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

Percentage Accurate: 60.6% → 99.3%

Time: 12.3s

Alternatives: 13

Speedup: 1.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) \cdot a\\ t_2 := x + \left(y + t\right)\\ t_3 := y + \left(x + t\right)\\ t_4 := \frac{\left(z \cdot \left(y + x\right) + t_1\right) - b \cdot y}{t_3}\\ \mathbf{if}\;t_4 \leq -\infty \lor \neg \left(t_4 \leq 10^{+243}\right):\\ \;\;\;\;\frac{z - b}{\frac{t_3}{y}} + \left(a \cdot \left(\frac{y}{t_2} + \frac{t}{t_2}\right) + x \cdot \frac{z}{t_2}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t_1\right) - b \cdot y}{t_3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y t) a))
        (t_2 (+ x (+ y t)))
        (t_3 (+ y (+ x t)))
        (t_4 (/ (- (+ (* z (+ y x)) t_1) (* b y)) t_3)))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 1e+243)))
     (+
      (/ (- z b) (/ t_3 y))
      (+ (* a (+ (/ y t_2) (/ t t_2))) (* x (/ z t_2))))
     (/ (- (fma (+ y x) z t_1) (* b y)) t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * a;
	double t_2 = x + (y + t);
	double t_3 = y + (x + t);
	double t_4 = (((z * (y + x)) + t_1) - (b * y)) / t_3;
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= 1e+243)) {
		tmp = ((z - b) / (t_3 / y)) + ((a * ((y / t_2) + (t / t_2))) + (x * (z / t_2)));
	} else {
		tmp = (fma((y + x), z, t_1) - (b * y)) / t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) * a)
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(y + Float64(x + t))
	t_4 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + t_1) - Float64(b * y)) / t_3)
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= 1e+243))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_3 / y)) + Float64(Float64(a * Float64(Float64(y / t_2) + Float64(t / t_2))) + Float64(x * Float64(z / t_2))));
	else
		tmp = Float64(Float64(fma(Float64(y + x), z, t_1) - Float64(b * y)) / t_3);
	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[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, 1e+243]], $MachinePrecision]], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$3 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(y / t$95$2), $MachinePrecision] + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.0000000000000001e243 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.3%

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

   3. Simplified 7.4%

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

   4. Taylor expanded in a around 0 35.7%

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

      1. associate-/l* 71.2%

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

      2. +-commutative 71.2%

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

      3. +-commutative 71.2%

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

      4. +-commutative 71.2%

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

      5. fma-def 71.2%

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

      6. +-commutative 71.2%

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

      7. +-commutative 71.2%

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

      8. +-commutative 71.2%

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

      9. +-commutative 71.2%

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

      10. associate-/l* 99.9%

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

      11. +-commutative 99.9%

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

      12. +-commutative 99.9%

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

   6. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-/r/ 99.8%

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

      5. associate-+l+ 99.8%

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

   8. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e243

   1. Initial program 99.7%

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

      1. fma-def 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)} \leq 10^{+243}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(a \cdot \left(\frac{y}{x + \left(y + t\right)} + \frac{t}{x + \left(y + t\right)}\right) + x \cdot \frac{z}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 2: 98.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \left(z - b\right) \cdot \frac{y}{x + \left(y + t\right)} + \mathsf{fma}\left(a, \frac{y}{t_1} + \frac{t}{t_1}, \frac{z}{\frac{t_1}{x}}\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (+
    (* (- z b) (/ y (+ x (+ y t))))
    (fma a (+ (/ y t_1) (/ t t_1)) (/ z (/ t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	return ((z - b) * (y / (x + (y + t)))) + fma(a, ((y / t_1) + (t / t_1)), (z / (t_1 / x)));
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	return Float64(Float64(Float64(z - b) * Float64(y / Float64(x + Float64(y + t)))) + fma(a, Float64(Float64(y / t_1) + Float64(t / t_1)), Float64(z / Float64(t_1 / x))))
end

Wolfram

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

Derivation

1. Initial program 57.1%

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

3. Simplified 57.2%

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

4. Taylor expanded in a around 0 69.7%

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

   1. associate-/l* 85.7%

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

   2. +-commutative 85.7%

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

   3. +-commutative 85.7%

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

   4. +-commutative 85.7%

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

   5. fma-def 85.7%

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

   6. +-commutative 85.7%

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

   7. +-commutative 85.7%

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

   8. +-commutative 85.7%

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

   9. +-commutative 85.7%

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

   10. associate-/l* 98.9%

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

   11. +-commutative 98.9%

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

   12. +-commutative 98.9%

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

6. Simplified 98.9%

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

   1. div-inv 98.9%

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

   2. clear-num 99.0%

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

   3. associate-+l+ 99.0%

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

8. Applied egg-rr 99.0%

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

9. Final simplification 99.0%

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

Alternative 3: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 10^{+243}\right):\\ \;\;\;\;\frac{z - b}{\frac{t_2}{y}} + \left(a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right) + x \cdot \frac{z}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* z (+ y x)) (* (+ y t) a)) (* b y)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 1e+243)))
     (+
      (/ (- z b) (/ t_2 y))
      (+ (* a (+ (/ y t_1) (/ t t_1))) (* x (/ z t_1))))
     t_3)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = y + (x + t);
	double t_3 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 1e+243)) {
		tmp = ((z - b) / (t_2 / y)) + ((a * ((y / t_1) + (t / t_1))) + (x * (z / t_1)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = y + (x + t);
	double t_3 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / t_2;
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 1e+243)) {
		tmp = ((z - b) / (t_2 / y)) + ((a * ((y / t_1) + (t / t_1))) + (x * (z / t_1)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = y + (x + t)
	t_3 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / t_2
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 1e+243):
		tmp = ((z - b) / (t_2 / y)) + ((a * ((y / t_1) + (t / t_1))) + (x * (z / t_1)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(Float64(y + t) * a)) - Float64(b * y)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 1e+243))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_2 / y)) + Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) + Float64(x * Float64(z / t_1))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = y + (x + t);
	t_3 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / t_2;
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 1e+243)))
		tmp = ((z - b) / (t_2 / y)) + ((a * ((y / t_1) + (t / t_1))) + (x * (z / t_1)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 1e+243]], $MachinePrecision]], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.0000000000000001e243 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.3%

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

   3. Simplified 7.4%

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

   4. Taylor expanded in a around 0 35.7%

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

      1. associate-/l* 71.2%

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

      2. +-commutative 71.2%

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

      3. +-commutative 71.2%

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

      4. +-commutative 71.2%

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

      5. fma-def 71.2%

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

      6. +-commutative 71.2%

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

      7. +-commutative 71.2%

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

      8. +-commutative 71.2%

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

      9. +-commutative 71.2%

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

      10. associate-/l* 99.9%

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

      11. +-commutative 99.9%

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

      12. +-commutative 99.9%

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

   6. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-/r/ 99.8%

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

      5. associate-+l+ 99.8%

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

   8. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e243

   1. Initial program 99.7%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)} \leq 10^{+243}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(a \cdot \left(\frac{y}{x + \left(y + t\right)} + \frac{t}{x + \left(y + t\right)}\right) + x \cdot \frac{z}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 4: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+283}\right):\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(a + x \cdot \frac{z}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ y x)) (* (+ y t) a)) (* b y)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+283)))
     (+ (/ (- z b) (/ t_1 y)) (+ a (* x (/ z (+ x (+ y t))))))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+283)) {
		tmp = ((z - b) / (t_1 / y)) + (a + (x * (z / (x + (y + t)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+283)) {
		tmp = ((z - b) / (t_1 / y)) + (a + (x * (z / (x + (y + t)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+283):
		tmp = ((z - b) / (t_1 / y)) + (a + (x * (z / (x + (y + t)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(Float64(y + t) * a)) - Float64(b * y)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+283))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(a + Float64(x * Float64(z / Float64(x + Float64(y + t))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+283)))
		tmp = ((z - b) / (t_1 / y)) + (a + (x * (z / (x + (y + t)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+283]], $MachinePrecision]], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(a + N[(x * N[(z / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.0000000000000004e283 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.7%

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

   3. Simplified 5.8%

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

   4. Taylor expanded in a around 0 34.6%

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

      1. associate-/l* 70.7%

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

      2. +-commutative 70.7%

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

      3. +-commutative 70.7%

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

      4. +-commutative 70.7%

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

      5. fma-def 70.7%

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

      6. +-commutative 70.7%

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

      7. +-commutative 70.7%

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

      8. +-commutative 70.7%

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

      9. +-commutative 70.7%

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

      10. associate-/l* 99.9%

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

      11. +-commutative 99.9%

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

      12. +-commutative 99.9%

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

   6. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-/r/ 99.8%

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

      5. associate-+l+ 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in y around inf 91.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000004e283

   1. Initial program 99.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)} \leq 5 \cdot 10^{+283}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(a + x \cdot \frac{z}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 5: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+283}\right):\\ \;\;\;\;z + \frac{y}{\frac{y + x}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ y x)) (* (+ y t) a)) (* b y)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+283)))
     (+ z (/ y (/ (+ y x) (- a b))))
     t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+283)) {
		tmp = z + (y / ((y + x) / (a - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+283)) {
		tmp = z + (y / ((y + x) / (a - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+283):
		tmp = z + (y / ((y + x) / (a - b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(Float64(y + t) * a)) - Float64(b * y)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+283))
		tmp = Float64(z + Float64(y / Float64(Float64(y + x) / Float64(a - b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (y + x)) + ((y + t) * a)) - (b * y)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+283)))
		tmp = z + (y / ((y + x) / (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[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+283]], $MachinePrecision]], N[(z + N[(y / N[(N[(y + x), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.0000000000000004e283 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.7%

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

   3. Simplified 5.8%

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

   4. Taylor expanded in t around 0 7.8%

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

   5. Taylor expanded in z around 0 37.8%

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

      1. +-commutative 37.8%

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

      2. associate-/l* 74.3%

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

   7. Simplified 74.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000004e283

   1. Initial program 99.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)} \leq 5 \cdot 10^{+283}\right):\\ \;\;\;\;z + \frac{y}{\frac{y + x}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + \left(y + t\right) \cdot a\right) - b \cdot y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 6: 80.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+64} \lor \neg \left(x \leq 7.5 \cdot 10^{+102}\right):\\ \;\;\;\;z + \frac{y}{\frac{y + x}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -6e+64) (not (<= x 7.5e+102)))
   (+ z (/ y (/ (+ y x) (- a b))))
   (+ a (/ (- z b) (/ (+ y (+ x t)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -6e+64) || !(x <= 7.5e+102)) {
		tmp = z + (y / ((y + x) / (a - b)));
	} else {
		tmp = a + ((z - b) / ((y + (x + t)) / 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 ((x <= (-6d+64)) .or. (.not. (x <= 7.5d+102))) then
        tmp = z + (y / ((y + x) / (a - b)))
    else
        tmp = a + ((z - b) / ((y + (x + t)) / 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 ((x <= -6e+64) || !(x <= 7.5e+102)) {
		tmp = z + (y / ((y + x) / (a - b)));
	} else {
		tmp = a + ((z - b) / ((y + (x + t)) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -6e+64) or not (x <= 7.5e+102):
		tmp = z + (y / ((y + x) / (a - b)))
	else:
		tmp = a + ((z - b) / ((y + (x + t)) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -6e+64) || !(x <= 7.5e+102))
		tmp = Float64(z + Float64(y / Float64(Float64(y + x) / Float64(a - b))));
	else
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + Float64(x + t)) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -6e+64) || ~((x <= 7.5e+102)))
		tmp = z + (y / ((y + x) / (a - b)));
	else
		tmp = a + ((z - b) / ((y + (x + t)) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -6e+64], N[Not[LessEqual[x, 7.5e+102]], $MachinePrecision]], N[(z + N[(y / N[(N[(y + x), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000004e64 or 7.5e102 < x

   1. Initial program 48.8%

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

   3. Simplified 48.5%

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

   4. Taylor expanded in t around 0 40.2%

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

   5. Taylor expanded in z around 0 65.4%

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

      1. +-commutative 65.4%

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

      2. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

   if -6.0000000000000004e64 < x < 7.5e102

   1. Initial program 63.7%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in a around 0 76.6%

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

      1. associate-/l* 97.9%

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

      2. +-commutative 97.9%

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

      3. +-commutative 97.9%

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

      4. +-commutative 97.9%

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

      5. fma-def 97.9%

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

      6. +-commutative 97.9%

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

      7. +-commutative 97.9%

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

      8. +-commutative 97.9%

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

      9. +-commutative 97.9%

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

      10. associate-/l* 99.2%

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

      11. +-commutative 99.2%

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

      12. +-commutative 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in y around inf 80.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+64} \lor \neg \left(x \leq 7.5 \cdot 10^{+102}\right):\\ \;\;\;\;z + \frac{y}{\frac{y + x}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\\ \end{array} \]

Alternative 7: 62.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+203} \lor \neg \left(x \leq 3.5 \cdot 10^{+137}\right):\\ \;\;\;\;z + a \cdot \left(\frac{y}{x} + \frac{t}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.4e+203) (not (<= x 3.5e+137)))
   (+ z (* a (+ (/ y x) (/ t x))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.4e+203) || !(x <= 3.5e+137)) {
		tmp = z + (a * ((y / x) + (t / x)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.4d+203)) .or. (.not. (x <= 3.5d+137))) then
        tmp = z + (a * ((y / x) + (t / x)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.4e+203) || !(x <= 3.5e+137)) {
		tmp = z + (a * ((y / x) + (t / x)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.4e+203) or not (x <= 3.5e+137):
		tmp = z + (a * ((y / x) + (t / x)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.4e+203) || !(x <= 3.5e+137))
		tmp = Float64(z + Float64(a * Float64(Float64(y / x) + Float64(t / x))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.4e+203) || ~((x <= 3.5e+137)))
		tmp = z + (a * ((y / x) + (t / x)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.4e+203], N[Not[LessEqual[x, 3.5e+137]], $MachinePrecision]], N[(z + N[(a * N[(N[(y / x), $MachinePrecision] + N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999995e203 or 3.5000000000000001e137 < x

   1. Initial program 44.8%

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

   3. Simplified 44.4%

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

   4. Taylor expanded in x around inf 59.7%

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

      1. associate--l+ 61.0%

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

      2. +-commutative 61.0%

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

      3. associate-/l* 61.2%

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

      4. associate-/l* 67.9%

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

      5. sub-neg 67.9%

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

      6. +-commutative 67.9%

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

      7. associate-+r+ 67.9%

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

      8. sub-neg 67.9%

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

      9. associate-/l* 82.3%

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

      10. +-commutative 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in a around inf 76.8%

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

   if -1.39999999999999995e203 < x < 3.5000000000000001e137

   1. Initial program 61.9%

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

      1. *-commutative 61.9%

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

      2. distribute-rgt-in 61.8%

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

      3. associate-+r+ 61.8%

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

      4. associate--l+ 61.8%

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

      5. +-commutative 61.8%

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

      6. +-commutative 61.8%

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

      7. distribute-lft-out-- 61.9%

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

      8. fma-def 62.2%

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

      9. +-commutative 62.2%

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

      10. fma-def 62.2%

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

      11. associate-+l+ 62.2%

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

      12. +-commutative 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in y around inf 56.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+203} \lor \neg \left(x \leq 3.5 \cdot 10^{+137}\right):\\ \;\;\;\;z + a \cdot \left(\frac{y}{x} + \frac{t}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 8: 71.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+164} \lor \neg \left(t \leq 5.7 \cdot 10^{+159}\right):\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;z + \frac{y}{\frac{y + x}{a - b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.5e+164) (not (<= t 5.7e+159)))
   (/ a (/ (+ x t) t))
   (+ z (/ y (/ (+ y x) (- a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.5e+164) || !(t <= 5.7e+159)) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = z + (y / ((y + x) / (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 ((t <= (-7.5d+164)) .or. (.not. (t <= 5.7d+159))) then
        tmp = a / ((x + t) / t)
    else
        tmp = z + (y / ((y + x) / (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 ((t <= -7.5e+164) || !(t <= 5.7e+159)) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = z + (y / ((y + x) / (a - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.5e+164) or not (t <= 5.7e+159):
		tmp = a / ((x + t) / t)
	else:
		tmp = z + (y / ((y + x) / (a - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.5e+164) || !(t <= 5.7e+159))
		tmp = Float64(a / Float64(Float64(x + t) / t));
	else
		tmp = Float64(z + Float64(y / Float64(Float64(y + x) / Float64(a - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.5e+164) || ~((t <= 5.7e+159)))
		tmp = a / ((x + t) / t);
	else
		tmp = z + (y / ((y + x) / (a - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.5e+164], N[Not[LessEqual[t, 5.7e+159]], $MachinePrecision]], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(z + N[(y / N[(N[(y + x), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.49999999999999976e164 or 5.6999999999999999e159 < t

   1. Initial program 47.3%

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

      1. *-commutative 47.3%

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

      2. distribute-rgt-in 47.2%

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

      3. associate-+r+ 47.2%

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

      4. associate--l+ 47.2%

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

      5. +-commutative 47.2%

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

      6. +-commutative 47.2%

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

      7. distribute-lft-out-- 47.2%

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

      8. fma-def 47.3%

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

      9. +-commutative 47.3%

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

      10. fma-def 47.5%

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

      11. associate-+l+ 47.5%

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

      12. +-commutative 47.5%

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

   3. Simplified 47.5%

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

   4. Taylor expanded in a around inf 29.0%

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

   5. Taylor expanded in y around 0 29.0%

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

      1. associate-/l* 59.1%

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

   7. Simplified 59.1%

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

   if -7.49999999999999976e164 < t < 5.6999999999999999e159

   1. Initial program 60.6%

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

   3. Simplified 60.7%

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

   4. Taylor expanded in t around 0 43.7%

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

   5. Taylor expanded in z around 0 60.1%

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

      1. +-commutative 60.1%

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

      2. associate-/l* 75.7%

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

   7. Simplified 75.7%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+164} \lor \neg \left(t \leq 5.7 \cdot 10^{+159}\right):\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;z + \frac{y}{\frac{y + x}{a - b}}\\ \end{array} \]

Alternative 9: 60.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+202} \lor \neg \left(x \leq 1.5 \cdot 10^{+138}\right):\\ \;\;\;\;z + a \cdot \frac{t}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -6e+202) (not (<= x 1.5e+138)))
   (+ z (* a (/ t x)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -6e+202) || !(x <= 1.5e+138)) {
		tmp = z + (a * (t / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-6d+202)) .or. (.not. (x <= 1.5d+138))) then
        tmp = z + (a * (t / x))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -6e+202) || !(x <= 1.5e+138)) {
		tmp = z + (a * (t / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -6e+202) or not (x <= 1.5e+138):
		tmp = z + (a * (t / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -6e+202) || !(x <= 1.5e+138))
		tmp = Float64(z + Float64(a * Float64(t / x)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -6e+202) || ~((x <= 1.5e+138)))
		tmp = z + (a * (t / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -6e+202], N[Not[LessEqual[x, 1.5e+138]], $MachinePrecision]], N[(z + N[(a * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000003e202 or 1.50000000000000005e138 < x

   1. Initial program 44.8%

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

   3. Simplified 44.4%

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

   4. Taylor expanded in x around inf 59.7%

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

      1. associate--l+ 61.0%

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

      2. +-commutative 61.0%

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

      3. associate-/l* 61.2%

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

      4. associate-/l* 67.9%

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

      5. sub-neg 67.9%

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

      6. +-commutative 67.9%

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

      7. associate-+r+ 67.9%

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

      8. sub-neg 67.9%

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

      9. associate-/l* 82.3%

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

      10. +-commutative 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in a around inf 76.8%

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

   8. Taylor expanded in y around 0 66.9%

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

   if -6.0000000000000003e202 < x < 1.50000000000000005e138

   1. Initial program 61.9%

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

      1. *-commutative 61.9%

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

      2. distribute-rgt-in 61.8%

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

      3. associate-+r+ 61.8%

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

      4. associate--l+ 61.8%

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

      5. +-commutative 61.8%

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

      6. +-commutative 61.8%

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

      7. distribute-lft-out-- 61.9%

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

      8. fma-def 62.2%

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

      9. +-commutative 62.2%

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

      10. fma-def 62.2%

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

      11. associate-+l+ 62.2%

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

      12. +-commutative 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in y around inf 56.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+202} \lor \neg \left(x \leq 1.5 \cdot 10^{+138}\right):\\ \;\;\;\;z + a \cdot \frac{t}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 59.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+203}:\\ \;\;\;\;z + \frac{y \cdot a}{x}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+135}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7e+203)
   (+ z (/ (* y a) x))
   (if (<= x 4.8e+135) (- (+ z a) b) (+ z (* a (/ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7e+203) {
		tmp = z + ((y * a) / x);
	} else if (x <= 4.8e+135) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a * (t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-7d+203)) then
        tmp = z + ((y * a) / x)
    else if (x <= 4.8d+135) then
        tmp = (z + a) - b
    else
        tmp = z + (a * (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7e+203) {
		tmp = z + ((y * a) / x);
	} else if (x <= 4.8e+135) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a * (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7e+203:
		tmp = z + ((y * a) / x)
	elif x <= 4.8e+135:
		tmp = (z + a) - b
	else:
		tmp = z + (a * (t / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7e+203)
		tmp = Float64(z + Float64(Float64(y * a) / x));
	elseif (x <= 4.8e+135)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(a * Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7e+203)
		tmp = z + ((y * a) / x);
	elseif (x <= 4.8e+135)
		tmp = (z + a) - b;
	else
		tmp = z + (a * (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7e+203], N[(z + N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+135], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(a * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.00000000000000062e203

   1. Initial program 49.3%

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

   3. Simplified 48.8%

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

   4. Taylor expanded in x around inf 75.4%

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

      1. associate--l+ 75.4%

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

      2. +-commutative 75.4%

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

      3. associate-/l* 75.8%

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

      4. associate-/l* 75.7%

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

      5. sub-neg 75.7%

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

      6. +-commutative 75.7%

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

      7. associate-+r+ 75.7%

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

      8. sub-neg 75.7%

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

      9. associate-/l* 79.4%

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

      10. +-commutative 79.4%

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

   6. Simplified 79.4%

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

   7. Taylor expanded in a around inf 77.9%

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

   8. Taylor expanded in y around inf 72.3%

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

   if -7.00000000000000062e203 < x < 4.79999999999999995e135

   1. Initial program 61.9%

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

      1. *-commutative 61.9%

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

      2. distribute-rgt-in 61.8%

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

      3. associate-+r+ 61.8%

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

      4. associate--l+ 61.8%

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

      5. +-commutative 61.8%

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

      6. +-commutative 61.8%

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

      7. distribute-lft-out-- 61.9%

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

      8. fma-def 62.2%

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

      9. +-commutative 62.2%

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

      10. fma-def 62.2%

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

      11. associate-+l+ 62.2%

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

      12. +-commutative 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in y around inf 56.7%

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

   if 4.79999999999999995e135 < x

   1. Initial program 41.9%

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

   3. Simplified 41.5%

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

   4. Taylor expanded in x around inf 49.7%

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

      1. associate--l+ 51.9%

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

      2. +-commutative 51.9%

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

      3. associate-/l* 51.9%

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

      4. associate-/l* 62.9%

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

      5. sub-neg 62.9%

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

      6. +-commutative 62.9%

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

      7. associate-+r+ 62.9%

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

      8. sub-neg 62.9%

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

      9. associate-/l* 84.2%

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

      10. +-commutative 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in a around inf 76.2%

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

   8. Taylor expanded in y around 0 70.8%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+203}:\\ \;\;\;\;z + \frac{y \cdot a}{x}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+135}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t}{x}\\ \end{array} \]

Alternative 11: 42.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+47}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-77}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-24}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+152}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.2e+47)
   z
   (if (<= z 9e-77) a (if (<= z 8.2e-24) z (if (<= z 3.4e+152) a z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e+47) {
		tmp = z;
	} else if (z <= 9e-77) {
		tmp = a;
	} else if (z <= 8.2e-24) {
		tmp = z;
	} else if (z <= 3.4e+152) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.2d+47)) then
        tmp = z
    else if (z <= 9d-77) then
        tmp = a
    else if (z <= 8.2d-24) then
        tmp = z
    else if (z <= 3.4d+152) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e+47) {
		tmp = z;
	} else if (z <= 9e-77) {
		tmp = a;
	} else if (z <= 8.2e-24) {
		tmp = z;
	} else if (z <= 3.4e+152) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.2e+47:
		tmp = z
	elif z <= 9e-77:
		tmp = a
	elif z <= 8.2e-24:
		tmp = z
	elif z <= 3.4e+152:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.2e+47)
		tmp = z;
	elseif (z <= 9e-77)
		tmp = a;
	elseif (z <= 8.2e-24)
		tmp = z;
	elseif (z <= 3.4e+152)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.2e+47)
		tmp = z;
	elseif (z <= 9e-77)
		tmp = a;
	elseif (z <= 8.2e-24)
		tmp = z;
	elseif (z <= 3.4e+152)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.2e+47], z, If[LessEqual[z, 9e-77], a, If[LessEqual[z, 8.2e-24], z, If[LessEqual[z, 3.4e+152], a, z]]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e47 or 9.0000000000000001e-77 < z < 8.20000000000000029e-24 or 3.4000000000000002e152 < z

   1. Initial program 49.3%

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

      1. *-commutative 49.3%

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

      2. distribute-rgt-in 49.2%

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

      3. associate-+r+ 49.2%

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

      4. associate--l+ 49.2%

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

      5. +-commutative 49.2%

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

      6. +-commutative 49.2%

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

      7. distribute-lft-out-- 49.2%

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

      8. fma-def 49.6%

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

      9. +-commutative 49.6%

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

      10. fma-def 49.7%

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

      11. associate-+l+ 49.7%

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

      12. +-commutative 49.7%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in x around inf 67.3%

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

   if -4.2e47 < z < 9.0000000000000001e-77 or 8.20000000000000029e-24 < z < 3.4000000000000002e152

   1. Initial program 62.0%

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

      1. *-commutative 62.0%

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

      2. distribute-rgt-in 61.9%

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

      3. associate-+r+ 61.9%

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

      4. associate--l+ 61.9%

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

      5. +-commutative 61.9%

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

      6. +-commutative 61.9%

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

      7. distribute-lft-out-- 62.0%

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

      8. fma-def 62.1%

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

      9. +-commutative 62.1%

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

      10. fma-def 62.1%

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

      11. associate-+l+ 62.1%

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

      12. +-commutative 62.1%

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

   3. Simplified 62.1%

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

   4. Taylor expanded in t around inf 40.0%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+47}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-77}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-24}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+152}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 12: 58.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+204}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+140}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.25e+204) z (if (<= x 5.2e+140) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.25e+204) {
		tmp = z;
	} else if (x <= 5.2e+140) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.25d+204)) then
        tmp = z
    else if (x <= 5.2d+140) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.25e+204) {
		tmp = z;
	} else if (x <= 5.2e+140) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.25e+204:
		tmp = z
	elif x <= 5.2e+140:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.25e+204)
		tmp = z;
	elseif (x <= 5.2e+140)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.25e+204)
		tmp = z;
	elseif (x <= 5.2e+140)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.25e+204], z, If[LessEqual[x, 5.2e+140], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25000000000000002e204 or 5.2000000000000002e140 < x

   1. Initial program 44.8%

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

      1. *-commutative 44.8%

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

      2. distribute-rgt-in 44.7%

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

      3. associate-+r+ 44.7%

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

      4. associate--l+ 44.7%

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

      5. +-commutative 44.7%

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

      6. +-commutative 44.7%

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

      7. distribute-lft-out-- 44.7%

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

      8. fma-def 44.8%

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

      9. +-commutative 44.8%

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

      10. fma-def 44.9%

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

      11. associate-+l+ 44.9%

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

      12. +-commutative 44.9%

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

   3. Simplified 44.9%

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

   4. Taylor expanded in x around inf 57.2%

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

   if -1.25000000000000002e204 < x < 5.2000000000000002e140

   1. Initial program 61.9%

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

      1. *-commutative 61.9%

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

      2. distribute-rgt-in 61.8%

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

      3. associate-+r+ 61.8%

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

      4. associate--l+ 61.8%

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

      5. +-commutative 61.8%

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

      6. +-commutative 61.8%

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

      7. distribute-lft-out-- 61.9%

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

      8. fma-def 62.2%

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

      9. +-commutative 62.2%

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

      10. fma-def 62.2%

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

      11. associate-+l+ 62.2%

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

      12. +-commutative 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in y around inf 56.7%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+204}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+140}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 13: 31.9% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.1%

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

   1. *-commutative 57.1%

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

   2. distribute-rgt-in 57.0%

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

   3. associate-+r+ 57.0%

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

   4. associate--l+ 57.0%

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

   5. +-commutative 57.0%

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

   6. +-commutative 57.0%

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

   7. distribute-lft-out-- 57.1%

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

   8. fma-def 57.3%

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

   9. +-commutative 57.3%

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

   10. fma-def 57.3%

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

   11. associate-+l+ 57.3%

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

   12. +-commutative 57.3%

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

3. Simplified 57.3%

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

4. Taylor expanded in t around inf 28.8%

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

5. Final simplification 28.8%

   \[\leadsto a \]

Developer target: 82.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t_2}{t_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t_1}{t_2}}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
        (t_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1.0 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b)))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))