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

Percentage Accurate: 60.7% → 86.1%

Time: 14.3s

Alternatives: 16

Speedup: 0.9×

• could not determine a ground truth

  1. x = -6.933150213183077e-14
  2. y = 3.785473524454049e+215
  3. z = 0.10255975672321423
  4. t = -1.1603524428869345e-85
  5. a = -0.0005447939259379322
  6. b = 1.4888561776064808e-254

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: 60.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := \left(y + t\right) \cdot a\\ t_3 := \frac{\left(t\_2 + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+281}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_2\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} + \mathsf{fma}\left(z, \frac{\frac{x + y}{a}}{t\_1}, \frac{y}{t\_1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t))
        (t_2 (* (+ y t) a))
        (t_3 (/ (- (+ t_2 (* (+ x y) z)) (* y b)) (+ y (+ x t)))))
   (if (<= t_3 -5e+281)
     (- (+ z a) b)
     (if (<= t_3 5e+292)
       (/ (- (fma (+ x y) z t_2) (* y b)) (+ x (+ y t)))
       (* a (+ (/ t t_1) (fma z (/ (/ (+ x y) a) t_1) (/ y t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = (y + t) * a;
	double t_3 = ((t_2 + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_3 <= -5e+281) {
		tmp = (z + a) - b;
	} else if (t_3 <= 5e+292) {
		tmp = (fma((x + y), z, t_2) - (y * b)) / (x + (y + t));
	} else {
		tmp = a * ((t / t_1) + fma(z, (((x + y) / a) / t_1), (y / t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(Float64(y + t) * a)
	t_3 = Float64(Float64(Float64(t_2 + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (t_3 <= -5e+281)
		tmp = Float64(Float64(z + a) - b);
	elseif (t_3 <= 5e+292)
		tmp = Float64(Float64(fma(Float64(x + y), z, t_2) - Float64(y * b)) / Float64(x + Float64(y + t)));
	else
		tmp = Float64(a * Float64(Float64(t / t_1) + fma(z, Float64(Float64(Float64(x + y) / a) / t_1), Float64(y / t_1))));
	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[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+281], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$3, 5e+292], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(z * N[(N[(N[(x + y), $MachinePrecision] / a), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $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)) < -5.00000000000000016e281

   1. Initial program 10.0%

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

   3. Taylor expanded in y around inf 63.9%

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

   if -5.00000000000000016e281 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999996e292

   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. Step-by-step derivation

      1. fma-define 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   if 4.9999999999999996e292 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.3%

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

   3. Taylor expanded in a around inf 33.3%

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

      1. associate--l+ 33.3%

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

      2. associate-+r+ 33.3%

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

      3. +-commutative 33.3%

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

      4. associate-/l* 50.5%

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

      5. fma-define 50.5%

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

      6. +-commutative 50.5%

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

      7. associate-+r+ 50.5%

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

      8. associate-+r+ 50.5%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in b around 0 35.5%

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

      1. +-commutative 35.5%

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

      2. associate-/l* 54.3%

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

      3. associate-/r* 68.7%

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

      4. +-commutative 68.7%

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

      5. associate-+r+ 68.7%

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

      6. +-commutative 68.7%

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

      7. +-commutative 68.7%

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

      8. fma-undefine 68.7%

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

      9. +-commutative 68.7%

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

      10. +-commutative 68.7%

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

      11. +-commutative 68.7%

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

      12. associate-+r+ 68.7%

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

   8. Simplified 68.7%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+281}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, \left(y + t\right) \cdot a\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{\left(x + y\right) + t} + \mathsf{fma}\left(z, \frac{\frac{x + y}{a}}{\left(x + y\right) + t}, \frac{y}{\left(x + y\right) + t}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) \cdot a\\ t_2 := \frac{\left(t\_1 + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+281} \lor \neg \left(t\_2 \leq 10^{+277}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_1\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y t) a))
        (t_2 (/ (- (+ t_1 (* (+ x y) z)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_2 -5e+281) (not (<= t_2 1e+277)))
     (- (+ z a) b)
     (/ (- (fma (+ x y) z t_1) (* y b)) (+ x (+ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * a;
	double t_2 = ((t_1 + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -5e+281) || !(t_2 <= 1e+277)) {
		tmp = (z + a) - b;
	} else {
		tmp = (fma((x + y), z, t_1) - (y * b)) / (x + (y + t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) * a)
	t_2 = Float64(Float64(Float64(t_1 + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_2 <= -5e+281) || !(t_2 <= 1e+277))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(fma(Float64(x + y), z, t_1) - Float64(y * b)) / Float64(x + Float64(y + t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+281], N[Not[LessEqual[t$95$2, 1e+277]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.00000000000000016e281 or 1e277 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.7%

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

   3. Taylor expanded in y around inf 63.2%

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

   if -5.00000000000000016e281 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e277

   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. Step-by-step derivation

      1. fma-define 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+281} \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+277}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, \left(y + t\right) \cdot a\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+281} \lor \neg \left(t\_1 \leq 10^{+277}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* (+ x y) z)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 -5e+281) (not (<= t_1 1e+277))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -5e+281) || !(t_1 <= 1e+277)) {
		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 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t))
    if ((t_1 <= (-5d+281)) .or. (.not. (t_1 <= 1d+277))) 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 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -5e+281) || !(t_1 <= 1e+277)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -5e+281) or not (t_1 <= 1e+277):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -5e+281) || !(t_1 <= 1e+277))
		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 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -5e+281) || ~((t_1 <= 1e+277)))
		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[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+281], N[Not[LessEqual[t$95$1, 1e+277]], $MachinePrecision]], N[(N[(z + a), $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)) < -5.00000000000000016e281 or 1e277 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.7%

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

   3. Taylor expanded in y around inf 63.2%

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

   if -5.00000000000000016e281 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e277

   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 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+281} \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+277}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) \cdot z\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{-41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + x \cdot \frac{\frac{z}{a}}{x + t}\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + t\_1}{\left(x + y\right) + t}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+137}:\\ \;\;\;\;\frac{t\_1 + y \cdot a}{x + y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ x y) z)) (t_2 (- (+ z a) b)))
   (if (<= y -8.8e-41)
     t_2
     (if (<= y 1.9e-306)
       (* a (+ (/ t (+ x t)) (* x (/ (/ z a) (+ x t)))))
       (if (<= y 1.35e+17)
         (/ (+ (* (+ y t) a) t_1) (+ (+ x y) t))
         (if (<= y 1.45e+99)
           (* a (+ (/ z a) (/ y (+ x y))))
           (if (<= y 6.2e+137) (/ (+ t_1 (* y a)) (+ x y)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) * z;
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -8.8e-41) {
		tmp = t_2;
	} else if (y <= 1.9e-306) {
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))));
	} else if (y <= 1.35e+17) {
		tmp = (((y + t) * a) + t_1) / ((x + y) + t);
	} else if (y <= 1.45e+99) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else if (y <= 6.2e+137) {
		tmp = (t_1 + (y * a)) / (x + y);
	} 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 = (x + y) * z
    t_2 = (z + a) - b
    if (y <= (-8.8d-41)) then
        tmp = t_2
    else if (y <= 1.9d-306) then
        tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))))
    else if (y <= 1.35d+17) then
        tmp = (((y + t) * a) + t_1) / ((x + y) + t)
    else if (y <= 1.45d+99) then
        tmp = a * ((z / a) + (y / (x + y)))
    else if (y <= 6.2d+137) then
        tmp = (t_1 + (y * a)) / (x + y)
    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 = (x + y) * z;
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -8.8e-41) {
		tmp = t_2;
	} else if (y <= 1.9e-306) {
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))));
	} else if (y <= 1.35e+17) {
		tmp = (((y + t) * a) + t_1) / ((x + y) + t);
	} else if (y <= 1.45e+99) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else if (y <= 6.2e+137) {
		tmp = (t_1 + (y * a)) / (x + y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) * z
	t_2 = (z + a) - b
	tmp = 0
	if y <= -8.8e-41:
		tmp = t_2
	elif y <= 1.9e-306:
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))))
	elif y <= 1.35e+17:
		tmp = (((y + t) * a) + t_1) / ((x + y) + t)
	elif y <= 1.45e+99:
		tmp = a * ((z / a) + (y / (x + y)))
	elif y <= 6.2e+137:
		tmp = (t_1 + (y * a)) / (x + y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) * z)
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -8.8e-41)
		tmp = t_2;
	elseif (y <= 1.9e-306)
		tmp = Float64(a * Float64(Float64(t / Float64(x + t)) + Float64(x * Float64(Float64(z / a) / Float64(x + t)))));
	elseif (y <= 1.35e+17)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) + t_1) / Float64(Float64(x + y) + t));
	elseif (y <= 1.45e+99)
		tmp = Float64(a * Float64(Float64(z / a) + Float64(y / Float64(x + y))));
	elseif (y <= 6.2e+137)
		tmp = Float64(Float64(t_1 + Float64(y * a)) / Float64(x + y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) * z;
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -8.8e-41)
		tmp = t_2;
	elseif (y <= 1.9e-306)
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))));
	elseif (y <= 1.35e+17)
		tmp = (((y + t) * a) + t_1) / ((x + y) + t);
	elseif (y <= 1.45e+99)
		tmp = a * ((z / a) + (y / (x + y)));
	elseif (y <= 6.2e+137)
		tmp = (t_1 + (y * a)) / (x + y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -8.8e-41], t$95$2, If[LessEqual[y, 1.9e-306], N[(a * N[(N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(z / a), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+17], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+99], N[(a * N[(N[(z / a), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+137], N[(N[(t$95$1 + N[(y * a), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.7999999999999999e-41 or 6.1999999999999999e137 < y

   1. Initial program 46.3%

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

   3. Taylor expanded in y around inf 72.5%

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

   if -8.7999999999999999e-41 < y < 1.9e-306

   1. Initial program 68.4%

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

   3. Taylor expanded in a around inf 82.9%

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

      1. associate--l+ 82.9%

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

      2. associate-+r+ 82.9%

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

      3. +-commutative 82.9%

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

      4. associate-/l* 89.7%

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

      5. fma-define 89.7%

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

      6. +-commutative 89.7%

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

      7. associate-+r+ 89.7%

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

      8. associate-+r+ 89.7%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in y around 0 71.0%

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

      1. +-commutative 71.0%

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

      2. associate-/l* 75.8%

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

      3. associate-/r* 82.0%

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

      4. +-commutative 82.0%

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

   8. Simplified 82.0%

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

   if 1.9e-306 < y < 1.35e17

   1. Initial program 88.7%

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

   3. Taylor expanded in b around 0 75.5%

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

   if 1.35e17 < y < 1.4500000000000001e99

   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 a around inf 69.0%

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

      1. associate--l+ 69.0%

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

      2. associate-+r+ 69.0%

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

      3. +-commutative 69.0%

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

      4. associate-/l* 79.0%

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

      5. fma-define 79.0%

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

      6. +-commutative 79.0%

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

      7. associate-+r+ 79.0%

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

      8. associate-+r+ 79.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in b around 0 48.8%

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

      1. +-commutative 48.8%

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

      2. associate-/l* 58.8%

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

      3. associate-/r* 59.0%

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

      4. +-commutative 59.0%

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

      5. associate-+r+ 59.0%

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

      6. +-commutative 59.0%

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

      7. +-commutative 59.0%

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

      8. fma-undefine 59.0%

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

      9. +-commutative 59.0%

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

      10. +-commutative 59.0%

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

      11. +-commutative 59.0%

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

      12. associate-+r+ 59.0%

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

   8. Simplified 59.0%

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

   9. Taylor expanded in t around 0 64.5%

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

       1. +-commutative 64.5%

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

   11. Simplified 64.5%

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

   if 1.4500000000000001e99 < y < 6.1999999999999999e137

   1. Initial program 87.3%

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

   3. Taylor expanded in b around 0 75.0%

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

   4. Taylor expanded in t around 0 75.0%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-41}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + x \cdot \frac{\frac{z}{a}}{x + t}\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + \left(x + y\right) \cdot z}{\left(x + y\right) + t}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+137}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + y \cdot a}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+43}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ (+ x y) (+ (+ x y) t)))))
   (if (<= x -3.1e+193)
     t_1
     (if (<= x -1.26e+116)
       (* a (/ (+ y t) (+ y (+ x t))))
       (if (<= x -7.5e+80)
         t_1
         (if (<= x 4.6e+43) (- (+ z a) b) (* a (+ (/ z a) (/ y (+ x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / ((x + y) + t));
	double tmp;
	if (x <= -3.1e+193) {
		tmp = t_1;
	} else if (x <= -1.26e+116) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (x <= -7.5e+80) {
		tmp = t_1;
	} else if (x <= 4.6e+43) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((z / a) + (y / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x + y) / ((x + y) + t))
    if (x <= (-3.1d+193)) then
        tmp = t_1
    else if (x <= (-1.26d+116)) then
        tmp = a * ((y + t) / (y + (x + t)))
    else if (x <= (-7.5d+80)) then
        tmp = t_1
    else if (x <= 4.6d+43) then
        tmp = (z + a) - b
    else
        tmp = a * ((z / a) + (y / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / ((x + y) + t));
	double tmp;
	if (x <= -3.1e+193) {
		tmp = t_1;
	} else if (x <= -1.26e+116) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (x <= -7.5e+80) {
		tmp = t_1;
	} else if (x <= 4.6e+43) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((z / a) + (y / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * ((x + y) / ((x + y) + t))
	tmp = 0
	if x <= -3.1e+193:
		tmp = t_1
	elif x <= -1.26e+116:
		tmp = a * ((y + t) / (y + (x + t)))
	elif x <= -7.5e+80:
		tmp = t_1
	elif x <= 4.6e+43:
		tmp = (z + a) - b
	else:
		tmp = a * ((z / a) + (y / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(Float64(x + y) / Float64(Float64(x + y) + t)))
	tmp = 0.0
	if (x <= -3.1e+193)
		tmp = t_1;
	elseif (x <= -1.26e+116)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	elseif (x <= -7.5e+80)
		tmp = t_1;
	elseif (x <= 4.6e+43)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(Float64(z / a) + Float64(y / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * ((x + y) / ((x + y) + t));
	tmp = 0.0;
	if (x <= -3.1e+193)
		tmp = t_1;
	elseif (x <= -1.26e+116)
		tmp = a * ((y + t) / (y + (x + t)));
	elseif (x <= -7.5e+80)
		tmp = t_1;
	elseif (x <= 4.6e+43)
		tmp = (z + a) - b;
	else
		tmp = a * ((z / a) + (y / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(N[(x + y), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.1e+193], t$95$1, If[LessEqual[x, -1.26e+116], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e+80], t$95$1, If[LessEqual[x, 4.6e+43], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(N[(z / a), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.09999999999999986e193 or -1.2599999999999999e116 < x < -7.49999999999999994e80

   1. Initial program 59.2%

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

   3. Taylor expanded in z around inf 43.0%

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

      1. associate-/l* 75.2%

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

      2. +-commutative 75.2%

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

      3. +-commutative 75.2%

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

   5. Simplified 75.2%

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

   if -3.09999999999999986e193 < x < -1.2599999999999999e116

   1. Initial program 58.0%

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

   3. Taylor expanded in a around inf 47.3%

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

      1. associate-/l* 78.7%

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

      2. associate-+r+ 78.7%

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

   5. Simplified 78.7%

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

   if -7.49999999999999994e80 < x < 4.6000000000000005e43

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 64.1%

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

   if 4.6000000000000005e43 < x

   1. Initial program 49.8%

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

   3. Taylor expanded in a around inf 52.2%

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

      1. associate--l+ 52.2%

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

      2. associate-+r+ 52.2%

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

      3. +-commutative 52.2%

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

      4. associate-/l* 67.0%

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

      5. fma-define 67.0%

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

      6. +-commutative 67.0%

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

      7. associate-+r+ 67.0%

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

      8. associate-+r+ 67.0%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in b around 0 44.1%

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

      1. +-commutative 44.1%

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

      2. associate-/l* 59.0%

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

      3. associate-/r* 57.4%

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

      4. +-commutative 57.4%

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

      5. associate-+r+ 57.4%

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

      6. +-commutative 57.4%

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

      7. +-commutative 57.4%

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

      8. fma-undefine 57.3%

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

      9. +-commutative 57.3%

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

      10. +-commutative 57.3%

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

      11. +-commutative 57.3%

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

      12. associate-+r+ 57.3%

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

   8. Simplified 57.3%

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

   9. Taylor expanded in t around 0 60.2%

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

       1. +-commutative 60.2%

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

   11. Simplified 60.2%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+193}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+43}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \frac{t + x \cdot \frac{z}{a}}{x + t}\\ \mathbf{elif}\;y \leq 2150000000000:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + y \cdot z}{y + t}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.05e-58)
     t_1
     (if (<= y 3.4e-124)
       (* a (/ (+ t (* x (/ z a))) (+ x t)))
       (if (<= y 2150000000000.0)
         (/ (+ (* (+ y t) a) (* y z)) (+ y t))
         (if (<= y 1.36e+80) (* a (+ (/ z a) (/ y (+ x y)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.05e-58) {
		tmp = t_1;
	} else if (y <= 3.4e-124) {
		tmp = a * ((t + (x * (z / a))) / (x + t));
	} else if (y <= 2150000000000.0) {
		tmp = (((y + t) * a) + (y * z)) / (y + t);
	} else if (y <= 1.36e+80) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.05d-58)) then
        tmp = t_1
    else if (y <= 3.4d-124) then
        tmp = a * ((t + (x * (z / a))) / (x + t))
    else if (y <= 2150000000000.0d0) then
        tmp = (((y + t) * a) + (y * z)) / (y + t)
    else if (y <= 1.36d+80) then
        tmp = a * ((z / a) + (y / (x + y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.05e-58) {
		tmp = t_1;
	} else if (y <= 3.4e-124) {
		tmp = a * ((t + (x * (z / a))) / (x + t));
	} else if (y <= 2150000000000.0) {
		tmp = (((y + t) * a) + (y * z)) / (y + t);
	} else if (y <= 1.36e+80) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.05e-58:
		tmp = t_1
	elif y <= 3.4e-124:
		tmp = a * ((t + (x * (z / a))) / (x + t))
	elif y <= 2150000000000.0:
		tmp = (((y + t) * a) + (y * z)) / (y + t)
	elif y <= 1.36e+80:
		tmp = a * ((z / a) + (y / (x + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.05e-58)
		tmp = t_1;
	elseif (y <= 3.4e-124)
		tmp = Float64(a * Float64(Float64(t + Float64(x * Float64(z / a))) / Float64(x + t)));
	elseif (y <= 2150000000000.0)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) + Float64(y * z)) / Float64(y + t));
	elseif (y <= 1.36e+80)
		tmp = Float64(a * Float64(Float64(z / a) + Float64(y / Float64(x + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.05e-58)
		tmp = t_1;
	elseif (y <= 3.4e-124)
		tmp = a * ((t + (x * (z / a))) / (x + t));
	elseif (y <= 2150000000000.0)
		tmp = (((y + t) * a) + (y * z)) / (y + t);
	elseif (y <= 1.36e+80)
		tmp = a * ((z / a) + (y / (x + y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.05e-58], t$95$1, If[LessEqual[y, 3.4e-124], N[(a * N[(N[(t + N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2150000000000.0], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.36e+80], N[(a * N[(N[(z / a), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.05000000000000014e-58 or 1.36000000000000013e80 < y

   1. Initial program 50.1%

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

   3. Taylor expanded in y around inf 70.8%

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

   if -2.05000000000000014e-58 < y < 3.4000000000000001e-124

   1. Initial program 75.9%

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

   3. Taylor expanded in a around inf 70.1%

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

   4. Taylor expanded in y around 0 58.0%

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

      1. associate-/l* 71.5%

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

      2. associate-/l* 76.2%

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

      3. +-commutative 76.2%

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

   6. Simplified 76.2%

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

   if 3.4000000000000001e-124 < y < 2.15e12

   1. Initial program 89.9%

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

   3. Taylor expanded in b around 0 68.0%

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

   4. Taylor expanded in x around 0 57.6%

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

   if 2.15e12 < y < 1.36000000000000013e80

   1. Initial program 73.2%

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

   3. Taylor expanded in a around inf 72.5%

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

      1. associate--l+ 72.5%

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

      2. associate-+r+ 72.5%

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

      3. +-commutative 72.5%

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

      4. associate-/l* 78.0%

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

      5. fma-define 78.0%

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

      6. +-commutative 78.0%

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

      7. associate-+r+ 78.0%

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

      8. associate-+r+ 78.0%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in b around 0 51.2%

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

      1. +-commutative 51.2%

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

      2. associate-/l* 56.6%

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

      3. associate-/r* 67.5%

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

      4. +-commutative 67.5%

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

      5. associate-+r+ 67.5%

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

      6. +-commutative 67.5%

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

      7. +-commutative 67.5%

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

      8. fma-undefine 67.5%

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

      9. +-commutative 67.5%

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

      10. +-commutative 67.5%

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

      11. +-commutative 67.5%

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

      12. associate-+r+ 67.5%

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

   8. Simplified 67.5%

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

   9. Taylor expanded in t around 0 57.2%

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

       1. +-commutative 57.2%

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

   11. Simplified 57.2%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-58}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \frac{t + x \cdot \frac{z}{a}}{x + t}\\ \mathbf{elif}\;y \leq 2150000000000:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + y \cdot z}{y + t}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + x \cdot \frac{\frac{z}{a}}{x + t}\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.25e-40)
     t_1
     (if (<= y 3.1e-124)
       (* a (+ (/ t (+ x t)) (* x (/ (/ z a) (+ x t)))))
       (if (<= y 3.2e+100) (* a (+ (/ z a) (/ y (+ x y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.25e-40) {
		tmp = t_1;
	} else if (y <= 3.1e-124) {
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))));
	} else if (y <= 3.2e+100) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.25d-40)) then
        tmp = t_1
    else if (y <= 3.1d-124) then
        tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))))
    else if (y <= 3.2d+100) then
        tmp = a * ((z / a) + (y / (x + y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.25e-40) {
		tmp = t_1;
	} else if (y <= 3.1e-124) {
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))));
	} else if (y <= 3.2e+100) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.25e-40:
		tmp = t_1
	elif y <= 3.1e-124:
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))))
	elif y <= 3.2e+100:
		tmp = a * ((z / a) + (y / (x + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.25e-40)
		tmp = t_1;
	elseif (y <= 3.1e-124)
		tmp = Float64(a * Float64(Float64(t / Float64(x + t)) + Float64(x * Float64(Float64(z / a) / Float64(x + t)))));
	elseif (y <= 3.2e+100)
		tmp = Float64(a * Float64(Float64(z / a) + Float64(y / Float64(x + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.25e-40)
		tmp = t_1;
	elseif (y <= 3.1e-124)
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))));
	elseif (y <= 3.2e+100)
		tmp = a * ((z / a) + (y / (x + y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.25e-40], t$95$1, If[LessEqual[y, 3.1e-124], N[(a * N[(N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(z / a), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+100], N[(a * N[(N[(z / a), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.24999999999999991e-40 or 3.1999999999999999e100 < y

   1. Initial program 48.6%

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

   3. Taylor expanded in y around inf 71.6%

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

   if -1.24999999999999991e-40 < y < 3.0999999999999998e-124

   1. Initial program 76.7%

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

   3. Taylor expanded in a around inf 84.7%

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

      1. associate--l+ 84.7%

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

      2. associate-+r+ 84.7%

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

      3. +-commutative 84.7%

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

      4. associate-/l* 90.7%

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

      5. fma-define 90.7%

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

      6. +-commutative 90.7%

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

      7. associate-+r+ 90.7%

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

      8. associate-+r+ 90.7%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in y around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 75.8%

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

      3. associate-/r* 79.2%

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

      4. +-commutative 79.2%

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

   8. Simplified 79.2%

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

   if 3.0999999999999998e-124 < y < 3.1999999999999999e100

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 74.1%

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

      1. associate--l+ 74.1%

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

      2. associate-+r+ 74.1%

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

      3. +-commutative 74.1%

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

      4. associate-/l* 78.1%

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

      5. fma-define 78.1%

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

      6. +-commutative 78.1%

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

      7. associate-+r+ 78.1%

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

      8. associate-+r+ 78.1%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in b around 0 57.9%

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

      1. +-commutative 57.9%

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

      2. associate-/l* 61.8%

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

      3. associate-/r* 68.0%

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

      4. +-commutative 68.0%

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

      5. associate-+r+ 68.0%

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

      6. +-commutative 68.0%

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

      7. +-commutative 68.0%

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

      8. fma-undefine 68.0%

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

      9. +-commutative 68.0%

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

      10. +-commutative 68.0%

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

      11. +-commutative 68.0%

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

      12. associate-+r+ 68.0%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in t around 0 55.5%

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

       1. +-commutative 55.5%

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

   11. Simplified 55.5%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + x \cdot \frac{\frac{z}{a}}{x + t}\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-131}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.05e-94)
     t_1
     (if (<= y 2.9e-131)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 2.1e+100) (* a (+ (/ z a) (/ y (+ x y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.05e-94) {
		tmp = t_1;
	} else if (y <= 2.9e-131) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 2.1e+100) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.05d-94)) then
        tmp = t_1
    else if (y <= 2.9d-131) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 2.1d+100) then
        tmp = a * ((z / a) + (y / (x + y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.05e-94) {
		tmp = t_1;
	} else if (y <= 2.9e-131) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 2.1e+100) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.05e-94:
		tmp = t_1
	elif y <= 2.9e-131:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 2.1e+100:
		tmp = a * ((z / a) + (y / (x + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.05e-94)
		tmp = t_1;
	elseif (y <= 2.9e-131)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 2.1e+100)
		tmp = Float64(a * Float64(Float64(z / a) + Float64(y / Float64(x + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.05e-94)
		tmp = t_1;
	elseif (y <= 2.9e-131)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 2.1e+100)
		tmp = a * ((z / a) + (y / (x + y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.05e-94], t$95$1, If[LessEqual[y, 2.9e-131], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+100], N[(a * N[(N[(z / a), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e-94 or 2.0999999999999999e100 < y

   1. Initial program 49.6%

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

   3. Taylor expanded in y around inf 70.0%

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

   if -2.05e-94 < y < 2.9000000000000002e-131

   1. Initial program 79.9%

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

   3. Taylor expanded in y around 0 67.9%

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

   if 2.9000000000000002e-131 < y < 2.0999999999999999e100

   1. Initial program 78.4%

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

   3. Taylor expanded in a around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. associate-+r+ 73.3%

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

      3. +-commutative 73.3%

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

      4. associate-/l* 78.9%

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

      5. fma-define 78.9%

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

      6. +-commutative 78.9%

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

      7. associate-+r+ 78.9%

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

      8. associate-+r+ 78.9%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in b around 0 57.7%

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

      1. +-commutative 57.7%

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

      2. associate-/l* 63.3%

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

      3. associate-/r* 67.4%

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

      4. +-commutative 67.4%

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

      5. associate-+r+ 67.4%

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

      6. +-commutative 67.4%

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

      7. +-commutative 67.4%

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

      8. fma-undefine 67.4%

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

      9. +-commutative 67.4%

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

      10. +-commutative 67.4%

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

      11. +-commutative 67.4%

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

      12. associate-+r+ 67.4%

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

   8. Simplified 67.4%

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

   9. Taylor expanded in t around 0 55.3%

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

       1. +-commutative 55.3%

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

   11. Simplified 55.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-94}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-131}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-58} \lor \neg \left(y \leq 2.3 \cdot 10^{+34}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + x \cdot \frac{z}{a}}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.4e-58) (not (<= y 2.3e+34)))
   (- (+ z a) b)
   (* a (/ (+ t (* x (/ z a))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4e-58) || !(y <= 2.3e+34)) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((t + (x * (z / a))) / (x + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.4d-58)) .or. (.not. (y <= 2.3d+34))) then
        tmp = (z + a) - b
    else
        tmp = a * ((t + (x * (z / a))) / (x + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4e-58) || !(y <= 2.3e+34)) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((t + (x * (z / a))) / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.4e-58) or not (y <= 2.3e+34):
		tmp = (z + a) - b
	else:
		tmp = a * ((t + (x * (z / a))) / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.4e-58) || !(y <= 2.3e+34))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(Float64(t + Float64(x * Float64(z / a))) / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.4e-58) || ~((y <= 2.3e+34)))
		tmp = (z + a) - b;
	else
		tmp = a * ((t + (x * (z / a))) / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.4e-58], N[Not[LessEqual[y, 2.3e+34]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(N[(t + N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e-58 or 2.2999999999999998e34 < y

   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 y around inf 68.6%

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

   if -1.4e-58 < y < 2.2999999999999998e34

   1. Initial program 80.1%

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

   3. Taylor expanded in a around inf 74.5%

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

   4. Taylor expanded in y around 0 53.7%

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

      1. associate-/l* 63.0%

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

      2. associate-/l* 67.9%

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

      3. +-commutative 67.9%

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

   6. Simplified 67.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-58} \lor \neg \left(y \leq 2.3 \cdot 10^{+34}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + x \cdot \frac{z}{a}}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 7800000000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.2e+54)
   (* a (/ (+ y t) (+ y (+ x t))))
   (if (<= a 7800000000000.0) (- (+ z a) b) (* a (+ (/ z a) (/ y (+ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.2e+54) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (a <= 7800000000000.0) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((z / a) + (y / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4.2d+54)) then
        tmp = a * ((y + t) / (y + (x + t)))
    else if (a <= 7800000000000.0d0) then
        tmp = (z + a) - b
    else
        tmp = a * ((z / a) + (y / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.2e+54) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (a <= 7800000000000.0) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((z / a) + (y / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.2e+54:
		tmp = a * ((y + t) / (y + (x + t)))
	elif a <= 7800000000000.0:
		tmp = (z + a) - b
	else:
		tmp = a * ((z / a) + (y / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.2e+54)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	elseif (a <= 7800000000000.0)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(Float64(z / a) + Float64(y / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.2e+54)
		tmp = a * ((y + t) / (y + (x + t)));
	elseif (a <= 7800000000000.0)
		tmp = (z + a) - b;
	else
		tmp = a * ((z / a) + (y / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.2e+54], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7800000000000.0], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(N[(z / a), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.19999999999999972e54

   1. Initial program 49.1%

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

   3. Taylor expanded in a around inf 44.9%

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

      1. associate-/l* 75.7%

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

      2. associate-+r+ 75.7%

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

   5. Simplified 75.7%

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

   if -4.19999999999999972e54 < a < 7.8e12

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf 53.4%

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

   if 7.8e12 < a

   1. Initial program 57.5%

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

   3. Taylor expanded in a around inf 77.2%

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

      1. associate--l+ 77.2%

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

      2. associate-+r+ 77.2%

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

      3. +-commutative 77.2%

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

      4. associate-/l* 80.6%

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

      5. fma-define 80.6%

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

      6. +-commutative 80.6%

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

      7. associate-+r+ 80.6%

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

      8. associate-+r+ 80.6%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in b around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-/l* 80.3%

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

      3. associate-/r* 90.0%

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

      4. +-commutative 90.0%

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

      5. associate-+r+ 90.0%

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

      6. +-commutative 90.0%

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

      7. +-commutative 90.0%

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

      8. fma-undefine 90.0%

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

      9. +-commutative 90.0%

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

      10. +-commutative 90.0%

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

      11. +-commutative 90.0%

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

      12. associate-+r+ 90.0%

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

   8. Simplified 90.0%

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

   9. Taylor expanded in t around 0 66.6%

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

       1. +-commutative 66.6%

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

   11. Simplified 66.6%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 7800000000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+81}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-236} \lor \neg \left(x \leq -2.7 \cdot 10^{-275}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.4e+81)
   z
   (if (or (<= x -1.6e-236) (not (<= x -2.7e-275))) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.4e+81) {
		tmp = z;
	} else if ((x <= -1.6e-236) || !(x <= -2.7e-275)) {
		tmp = (z + a) - 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 (x <= (-1.4d+81)) then
        tmp = z
    else if ((x <= (-1.6d-236)) .or. (.not. (x <= (-2.7d-275)))) then
        tmp = (z + a) - 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 (x <= -1.4e+81) {
		tmp = z;
	} else if ((x <= -1.6e-236) || !(x <= -2.7e-275)) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.4e+81:
		tmp = z
	elif (x <= -1.6e-236) or not (x <= -2.7e-275):
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.4e+81)
		tmp = z;
	elseif ((x <= -1.6e-236) || !(x <= -2.7e-275))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.4e+81)
		tmp = z;
	elseif ((x <= -1.6e-236) || ~((x <= -2.7e-275)))
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.4e+81], z, If[Or[LessEqual[x, -1.6e-236], N[Not[LessEqual[x, -2.7e-275]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if x < -1.39999999999999997e81

   1. Initial program 58.9%

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

   3. Taylor expanded in x around inf 53.6%

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

   if -1.39999999999999997e81 < x < -1.6e-236 or -2.69999999999999993e-275 < x

   1. Initial program 64.3%

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

   3. Taylor expanded in y around inf 59.8%

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

   if -1.6e-236 < x < -2.69999999999999993e-275

   1. Initial program 85.1%

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

   3. Taylor expanded in t around inf 92.3%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+81}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-236} \lor \neg \left(x \leq -2.7 \cdot 10^{-275}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.18 \cdot 10^{+107} \lor \neg \left(b \leq 2.2 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot \frac{b}{\left(\left(-x\right) - t\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.18e+107) (not (<= b 2.2e+77)))
   (* y (/ b (- (- (- x) t) y)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.18e+107) || !(b <= 2.2e+77)) {
		tmp = y * (b / ((-x - t) - y));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.18d+107)) .or. (.not. (b <= 2.2d+77))) then
        tmp = y * (b / ((-x - t) - y))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.18e+107) || !(b <= 2.2e+77)) {
		tmp = y * (b / ((-x - t) - y));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.18e+107) or not (b <= 2.2e+77):
		tmp = y * (b / ((-x - t) - y))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.18e+107) || !(b <= 2.2e+77))
		tmp = Float64(y * Float64(b / Float64(Float64(Float64(-x) - t) - y)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.18e+107) || ~((b <= 2.2e+77)))
		tmp = y * (b / ((-x - t) - y));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.18e+107], N[Not[LessEqual[b, 2.2e+77]], $MachinePrecision]], N[(y * N[(b / N[(N[((-x) - t), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.18000000000000005e107 or 2.2e77 < b

   1. Initial program 51.3%

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

   3. Taylor expanded in b around inf 30.3%

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

      1. associate-*r* 30.3%

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

      2. neg-mul-1 30.3%

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

      3. *-commutative 30.3%

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

   5. Simplified 30.3%

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

      1. associate-/l* 53.5%

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

      2. +-commutative 53.5%

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

      3. +-commutative 53.5%

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

      4. +-commutative 53.5%

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

   7. Applied egg-rr 53.5%

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

   if -1.18000000000000005e107 < b < 2.2e77

   1. Initial program 71.0%

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

   3. Taylor expanded in y around inf 62.8%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.18 \cdot 10^{+107} \lor \neg \left(b \leq 2.2 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot \frac{b}{\left(\left(-x\right) - t\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 126000000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 126000000000.0) (- (+ z a) b) (* a (+ (/ z a) (/ y (+ x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 126000000000.0) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((z / a) + (y / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 126000000000.0d0) then
        tmp = (z + a) - b
    else
        tmp = a * ((z / a) + (y / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 126000000000.0) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((z / a) + (y / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 126000000000.0:
		tmp = (z + a) - b
	else:
		tmp = a * ((z / a) + (y / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 126000000000.0)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(Float64(z / a) + Float64(y / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 126000000000.0)
		tmp = (z + a) - b;
	else
		tmp = a * ((z / a) + (y / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 126000000000.0], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(N[(z / a), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.26e11

   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 57.0%

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

   if 1.26e11 < a

   1. Initial program 57.5%

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

   3. Taylor expanded in a around inf 77.2%

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

      1. associate--l+ 77.2%

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

      2. associate-+r+ 77.2%

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

      3. +-commutative 77.2%

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

      4. associate-/l* 80.6%

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

      5. fma-define 80.6%

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

      6. +-commutative 80.6%

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

      7. associate-+r+ 80.6%

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

      8. associate-+r+ 80.6%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in b around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-/l* 80.3%

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

      3. associate-/r* 90.0%

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

      4. +-commutative 90.0%

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

      5. associate-+r+ 90.0%

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

      6. +-commutative 90.0%

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

      7. +-commutative 90.0%

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

      8. fma-undefine 90.0%

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

      9. +-commutative 90.0%

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

      10. +-commutative 90.0%

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

      11. +-commutative 90.0%

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

      12. associate-+r+ 90.0%

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

   8. Simplified 90.0%

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

   9. Taylor expanded in t around 0 66.6%

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

       1. +-commutative 66.6%

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

   11. Simplified 66.6%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 126000000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+119}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+134}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.2e+119) a (if (<= t 1.1e+134) (+ z a) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+119) {
		tmp = a;
	} else if (t <= 1.1e+134) {
		tmp = z + a;
	} 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 <= (-7.2d+119)) then
        tmp = a
    else if (t <= 1.1d+134) then
        tmp = z + a
    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 <= -7.2e+119) {
		tmp = a;
	} else if (t <= 1.1e+134) {
		tmp = z + a;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.2e+119:
		tmp = a
	elif t <= 1.1e+134:
		tmp = z + a
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.2e+119)
		tmp = a;
	elseif (t <= 1.1e+134)
		tmp = Float64(z + a);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.2e+119)
		tmp = a;
	elseif (t <= 1.1e+134)
		tmp = z + a;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.2e+119], a, If[LessEqual[t, 1.1e+134], N[(z + a), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -7.20000000000000003e119 or 1.1e134 < t

   1. Initial program 44.3%

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

   3. Taylor expanded in t around inf 55.1%

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

   if -7.20000000000000003e119 < t < 1.1e134

   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 0 59.5%

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

   4. Taylor expanded in y around inf 56.3%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+119}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+134}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-103}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 65000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.8e-103) a (if (<= t 65000000.0) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.8e-103) {
		tmp = a;
	} else if (t <= 65000000.0) {
		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 <= (-7.8d-103)) then
        tmp = a
    else if (t <= 65000000.0d0) 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 <= -7.8e-103) {
		tmp = a;
	} else if (t <= 65000000.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.8e-103:
		tmp = a
	elif t <= 65000000.0:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.8e-103)
		tmp = a;
	elseif (t <= 65000000.0)
		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 <= -7.8e-103)
		tmp = a;
	elseif (t <= 65000000.0)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.8e-103], a, If[LessEqual[t, 65000000.0], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -7.8000000000000004e-103 or 6.5e7 < t

   1. Initial program 54.5%

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

   3. Taylor expanded in t around inf 48.2%

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

   if -7.8000000000000004e-103 < t < 6.5e7

   1. Initial program 79.1%

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

   3. Taylor expanded in x around inf 48.8%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-103}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 65000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.6%

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

3. Taylor expanded in t around inf 37.1%

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

4. Final simplification 37.1%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 83.3% 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 2024079 
(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)))