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

Percentage Accurate: 60.2% → 90.9%

Time: 12.0s

Alternatives: 13

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: 60.2% 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: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ t_2 := \frac{y}{t\_1}\\ t_3 := t\_1 \cdot z\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{-126} \lor \neg \left(b \leq 1.75 \cdot 10^{-103}\right):\\ \;\;\;\;b \cdot \left(-\mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{t\_1} + z \cdot \frac{y + x}{t\_1}}{b}, t\_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\mathsf{fma}\left(a, \frac{y + t}{t\_3}, t\_2\right) - b \cdot \frac{y}{t\_3}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x)) (t_2 (/ y t_1)) (t_3 (* t_1 z)))
   (if (or (<= b -1.35e-126) (not (<= b 1.75e-103)))
     (*
      b
      (- (fma -1.0 (/ (+ (* a (/ (+ y t) t_1)) (* z (/ (+ y x) t_1))) b) t_2)))
     (* z (+ (/ x t_1) (- (fma a (/ (+ y t) t_3) t_2) (* b (/ y t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double t_2 = y / t_1;
	double t_3 = t_1 * z;
	double tmp;
	if ((b <= -1.35e-126) || !(b <= 1.75e-103)) {
		tmp = b * -fma(-1.0, (((a * ((y + t) / t_1)) + (z * ((y + x) / t_1))) / b), t_2);
	} else {
		tmp = z * ((x / t_1) + (fma(a, ((y + t) / t_3), t_2) - (b * (y / t_3))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) + x)
	t_2 = Float64(y / t_1)
	t_3 = Float64(t_1 * z)
	tmp = 0.0
	if ((b <= -1.35e-126) || !(b <= 1.75e-103))
		tmp = Float64(b * Float64(-fma(-1.0, Float64(Float64(Float64(a * Float64(Float64(y + t) / t_1)) + Float64(z * Float64(Float64(y + x) / t_1))) / b), t_2)));
	else
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(fma(a, Float64(Float64(y + t) / t_3), t_2) - Float64(b * Float64(y / t_3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 * z), $MachinePrecision]}, If[Or[LessEqual[b, -1.35e-126], N[Not[LessEqual[b, 1.75e-103]], $MachinePrecision]], N[(b * (-N[(-1.0 * N[(N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + t$95$2), $MachinePrecision])), $MachinePrecision], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$3), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(b * N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.34999999999999998e-126 or 1.75000000000000008e-103 < b

   1. Initial program 59.8%

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

   3. Taylor expanded in b around -inf 68.1%

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

      1. associate-*r* 68.1%

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

      2. neg-mul-1 68.1%

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

      3. fma-define 68.1%

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

   5. Simplified 95.8%

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

   if -1.34999999999999998e-126 < b < 1.75000000000000008e-103

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. +-commutative 81.6%

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

      3. associate-+r+ 81.6%

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

   5. Simplified 87.8%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-126} \lor \neg \left(b \leq 1.75 \cdot 10^{-103}\right):\\ \;\;\;\;b \cdot \left(-\mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}}{b}, \frac{y}{\left(y + t\right) + x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{\left(y + t\right) + x} + \left(\mathsf{fma}\left(a, \frac{y + t}{\left(\left(y + t\right) + x\right) \cdot z}, \frac{y}{\left(y + t\right) + x}\right) - b \cdot \frac{y}{\left(\left(y + t\right) + x\right) \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ t_2 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-\mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{t\_1} + z \cdot \frac{y + x}{t\_1}}{b}, \frac{y}{t\_1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x))
        (t_2 (/ (- (+ (* a (+ y t)) (* z (+ y x))) (* b y)) (+ y (+ t x)))))
   (if (<= t_2 (- INFINITY))
     (- (+ a z) b)
     (if (<= t_2 2e+297)
       t_2
       (*
        b
        (-
         (fma
          -1.0
          (/ (+ (* a (/ (+ y t) t_1)) (* z (/ (+ y x) t_1))) b)
          (/ y t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double t_2 = (((a * (y + t)) + (z * (y + x))) - (b * y)) / (y + (t + x));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (a + z) - b;
	} else if (t_2 <= 2e+297) {
		tmp = t_2;
	} else {
		tmp = b * -fma(-1.0, (((a * ((y + t) / t_1)) + (z * ((y + x) / t_1))) / b), (y / t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) + x)
	t_2 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(y + x))) - Float64(b * y)) / Float64(y + Float64(t + x)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(a + z) - b);
	elseif (t_2 <= 2e+297)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(-fma(-1.0, Float64(Float64(Float64(a * Float64(Float64(y + t) / t_1)) + Float64(z * Float64(Float64(y + x) / t_1))) / b), Float64(y / t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$2, 2e+297], t$95$2, N[(b * (-N[(-1.0 * N[(N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.2%

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

   3. Taylor expanded in y around inf 75.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e297

   1. Initial program 99.7%

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

   if 2e297 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.7%

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

   3. Taylor expanded in b around -inf 19.9%

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

      1. associate-*r* 19.9%

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

      2. neg-mul-1 19.9%

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

      3. fma-define 19.9%

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

   5. Simplified 73.0%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-\mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}}{b}, \frac{y}{\left(y + t\right) + x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ t_2 := \frac{y}{t\_1}\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{-167} \lor \neg \left(b \leq 1.32 \cdot 10^{-133}\right):\\ \;\;\;\;b \cdot \left(-\mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{t\_1} + z \cdot \frac{y + x}{t\_1}}{b}, t\_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} + \left(\mathsf{fma}\left(z, \frac{y + x}{a \cdot t\_1}, t\_2\right) - \frac{\frac{b \cdot y}{a}}{t\_1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x)) (t_2 (/ y t_1)))
   (if (or (<= b -2.6e-167) (not (<= b 1.32e-133)))
     (*
      b
      (- (fma -1.0 (/ (+ (* a (/ (+ y t) t_1)) (* z (/ (+ y x) t_1))) b) t_2)))
     (*
      a
      (+
       (/ t t_1)
       (- (fma z (/ (+ y x) (* a t_1)) t_2) (/ (/ (* b y) a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double t_2 = y / t_1;
	double tmp;
	if ((b <= -2.6e-167) || !(b <= 1.32e-133)) {
		tmp = b * -fma(-1.0, (((a * ((y + t) / t_1)) + (z * ((y + x) / t_1))) / b), t_2);
	} else {
		tmp = a * ((t / t_1) + (fma(z, ((y + x) / (a * t_1)), t_2) - (((b * y) / a) / t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) + x)
	t_2 = Float64(y / t_1)
	tmp = 0.0
	if ((b <= -2.6e-167) || !(b <= 1.32e-133))
		tmp = Float64(b * Float64(-fma(-1.0, Float64(Float64(Float64(a * Float64(Float64(y + t) / t_1)) + Float64(z * Float64(Float64(y + x) / t_1))) / b), t_2)));
	else
		tmp = Float64(a * Float64(Float64(t / t_1) + Float64(fma(z, Float64(Float64(y + x) / Float64(a * t_1)), t_2) - Float64(Float64(Float64(b * y) / a) / t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, If[Or[LessEqual[b, -2.6e-167], N[Not[LessEqual[b, 1.32e-133]], $MachinePrecision]], N[(b * (-N[(-1.0 * N[(N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + t$95$2), $MachinePrecision])), $MachinePrecision], N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(z * N[(N[(y + x), $MachinePrecision] / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(N[(N[(b * y), $MachinePrecision] / a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5999999999999999e-167 or 1.32000000000000008e-133 < b

   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 b around -inf 67.8%

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

      1. associate-*r* 67.8%

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

      2. neg-mul-1 67.8%

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

      3. fma-define 67.8%

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

   5. Simplified 93.7%

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

   if -2.5999999999999999e-167 < b < 1.32000000000000008e-133

   1. Initial program 62.7%

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

   3. Taylor expanded in a around inf 67.4%

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

      1. associate--l+ 67.4%

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

      2. +-commutative 67.4%

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

      3. associate-+r+ 67.4%

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

   5. Simplified 79.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{-167} \lor \neg \left(b \leq 1.32 \cdot 10^{-133}\right):\\ \;\;\;\;b \cdot \left(-\mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}}{b}, \frac{y}{\left(y + t\right) + x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{\left(y + t\right) + x} + \left(\mathsf{fma}\left(z, \frac{y + x}{a \cdot \left(\left(y + t\right) + x\right)}, \frac{y}{\left(y + t\right) + x}\right) - \frac{\frac{b \cdot y}{a}}{\left(y + t\right) + x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+221}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ y t)) (* z (+ y x))) (* b y)) (+ y (+ t x)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+221))) (- (+ a z) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (y + x))) - (b * y)) / (y + (t + x));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+221)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (y + x))) - (b * y)) / (y + (t + x));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+221)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (y + t)) + (z * (y + x))) - (b * y)) / (y + (t + x))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+221):
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(y + x))) - Float64(b * y)) / Float64(y + Float64(t + x)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+221))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((a * (y + t)) + (z * (y + x))) - (b * y)) / (y + (t + x));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+221)))
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+221]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.0000000000000002e221 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 10.6%

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

   3. Taylor expanded in y around inf 75.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000002e221

   1. Initial program 99.7%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 4 \cdot 10^{+221}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ t_2 := a \cdot \left(\frac{y + t}{t\_1} + \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -0.155:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-211}:\\ \;\;\;\;z \cdot \frac{y + x}{t\_1}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{z \cdot \left(y + x\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x)) (t_2 (* a (+ (/ (+ y t) t_1) (/ z a)))))
   (if (<= a -0.155)
     t_2
     (if (<= a -7.2e-211)
       (* z (/ (+ y x) t_1))
       (if (<= a 3.4e-97) (/ (- (* z (+ y x)) (* b y)) (+ y (+ t x))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double t_2 = a * (((y + t) / t_1) + (z / a));
	double tmp;
	if (a <= -0.155) {
		tmp = t_2;
	} else if (a <= -7.2e-211) {
		tmp = z * ((y + x) / t_1);
	} else if (a <= 3.4e-97) {
		tmp = ((z * (y + x)) - (b * y)) / (y + (t + x));
	} 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 + t) + x
    t_2 = a * (((y + t) / t_1) + (z / a))
    if (a <= (-0.155d0)) then
        tmp = t_2
    else if (a <= (-7.2d-211)) then
        tmp = z * ((y + x) / t_1)
    else if (a <= 3.4d-97) then
        tmp = ((z * (y + x)) - (b * y)) / (y + (t + x))
    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 + t) + x;
	double t_2 = a * (((y + t) / t_1) + (z / a));
	double tmp;
	if (a <= -0.155) {
		tmp = t_2;
	} else if (a <= -7.2e-211) {
		tmp = z * ((y + x) / t_1);
	} else if (a <= 3.4e-97) {
		tmp = ((z * (y + x)) - (b * y)) / (y + (t + x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + t) + x
	t_2 = a * (((y + t) / t_1) + (z / a))
	tmp = 0
	if a <= -0.155:
		tmp = t_2
	elif a <= -7.2e-211:
		tmp = z * ((y + x) / t_1)
	elif a <= 3.4e-97:
		tmp = ((z * (y + x)) - (b * y)) / (y + (t + x))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) + x)
	t_2 = Float64(a * Float64(Float64(Float64(y + t) / t_1) + Float64(z / a)))
	tmp = 0.0
	if (a <= -0.155)
		tmp = t_2;
	elseif (a <= -7.2e-211)
		tmp = Float64(z * Float64(Float64(y + x) / t_1));
	elseif (a <= 3.4e-97)
		tmp = Float64(Float64(Float64(z * Float64(y + x)) - Float64(b * y)) / Float64(y + Float64(t + x)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + t) + x;
	t_2 = a * (((y + t) / t_1) + (z / a));
	tmp = 0.0;
	if (a <= -0.155)
		tmp = t_2;
	elseif (a <= -7.2e-211)
		tmp = z * ((y + x) / t_1);
	elseif (a <= 3.4e-97)
		tmp = ((z * (y + x)) - (b * y)) / (y + (t + x));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.155], t$95$2, If[LessEqual[a, -7.2e-211], N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-97], N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.154999999999999999 or 3.3999999999999999e-97 < a

   1. Initial program 53.8%

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

   3. Taylor expanded in a around -inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. distribute-rgt-neg-in 69.4%

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

      3. mul-1-neg 69.4%

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

      4. unsub-neg 69.4%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in x around inf 76.2%

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

   if -0.154999999999999999 < a < -7.1999999999999998e-211

   1. Initial program 64.5%

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

   3. Taylor expanded in z around inf 39.8%

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

      1. associate-/l* 63.7%

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

      2. +-commutative 63.7%

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

      3. +-commutative 63.7%

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

      4. associate-+r+ 63.7%

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

   5. Simplified 63.7%

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

   if -7.1999999999999998e-211 < a < 3.3999999999999999e-97

   1. Initial program 77.3%

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

   3. Taylor expanded in a around 0 71.3%

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

      1. +-commutative 71.3%

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

      2. *-commutative 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.155:\\ \;\;\;\;a \cdot \left(\frac{y + t}{\left(y + t\right) + x} + \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-211}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + t\right) + x}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{z \cdot \left(y + x\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{y + t}{\left(y + t\right) + x} + \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ t_2 := a \cdot \frac{y + t}{t\_1}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+152}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-9}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{y + x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x)) (t_2 (* a (/ (+ y t) t_1))))
   (if (<= a -2.8e+152)
     t_2
     (if (<= a -9.5e-9)
       (- (+ a z) b)
       (if (<= a 8.8e+38) (* z (/ (+ y x) t_1)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (a <= -2.8e+152) {
		tmp = t_2;
	} else if (a <= -9.5e-9) {
		tmp = (a + z) - b;
	} else if (a <= 8.8e+38) {
		tmp = z * ((y + x) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + t) + x
    t_2 = a * ((y + t) / t_1)
    if (a <= (-2.8d+152)) then
        tmp = t_2
    else if (a <= (-9.5d-9)) then
        tmp = (a + z) - b
    else if (a <= 8.8d+38) then
        tmp = z * ((y + x) / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (a <= -2.8e+152) {
		tmp = t_2;
	} else if (a <= -9.5e-9) {
		tmp = (a + z) - b;
	} else if (a <= 8.8e+38) {
		tmp = z * ((y + x) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + t) + x
	t_2 = a * ((y + t) / t_1)
	tmp = 0
	if a <= -2.8e+152:
		tmp = t_2
	elif a <= -9.5e-9:
		tmp = (a + z) - b
	elif a <= 8.8e+38:
		tmp = z * ((y + x) / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) + x)
	t_2 = Float64(a * Float64(Float64(y + t) / t_1))
	tmp = 0.0
	if (a <= -2.8e+152)
		tmp = t_2;
	elseif (a <= -9.5e-9)
		tmp = Float64(Float64(a + z) - b);
	elseif (a <= 8.8e+38)
		tmp = Float64(z * Float64(Float64(y + x) / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + t) + x;
	t_2 = a * ((y + t) / t_1);
	tmp = 0.0;
	if (a <= -2.8e+152)
		tmp = t_2;
	elseif (a <= -9.5e-9)
		tmp = (a + z) - b;
	elseif (a <= 8.8e+38)
		tmp = z * ((y + x) / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+152], t$95$2, If[LessEqual[a, -9.5e-9], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, 8.8e+38], N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.8000000000000002e152 or 8.80000000000000026e38 < a

   1. Initial program 47.4%

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

   3. Taylor expanded in a around inf 37.1%

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

      1. associate-/l* 73.3%

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

      2. +-commutative 73.3%

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

      3. +-commutative 73.3%

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

      4. associate-+r+ 73.3%

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

   5. Simplified 73.3%

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

   if -2.8000000000000002e152 < a < -9.5000000000000007e-9

   1. Initial program 62.7%

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

   3. Taylor expanded in y around inf 70.4%

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

   if -9.5000000000000007e-9 < a < 8.80000000000000026e38

   1. Initial program 70.7%

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

   3. Taylor expanded in z around inf 40.6%

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

      1. associate-/l* 60.0%

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

      2. +-commutative 60.0%

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

      3. +-commutative 60.0%

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

      4. associate-+r+ 60.0%

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

   5. Simplified 60.0%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \frac{y + t}{\left(y + t\right) + x}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-9}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + t\right) + x}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{\left(y + t\right) + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-94} \lor \neg \left(y \leq 4 \cdot 10^{-63}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{t + x} + \frac{x \cdot z}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.5e-94) (not (<= y 4e-63)))
   (- (+ a z) b)
   (+ (/ (* a t) (+ t x)) (/ (* x z) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e-94) || !(y <= 4e-63)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.5d-94)) .or. (.not. (y <= 4d-63))) then
        tmp = (a + z) - b
    else
        tmp = ((a * t) / (t + x)) + ((x * z) / (t + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e-94) || !(y <= 4e-63)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.5e-94) or not (y <= 4e-63):
		tmp = (a + z) - b
	else:
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.5e-94) || !(y <= 4e-63))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(Float64(a * t) / Float64(t + x)) + Float64(Float64(x * z) / Float64(t + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.5e-94) || ~((y <= 4e-63)))
		tmp = (a + z) - b;
	else
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.5e-94], N[Not[LessEqual[y, 4e-63]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(a * t), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999989e-94 or 4.00000000000000027e-63 < y

   1. Initial program 52.1%

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

   3. Taylor expanded in y around inf 69.2%

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

   if -5.49999999999999989e-94 < y < 4.00000000000000027e-63

   1. Initial program 78.0%

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

   3. Taylor expanded in b around -inf 70.0%

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

      1. associate-*r* 70.0%

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

      2. neg-mul-1 70.0%

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

      3. fma-define 70.0%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in y around 0 63.0%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-94} \lor \neg \left(y \leq 4 \cdot 10^{-63}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{t + x} + \frac{x \cdot z}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-94} \lor \neg \left(y \leq 2.35 \cdot 10^{-63}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t + x \cdot z}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.5e-94) (not (<= y 2.35e-63)))
   (- (+ a z) b)
   (/ (+ (* a t) (* x z)) (+ t x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e-94) || !(y <= 2.35e-63)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((a * t) + (x * z)) / (t + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.5d-94)) .or. (.not. (y <= 2.35d-63))) then
        tmp = (a + z) - b
    else
        tmp = ((a * t) + (x * z)) / (t + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e-94) || !(y <= 2.35e-63)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((a * t) + (x * z)) / (t + x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.5e-94) or not (y <= 2.35e-63):
		tmp = (a + z) - b
	else:
		tmp = ((a * t) + (x * z)) / (t + x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.5e-94) || !(y <= 2.35e-63))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(Float64(a * t) + Float64(x * z)) / Float64(t + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.5e-94) || ~((y <= 2.35e-63)))
		tmp = (a + z) - b;
	else
		tmp = ((a * t) + (x * z)) / (t + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.5e-94], N[Not[LessEqual[y, 2.35e-63]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(a * t), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999989e-94 or 2.35e-63 < y

   1. Initial program 52.1%

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

   3. Taylor expanded in y around inf 69.2%

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

   if -5.49999999999999989e-94 < y < 2.35e-63

   1. Initial program 78.0%

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

   3. Taylor expanded in y around 0 62.9%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-94} \lor \neg \left(y \leq 2.35 \cdot 10^{-63}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t + x \cdot z}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+118} \lor \neg \left(x \leq 5.5 \cdot 10^{+216}\right):\\ \;\;\;\;z + \frac{a \cdot \left(y + t\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -2.6e+118) (not (<= x 5.5e+216)))
   (+ z (/ (* a (+ y t)) x))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.6e+118) || !(x <= 5.5e+216)) {
		tmp = z + ((a * (y + t)) / x);
	} else {
		tmp = (a + 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) :: tmp
    if ((x <= (-2.6d+118)) .or. (.not. (x <= 5.5d+216))) then
        tmp = z + ((a * (y + t)) / x)
    else
        tmp = (a + 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 tmp;
	if ((x <= -2.6e+118) || !(x <= 5.5e+216)) {
		tmp = z + ((a * (y + t)) / x);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.6e+118) or not (x <= 5.5e+216):
		tmp = z + ((a * (y + t)) / x)
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -2.6e+118) || !(x <= 5.5e+216))
		tmp = Float64(z + Float64(Float64(a * Float64(y + t)) / x));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -2.6e+118) || ~((x <= 5.5e+216)))
		tmp = z + ((a * (y + t)) / x);
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -2.6e+118], N[Not[LessEqual[x, 5.5e+216]], $MachinePrecision]], N[(z + N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000016e118 or 5.5e216 < x

   1. Initial program 52.9%

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

   3. Taylor expanded in a around -inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. distribute-rgt-neg-in 54.7%

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

      3. mul-1-neg 54.7%

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

      4. unsub-neg 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in x around inf 69.7%

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

   7. Taylor expanded in x around inf 68.0%

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

   if -2.60000000000000016e118 < x < 5.5e216

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 62.3%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+118} \lor \neg \left(x \leq 5.5 \cdot 10^{+216}\right):\\ \;\;\;\;z + \frac{a \cdot \left(y + t\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+67}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.4e+67) a (if (<= a 3.6e+37) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.4e+67) {
		tmp = a;
	} else if (a <= 3.6e+37) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.4d+67)) then
        tmp = a
    else if (a <= 3.6d+37) then
        tmp = z - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.4e+67) {
		tmp = a;
	} else if (a <= 3.6e+37) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.4e+67:
		tmp = a
	elif a <= 3.6e+37:
		tmp = z - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.4e+67)
		tmp = a;
	elseif (a <= 3.6e+37)
		tmp = Float64(z - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.4e+67)
		tmp = a;
	elseif (a <= 3.6e+37)
		tmp = z - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.4e+67], a, If[LessEqual[a, 3.6e+37], N[(z - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3999999999999999e67 or 3.59999999999999998e37 < a

   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 t around inf 57.0%

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

   if -1.3999999999999999e67 < a < 3.59999999999999998e37

   1. Initial program 69.0%

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

   3. Taylor expanded in a around 0 53.9%

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

      1. +-commutative 53.9%

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

      2. *-commutative 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in y around inf 50.5%

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

Alternative 11: 44.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9600:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+37}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -9600.0) a (if (<= a 2.8e+37) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9600.0) {
		tmp = a;
	} else if (a <= 2.8e+37) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-9600.0d0)) then
        tmp = a
    else if (a <= 2.8d+37) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9600.0) {
		tmp = a;
	} else if (a <= 2.8e+37) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -9600.0:
		tmp = a
	elif a <= 2.8e+37:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -9600.0)
		tmp = a;
	elseif (a <= 2.8e+37)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -9600.0)
		tmp = a;
	elseif (a <= 2.8e+37)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -9600.0], a, If[LessEqual[a, 2.8e+37], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -9600 or 2.7999999999999998e37 < a

   1. Initial program 51.6%

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

   3. Taylor expanded in t around inf 53.4%

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

   if -9600 < a < 2.7999999999999998e37

   1. Initial program 70.4%

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

   3. Taylor expanded in x around inf 47.2%

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

Alternative 12: 56.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+120}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.45e+120) z (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.45e+120) {
		tmp = z;
	} else {
		tmp = (a + 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) :: tmp
    if (x <= (-1.45d+120)) then
        tmp = z
    else
        tmp = (a + 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 tmp;
	if (x <= -1.45e+120) {
		tmp = z;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.45e+120:
		tmp = z
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.45e+120)
		tmp = z;
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.45e+120)
		tmp = z;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.45e+120], z, N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4500000000000001e120

   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 x around inf 48.4%

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

   if -1.4500000000000001e120 < x

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf 61.0%

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

Alternative 13: 32.3% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.7%

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

3. Taylor expanded in t around inf 32.0%

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

Developer Target 1: 82.6% 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 2024180 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ 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)))