t) / t_1)) + (z - b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (b <= -1.12e+178) or not (b <= 1.7e+170):
		tmp = b * ((a / b) - (y / t_1))
	else:
		tmp = (a * ((y + t) / t_1)) + (z - b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((b <= -1.12e+178) || !(b <= 1.7e+170))
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / t_1)));
	else
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_1)) + Float64(z - b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if ((b <= -1.12e+178) || ~((b <= 1.7e+170)))
		tmp = b * ((a / b) - (y / t_1));
	else
		tmp = (a * ((y + t) / t_1)) + (z - b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.12e+178], N[Not[LessEqual[b, 1.7e+170]], $MachinePrecision]], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z - b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.12000000000000001e178 or 1.7000000000000001e170 < b

   1. Initial program 45.2%

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

   3. Taylor expanded in b around -inf 49.5%

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

      1. mul-1-neg 49.5%

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

      2. distribute-rgt-neg-in 49.5%

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

      3. +-commutative 49.5%

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

      4. mul-1-neg 49.5%

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

      5. unsub-neg 49.5%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in t around inf 70.0%

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

   if -1.12000000000000001e178 < b < 1.7000000000000001e170

   1. Initial program 62.3%

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

   3. Taylor expanded in b around 0 62.3%

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

      1. mul-1-neg 62.3%

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

      2. +-commutative 62.3%

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

      3. associate-+l+ 62.3%

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

      4. associate-/l* 76.0%

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

      5. +-commutative 76.0%

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

      6. associate-+r+ 76.0%

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

      7. +-commutative 76.0%

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

      8. associate-+l+ 76.0%

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

      9. sub-neg 76.0%

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

      10. div-sub 75.9%

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

      11. +-commutative 75.9%

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

      12. *-commutative 75.9%

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

      13. +-commutative 75.9%

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

      14. associate-+r+ 75.9%

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

      15. +-commutative 75.9%

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

      16. associate-+l+ 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in y around inf 77.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+178} \lor \neg \left(b \leq 1.7 \cdot 10^{+170}\right):\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} + \left(z - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+128} \lor \neg \left(a \leq 3.1 \cdot 10^{+154}\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.05e+128) (not (<= a 3.1e+154)))
   (* a (/ (+ y t) (+ y (+ x t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.05e+128) || !(a <= 3.1e+154)) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.05d+128)) .or. (.not. (a <= 3.1d+154))) then
        tmp = a * ((y + t) / (y + (x + t)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.05e+128) || !(a <= 3.1e+154)) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.05e+128) or not (a <= 3.1e+154):
		tmp = a * ((y + t) / (y + (x + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.05e+128) || !(a <= 3.1e+154))
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.05e+128) || ~((a <= 3.1e+154)))
		tmp = a * ((y + t) / (y + (x + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.05e+128], N[Not[LessEqual[a, 3.1e+154]], $MachinePrecision]], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.05e128 or 3.1000000000000001e154 < a

   1. Initial program 39.0%

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

   3. Taylor expanded in a around inf 30.9%

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

      1. associate-/l* 75.9%

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

      2. +-commutative 75.9%

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

      3. associate-+r+ 75.9%

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

      4. +-commutative 75.9%

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

      5. associate-+l+ 75.9%

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

   5. Simplified 75.9%

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

   if -1.05e128 < a < 3.1000000000000001e154

   1. Initial program 67.3%

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

   3. Taylor expanded in y around inf 57.3%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+128} \lor \neg \left(a \leq 3.1 \cdot 10^{+154}\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+181} \lor \neg \left(b \leq 1.35 \cdot 10^{+231}\right):\\ \;\;\;\;\frac{y}{\left(x + y\right) + t} \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.5e+181) (not (<= b 1.35e+231)))
   (* (/ y (+ (+ x y) t)) (- b))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.5e+181) || !(b <= 1.35e+231)) {
		tmp = (y / ((x + y) + t)) * -b;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.5d+181)) .or. (.not. (b <= 1.35d+231))) then
        tmp = (y / ((x + y) + t)) * -b
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.5e+181) || !(b <= 1.35e+231)) {
		tmp = (y / ((x + y) + t)) * -b;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.5e+181) or not (b <= 1.35e+231):
		tmp = (y / ((x + y) + t)) * -b
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.5e+181) || !(b <= 1.35e+231))
		tmp = Float64(Float64(y / Float64(Float64(x + y) + t)) * Float64(-b));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.5e+181) || ~((b <= 1.35e+231)))
		tmp = (y / ((x + y) + t)) * -b;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.5e+181], N[Not[LessEqual[b, 1.35e+231]], $MachinePrecision]], N[(N[(y / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * (-b)), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.5e181 or 1.35e231 < b

   1. Initial program 49.3%

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

   3. Taylor expanded in b around -inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. distribute-rgt-neg-in 52.3%

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

      3. +-commutative 52.3%

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

      4. mul-1-neg 52.3%

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

      5. unsub-neg 52.3%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in b around inf 32.3%

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

      1. mul-1-neg 32.3%

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

      2. associate-/l* 52.4%

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

      3. associate-+r+ 52.4%

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

      4. +-commutative 52.4%

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

      5. distribute-rgt-neg-out 52.4%

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

      6. distribute-neg-frac 52.4%

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

      7. +-commutative 52.4%

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

      8. associate-+r+ 52.4%

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

      9. +-commutative 52.4%

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

   8. Simplified 52.4%

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

   if -4.5e181 < b < 1.35e231

   1. Initial program 60.8%

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

   3. Taylor expanded in y around inf 63.7%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+181} \lor \neg \left(b \leq 1.35 \cdot 10^{+231}\right):\\ \;\;\;\;\frac{y}{\left(x + y\right) + t} \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+95} \lor \neg \left(x \leq 3.2 \cdot 10^{-7}\right):\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -4.4e+95) (not (<= x 3.2e-7)))
   (- z (/ (* y b) x))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -4.4e+95) || !(x <= 3.2e-7)) {
		tmp = z - ((y * b) / x);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-4.4d+95)) .or. (.not. (x <= 3.2d-7))) then
        tmp = z - ((y * b) / x)
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -4.4e+95) || !(x <= 3.2e-7)) {
		tmp = z - ((y * b) / x);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -4.4e+95) or not (x <= 3.2e-7):
		tmp = z - ((y * b) / x)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -4.4e+95) || !(x <= 3.2e-7))
		tmp = Float64(z - Float64(Float64(y * b) / x));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -4.4e+95) || ~((x <= 3.2e-7)))
		tmp = z - ((y * b) / x);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -4.4e+95], N[Not[LessEqual[x, 3.2e-7]], $MachinePrecision]], N[(z - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3999999999999998e95 or 3.2000000000000001e-7 < x

   1. Initial program 50.9%

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

   3. Taylor expanded in b around -inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. distribute-rgt-neg-in 47.8%

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

      3. +-commutative 47.8%

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

      4. mul-1-neg 47.8%

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

      5. unsub-neg 47.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in x around inf 50.9%

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

   7. Taylor expanded in x around inf 52.2%

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

      1. associate-*r/ 52.2%

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

      2. neg-mul-1 52.2%

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

      3. distribute-lft-neg-in 52.2%

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

   9. Simplified 52.2%

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

   if -4.3999999999999998e95 < x < 3.2000000000000001e-7

   1. Initial program 64.7%

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

   3. Taylor expanded in y around inf 67.0%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+95} \lor \neg \left(x \leq 3.2 \cdot 10^{-7}\right):\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+162}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-77}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.55e+162) a (if (<= t 4.5e-77) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.55e+162) {
		tmp = a;
	} else if (t <= 4.5e-77) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.55d+162)) then
        tmp = a
    else if (t <= 4.5d-77) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.55e+162) {
		tmp = a;
	} else if (t <= 4.5e-77) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.55e+162:
		tmp = a
	elif t <= 4.5e-77:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.55e+162)
		tmp = a;
	elseif (t <= 4.5e-77)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.55e+162)
		tmp = a;
	elseif (t <= 4.5e-77)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.55e+162], a, If[LessEqual[t, 4.5e-77], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55e162 or 4.5000000000000001e-77 < t

   1. Initial program 45.7%

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

   3. Taylor expanded in t around inf 53.0%

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

   if -1.55e162 < t < 4.5000000000000001e-77

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf 45.3%

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

Alternative 14: 56.4% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \left(z + a\right) - b \end{array} \]

FPCore

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

C

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

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 = (z + a) - b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.7%

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

3. Taylor expanded in y around inf 56.7%

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

4. Final simplification 56.7%

   \[\leadsto \left(z + a\right) - b \]
5. Add Preprocessing

Alternative 15: 32.6% 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 58.7%

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

3. Taylor expanded in t around inf 32.7%

   \[\leadsto \color{blue}{a} \]
4. Add Preprocessing

Developer target: 82.1% 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 2024100 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (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)))