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

Percentage Accurate: 59.6% → 95.8%

Time: 16.6s

Alternatives: 16

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \left(y + t\right) \cdot a\\ t_4 := \frac{\left(t\_3 + t\_1\right) - y \cdot b}{t\_2}\\ t_5 := t + \left(x + y\right)\\ \mathbf{if}\;t\_4 \leq -\infty \lor \neg \left(t\_4 \leq 5 \cdot 10^{+241}\right):\\ \;\;\;\;a + \mathsf{fma}\left(z, \frac{x}{t\_2} + \frac{y}{t\_2}, y \cdot \frac{b}{\left(-y\right) - \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_3}{t\_5} + \frac{t\_1 - y \cdot b}{t\_5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ x y)))
        (t_2 (+ y (+ x t)))
        (t_3 (* (+ y t) a))
        (t_4 (/ (- (+ t_3 t_1) (* y b)) t_2))
        (t_5 (+ t (+ x y))))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 5e+241)))
     (+ a (fma z (+ (/ x t_2) (/ y t_2)) (* y (/ b (- (- y) (+ x t))))))
     (+ (/ t_3 t_5) (/ (- t_1 (* y b)) t_5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x + y);
	double t_2 = y + (x + t);
	double t_3 = (y + t) * a;
	double t_4 = ((t_3 + t_1) - (y * b)) / t_2;
	double t_5 = t + (x + y);
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= 5e+241)) {
		tmp = a + fma(z, ((x / t_2) + (y / t_2)), (y * (b / (-y - (x + t)))));
	} else {
		tmp = (t_3 / t_5) + ((t_1 - (y * b)) / t_5);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(y + t) * a)
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(y * b)) / t_2)
	t_5 = Float64(t + Float64(x + y))
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= 5e+241))
		tmp = Float64(a + fma(z, Float64(Float64(x / t_2) + Float64(y / t_2)), Float64(y * Float64(b / Float64(Float64(-y) - Float64(x + t))))));
	else
		tmp = Float64(Float64(t_3 / t_5) + Float64(Float64(t_1 - Float64(y * b)) / t_5));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, 5e+241]], $MachinePrecision]], N[(a + N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y * N[(b / N[((-y) - N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 / t$95$5), $MachinePrecision] + N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.00000000000000025e241 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.0%

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

   3. Taylor expanded in z around inf 7.0%

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

      1. associate--l+ 7.0%

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

      2. +-commutative 7.0%

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

      3. div-sub 7.0%

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

      4. +-commutative 7.0%

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

      5. *-commutative 7.0%

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

      6. +-commutative 7.0%

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

   5. Simplified 7.0%

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

   6. Taylor expanded in z around 0 37.8%

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

      1. +-commutative 37.8%

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

      2. fma-define 37.8%

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

      3. associate-+r+ 37.8%

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

      4. +-commutative 37.8%

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

      5. associate-+r+ 37.8%

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

      6. +-commutative 37.8%

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

      7. mul-1-neg 37.8%

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

      8. *-commutative 37.8%

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

      9. +-commutative 37.8%

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

      10. +-commutative 37.8%

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

      11. associate-+r+ 37.8%

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

      12. associate-/l* 54.6%

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

      13. distribute-rgt-neg-in 54.6%

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

      14. +-commutative 54.6%

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

   8. Simplified 54.6%

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

   9. Taylor expanded in t around inf 90.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000025e241

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. div-sub 99.8%

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

      4. +-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+241}\right):\\ \;\;\;\;a + \mathsf{fma}\left(z, \frac{x}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)}, y \cdot \frac{b}{\left(-y\right) - \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a}{t + \left(x + y\right)} + \frac{z \cdot \left(x + y\right) - y \cdot b}{t + \left(x + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x + y\right)\\ t_2 := t + \left(x + y\right)\\ t_3 := \left(y + t\right) \cdot a\\ t_4 := \frac{\left(t\_3 + t\_1\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_4 \leq -\infty \lor \neg \left(t\_4 \leq 10^{+301}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_3}{t\_2} + \frac{t\_1 - y \cdot b}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ x y)))
        (t_2 (+ t (+ x y)))
        (t_3 (* (+ y t) a))
        (t_4 (/ (- (+ t_3 t_1) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 1e+301)))
     (- (+ z a) b)
     (+ (/ t_3 t_2) (/ (- t_1 (* y b)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x + y);
	double t_2 = t + (x + y);
	double t_3 = (y + t) * a;
	double t_4 = ((t_3 + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= 1e+301)) {
		tmp = (z + a) - b;
	} else {
		tmp = (t_3 / t_2) + ((t_1 - (y * b)) / t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x + y);
	double t_2 = t + (x + y);
	double t_3 = (y + t) * a;
	double t_4 = ((t_3 + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_4 <= -Double.POSITIVE_INFINITY) || !(t_4 <= 1e+301)) {
		tmp = (z + a) - b;
	} else {
		tmp = (t_3 / t_2) + ((t_1 - (y * b)) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (x + y)
	t_2 = t + (x + y)
	t_3 = (y + t) * a
	t_4 = ((t_3 + t_1) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_4 <= -math.inf) or not (t_4 <= 1e+301):
		tmp = (z + a) - b
	else:
		tmp = (t_3 / t_2) + ((t_1 - (y * b)) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x + y))
	t_2 = Float64(t + Float64(x + y))
	t_3 = Float64(Float64(y + t) * a)
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= 1e+301))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(t_3 / t_2) + Float64(Float64(t_1 - Float64(y * b)) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (x + y);
	t_2 = t + (x + y);
	t_3 = (y + t) * a;
	t_4 = ((t_3 + t_1) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_4 <= -Inf) || ~((t_4 <= 1e+301)))
		tmp = (z + a) - b;
	else
		tmp = (t_3 / t_2) + ((t_1 - (y * b)) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, 1e+301]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(t$95$3 / t$95$2), $MachinePrecision] + N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.00000000000000005e301 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.4%

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

   3. Taylor expanded in y around inf 71.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000005e301

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. div-sub 99.8%

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

      4. +-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+301}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a}{t + \left(x + y\right)} + \frac{z \cdot \left(x + y\right) - y \cdot b}{t + \left(x + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+301}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+301))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+301)) {
		tmp = (z + 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 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+301)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+301):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+301))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+301)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+301]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.00000000000000005e301 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.4%

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

   3. Taylor expanded in y around inf 71.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000005e301

   1. Initial program 99.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+301}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \frac{x + y}{t\_2}\\ t_4 := a \cdot \frac{y + t}{t\_2}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+143}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -620000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-90}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+29}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (* z (/ (+ x y) t_2)))
        (t_4 (* a (/ (+ y t) t_2))))
   (if (<= z -1.45e+143)
     t_3
     (if (<= z -620000.0)
       t_1
       (if (<= z -8.5e-90)
         t_4
         (if (<= z -1.5e-164) t_1 (if (<= z 6.8e+29) t_4 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = z * ((x + y) / t_2);
	double t_4 = a * ((y + t) / t_2);
	double tmp;
	if (z <= -1.45e+143) {
		tmp = t_3;
	} else if (z <= -620000.0) {
		tmp = t_1;
	} else if (z <= -8.5e-90) {
		tmp = t_4;
	} else if (z <= -1.5e-164) {
		tmp = t_1;
	} else if (z <= 6.8e+29) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	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 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = z * ((x + y) / t_2)
    t_4 = a * ((y + t) / t_2)
    if (z <= (-1.45d+143)) then
        tmp = t_3
    else if (z <= (-620000.0d0)) then
        tmp = t_1
    else if (z <= (-8.5d-90)) then
        tmp = t_4
    else if (z <= (-1.5d-164)) then
        tmp = t_1
    else if (z <= 6.8d+29) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = z * ((x + y) / t_2);
	double t_4 = a * ((y + t) / t_2);
	double tmp;
	if (z <= -1.45e+143) {
		tmp = t_3;
	} else if (z <= -620000.0) {
		tmp = t_1;
	} else if (z <= -8.5e-90) {
		tmp = t_4;
	} else if (z <= -1.5e-164) {
		tmp = t_1;
	} else if (z <= 6.8e+29) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = z * ((x + y) / t_2)
	t_4 = a * ((y + t) / t_2)
	tmp = 0
	if z <= -1.45e+143:
		tmp = t_3
	elif z <= -620000.0:
		tmp = t_1
	elif z <= -8.5e-90:
		tmp = t_4
	elif z <= -1.5e-164:
		tmp = t_1
	elif z <= 6.8e+29:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(Float64(x + y) / t_2))
	t_4 = Float64(a * Float64(Float64(y + t) / t_2))
	tmp = 0.0
	if (z <= -1.45e+143)
		tmp = t_3;
	elseif (z <= -620000.0)
		tmp = t_1;
	elseif (z <= -8.5e-90)
		tmp = t_4;
	elseif (z <= -1.5e-164)
		tmp = t_1;
	elseif (z <= 6.8e+29)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = z * ((x + y) / t_2);
	t_4 = a * ((y + t) / t_2);
	tmp = 0.0;
	if (z <= -1.45e+143)
		tmp = t_3;
	elseif (z <= -620000.0)
		tmp = t_1;
	elseif (z <= -8.5e-90)
		tmp = t_4;
	elseif (z <= -1.5e-164)
		tmp = t_1;
	elseif (z <= 6.8e+29)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+143], t$95$3, If[LessEqual[z, -620000.0], t$95$1, If[LessEqual[z, -8.5e-90], t$95$4, If[LessEqual[z, -1.5e-164], t$95$1, If[LessEqual[z, 6.8e+29], t$95$4, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e143 or 6.79999999999999963e29 < z

   1. Initial program 45.7%

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

   3. Taylor expanded in z around inf 36.6%

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

      1. associate-/l* 75.1%

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

      2. +-commutative 75.1%

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

      3. +-commutative 75.1%

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

      4. +-commutative 75.1%

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

      5. associate-+l+ 75.1%

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

      6. +-commutative 75.1%

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

   5. Simplified 75.1%

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

   if -1.4499999999999999e143 < z < -6.2e5 or -8.5000000000000001e-90 < z < -1.5e-164

   1. Initial program 54.7%

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

   3. Taylor expanded in y around inf 69.8%

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

   if -6.2e5 < z < -8.5000000000000001e-90 or -1.5e-164 < z < 6.79999999999999963e29

   1. Initial program 69.8%

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

   3. Taylor expanded in a around inf 44.0%

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

      1. associate-/l* 65.7%

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

      2. +-commutative 65.7%

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

      3. +-commutative 65.7%

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

      4. associate-+l+ 65.7%

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

      5. +-commutative 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+143}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -620000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-164}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-220}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-24}:\\ \;\;\;\;z + \frac{\left(y + t\right) \cdot a}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.12e-35)
     t_1
     (if (<= y 2.2e-220)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 3.7e-24)
         (+ z (/ (* (+ y t) a) (+ t (+ x y))))
         (if (<= y 5.5e+91)
           (/ (- (* z (+ x y)) (* y b)) (+ y (+ x t)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.12e-35) {
		tmp = t_1;
	} else if (y <= 2.2e-220) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 3.7e-24) {
		tmp = z + (((y + t) * a) / (t + (x + y)));
	} else if (y <= 5.5e+91) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.12d-35)) then
        tmp = t_1
    else if (y <= 2.2d-220) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 3.7d-24) then
        tmp = z + (((y + t) * a) / (t + (x + y)))
    else if (y <= 5.5d+91) then
        tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.12e-35) {
		tmp = t_1;
	} else if (y <= 2.2e-220) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 3.7e-24) {
		tmp = z + (((y + t) * a) / (t + (x + y)));
	} else if (y <= 5.5e+91) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.12e-35:
		tmp = t_1
	elif y <= 2.2e-220:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 3.7e-24:
		tmp = z + (((y + t) * a) / (t + (x + y)))
	elif y <= 5.5e+91:
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.12e-35)
		tmp = t_1;
	elseif (y <= 2.2e-220)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 3.7e-24)
		tmp = Float64(z + Float64(Float64(Float64(y + t) * a) / Float64(t + Float64(x + y))));
	elseif (y <= 5.5e+91)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.12e-35)
		tmp = t_1;
	elseif (y <= 2.2e-220)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 3.7e-24)
		tmp = z + (((y + t) * a) / (t + (x + y)));
	elseif (y <= 5.5e+91)
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.12e-35], t$95$1, If[LessEqual[y, 2.2e-220], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-24], N[(z + N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+91], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.12e-35 or 5.4999999999999998e91 < y

   1. Initial program 38.5%

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

   3. Taylor expanded in y around inf 74.1%

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

   if -1.12e-35 < y < 2.19999999999999987e-220

   1. Initial program 76.3%

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

   3. Taylor expanded in y around 0 65.6%

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

   if 2.19999999999999987e-220 < y < 3.69999999999999981e-24

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. +-commutative 69.4%

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

      3. div-sub 69.4%

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

      4. +-commutative 69.4%

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

      5. *-commutative 69.4%

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

      6. +-commutative 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in x around inf 68.4%

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

   if 3.69999999999999981e-24 < y < 5.4999999999999998e91

   1. Initial program 77.0%

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

   3. Taylor expanded in z around inf 65.5%

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

      1. +-commutative 65.5%

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

   5. Simplified 65.5%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-35}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-220}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-24}:\\ \;\;\;\;z + \frac{\left(y + t\right) \cdot a}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-220}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-19}:\\ \;\;\;\;z + \frac{\left(y + t\right) \cdot a}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{y \cdot t\_1}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.15e-36)
     t_1
     (if (<= y 8.5e-220)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 7.4e-19)
         (+ z (/ (* (+ y t) a) (+ t (+ x y))))
         (if (<= y 5.9e+91) (/ (* y t_1) (+ y (+ x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.15e-36) {
		tmp = t_1;
	} else if (y <= 8.5e-220) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 7.4e-19) {
		tmp = z + (((y + t) * a) / (t + (x + y)));
	} else if (y <= 5.9e+91) {
		tmp = (y * t_1) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.15d-36)) then
        tmp = t_1
    else if (y <= 8.5d-220) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 7.4d-19) then
        tmp = z + (((y + t) * a) / (t + (x + y)))
    else if (y <= 5.9d+91) then
        tmp = (y * t_1) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.15e-36) {
		tmp = t_1;
	} else if (y <= 8.5e-220) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 7.4e-19) {
		tmp = z + (((y + t) * a) / (t + (x + y)));
	} else if (y <= 5.9e+91) {
		tmp = (y * t_1) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.15e-36:
		tmp = t_1
	elif y <= 8.5e-220:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 7.4e-19:
		tmp = z + (((y + t) * a) / (t + (x + y)))
	elif y <= 5.9e+91:
		tmp = (y * t_1) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.15e-36)
		tmp = t_1;
	elseif (y <= 8.5e-220)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 7.4e-19)
		tmp = Float64(z + Float64(Float64(Float64(y + t) * a) / Float64(t + Float64(x + y))));
	elseif (y <= 5.9e+91)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.15e-36)
		tmp = t_1;
	elseif (y <= 8.5e-220)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 7.4e-19)
		tmp = z + (((y + t) * a) / (t + (x + y)));
	elseif (y <= 5.9e+91)
		tmp = (y * t_1) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.15e-36], t$95$1, If[LessEqual[y, 8.5e-220], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4e-19], N[(z + N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.9e+91], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.1500000000000001e-36 or 5.9000000000000002e91 < y

   1. Initial program 38.5%

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

   3. Taylor expanded in y around inf 74.1%

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

   if -2.1500000000000001e-36 < y < 8.4999999999999996e-220

   1. Initial program 76.3%

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

   3. Taylor expanded in y around 0 65.6%

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

   if 8.4999999999999996e-220 < y < 7.40000000000000011e-19

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. +-commutative 69.4%

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

      3. div-sub 69.4%

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

      4. +-commutative 69.4%

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

      5. *-commutative 69.4%

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

      6. +-commutative 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in x around inf 68.4%

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

   if 7.40000000000000011e-19 < y < 5.9000000000000002e91

   1. Initial program 77.0%

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

   3. Taylor expanded in y around inf 61.4%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-36}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-220}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-19}:\\ \;\;\;\;z + \frac{\left(y + t\right) \cdot a}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+161} \lor \neg \left(t \leq -5.2 \cdot 10^{+97} \lor \neg \left(t \leq -6.5 \cdot 10^{+59}\right) \land t \leq 9.5 \cdot 10^{+38}\right):\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.1e+161)
         (not (or (<= t -5.2e+97) (and (not (<= t -6.5e+59)) (<= t 9.5e+38)))))
   (+ a (* z (/ (+ x y) t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.1e+161) || !((t <= -5.2e+97) || (!(t <= -6.5e+59) && (t <= 9.5e+38)))) {
		tmp = a + (z * ((x + y) / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.1d+161)) .or. (.not. (t <= (-5.2d+97)) .or. (.not. (t <= (-6.5d+59))) .and. (t <= 9.5d+38))) then
        tmp = a + (z * ((x + y) / t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.1e+161) || !((t <= -5.2e+97) || (!(t <= -6.5e+59) && (t <= 9.5e+38)))) {
		tmp = a + (z * ((x + y) / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.1e+161) or not ((t <= -5.2e+97) or (not (t <= -6.5e+59) and (t <= 9.5e+38))):
		tmp = a + (z * ((x + y) / t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.1e+161) || !((t <= -5.2e+97) || (!(t <= -6.5e+59) && (t <= 9.5e+38))))
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.1e+161) || ~(((t <= -5.2e+97) || (~((t <= -6.5e+59)) && (t <= 9.5e+38)))))
		tmp = a + (z * ((x + y) / t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.1e+161], N[Not[Or[LessEqual[t, -5.2e+97], And[N[Not[LessEqual[t, -6.5e+59]], $MachinePrecision], LessEqual[t, 9.5e+38]]]], $MachinePrecision]], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e161 or -5.2e97 < t < -6.50000000000000021e59 or 9.4999999999999995e38 < t

   1. Initial program 55.8%

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

   3. Taylor expanded in t around inf 60.3%

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

      1. associate--l+ 61.3%

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

      2. associate-/l* 61.4%

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

      3. associate-/l* 67.6%

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

      4. +-commutative 67.6%

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

      5. associate-/l* 72.8%

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

      6. +-commutative 72.8%

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

      7. associate-/l* 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in z around -inf 63.2%

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

      1. associate-*r/ 69.4%

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

      2. +-commutative 69.4%

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

   8. Simplified 69.4%

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

   if -1.1e161 < t < -5.2e97 or -6.50000000000000021e59 < t < 9.4999999999999995e38

   1. Initial program 60.1%

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

   3. Taylor expanded in y around inf 64.3%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+161} \lor \neg \left(t \leq -5.2 \cdot 10^{+97} \lor \neg \left(t \leq -6.5 \cdot 10^{+59}\right) \land t \leq 9.5 \cdot 10^{+38}\right):\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4700000:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + z \cdot \left(x + y\right)}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+92}:\\ \;\;\;\;\frac{y \cdot t\_1}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.3e-35)
     t_1
     (if (<= y 4700000.0)
       (/ (+ (* (+ y t) a) (* z (+ x y))) (+ t (+ x y)))
       (if (<= y 1.05e+92) (/ (* y t_1) (+ y (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.3e-35) {
		tmp = t_1;
	} else if (y <= 4700000.0) {
		tmp = (((y + t) * a) + (z * (x + y))) / (t + (x + y));
	} else if (y <= 1.05e+92) {
		tmp = (y * t_1) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.3d-35)) then
        tmp = t_1
    else if (y <= 4700000.0d0) then
        tmp = (((y + t) * a) + (z * (x + y))) / (t + (x + y))
    else if (y <= 1.05d+92) then
        tmp = (y * t_1) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.3e-35) {
		tmp = t_1;
	} else if (y <= 4700000.0) {
		tmp = (((y + t) * a) + (z * (x + y))) / (t + (x + y));
	} else if (y <= 1.05e+92) {
		tmp = (y * t_1) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.3e-35:
		tmp = t_1
	elif y <= 4700000.0:
		tmp = (((y + t) * a) + (z * (x + y))) / (t + (x + y))
	elif y <= 1.05e+92:
		tmp = (y * t_1) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.3e-35)
		tmp = t_1;
	elseif (y <= 4700000.0)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) / Float64(t + Float64(x + y)));
	elseif (y <= 1.05e+92)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.3e-35)
		tmp = t_1;
	elseif (y <= 4700000.0)
		tmp = (((y + t) * a) + (z * (x + y))) / (t + (x + y));
	elseif (y <= 1.05e+92)
		tmp = (y * t_1) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.3e-35], t$95$1, If[LessEqual[y, 4700000.0], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+92], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2999999999999999e-35 or 1.04999999999999993e92 < y

   1. Initial program 38.5%

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

   3. Taylor expanded in y around inf 74.1%

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

   if -2.2999999999999999e-35 < y < 4.7e6

   1. Initial program 75.3%

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

   3. Taylor expanded in b around 0 70.6%

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

   if 4.7e6 < y < 1.04999999999999993e92

   1. Initial program 73.4%

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

   3. Taylor expanded in y around inf 68.1%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-35}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 4700000:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + z \cdot \left(x + y\right)}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+92}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a + y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ a (* y (/ z t)))))
   (if (<= t -3.3e+160)
     t_2
     (if (<= t -1.2e+98)
       t_1
       (if (<= t -3.5e+59)
         t_2
         (if (<= t 2.2e+123) t_1 (+ a (* x (/ z t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (y * (z / t));
	double tmp;
	if (t <= -3.3e+160) {
		tmp = t_2;
	} else if (t <= -1.2e+98) {
		tmp = t_1;
	} else if (t <= -3.5e+59) {
		tmp = t_2;
	} else if (t <= 2.2e+123) {
		tmp = t_1;
	} else {
		tmp = a + (x * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a + (y * (z / t))
    if (t <= (-3.3d+160)) then
        tmp = t_2
    else if (t <= (-1.2d+98)) then
        tmp = t_1
    else if (t <= (-3.5d+59)) then
        tmp = t_2
    else if (t <= 2.2d+123) then
        tmp = t_1
    else
        tmp = a + (x * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (y * (z / t));
	double tmp;
	if (t <= -3.3e+160) {
		tmp = t_2;
	} else if (t <= -1.2e+98) {
		tmp = t_1;
	} else if (t <= -3.5e+59) {
		tmp = t_2;
	} else if (t <= 2.2e+123) {
		tmp = t_1;
	} else {
		tmp = a + (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a + (y * (z / t))
	tmp = 0
	if t <= -3.3e+160:
		tmp = t_2
	elif t <= -1.2e+98:
		tmp = t_1
	elif t <= -3.5e+59:
		tmp = t_2
	elif t <= 2.2e+123:
		tmp = t_1
	else:
		tmp = a + (x * (z / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -3.3e+160)
		tmp = t_2;
	elseif (t <= -1.2e+98)
		tmp = t_1;
	elseif (t <= -3.5e+59)
		tmp = t_2;
	elseif (t <= 2.2e+123)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a + (y * (z / t));
	tmp = 0.0;
	if (t <= -3.3e+160)
		tmp = t_2;
	elseif (t <= -1.2e+98)
		tmp = t_1;
	elseif (t <= -3.5e+59)
		tmp = t_2;
	elseif (t <= 2.2e+123)
		tmp = t_1;
	else
		tmp = a + (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+160], t$95$2, If[LessEqual[t, -1.2e+98], t$95$1, If[LessEqual[t, -3.5e+59], t$95$2, If[LessEqual[t, 2.2e+123], t$95$1, N[(a + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2999999999999997e160 or -1.1999999999999999e98 < t < -3.5e59

   1. Initial program 59.9%

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

   3. Taylor expanded in t around inf 74.3%

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

      1. associate--l+ 74.3%

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

      2. associate-/l* 74.4%

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

      3. associate-/l* 79.3%

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

      4. +-commutative 79.3%

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

      5. associate-/l* 84.3%

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

      6. +-commutative 84.3%

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

      7. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in z around -inf 73.4%

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

   7. Taylor expanded in x around 0 71.5%

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

      1. associate-/l* 73.7%

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

   9. Simplified 73.7%

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

   if -3.2999999999999997e160 < t < -1.1999999999999999e98 or -3.5e59 < t < 2.19999999999999992e123

   1. Initial program 59.5%

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

   3. Taylor expanded in y around inf 61.7%

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

   if 2.19999999999999992e123 < t

   1. Initial program 52.0%

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

   3. Taylor expanded in t around inf 53.7%

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

      1. associate--l+ 56.2%

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

      2. associate-/l* 56.3%

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

      3. associate-/l* 66.4%

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

      4. +-commutative 66.4%

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

      5. associate-/l* 74.2%

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

      6. +-commutative 74.2%

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

      7. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in z around -inf 61.1%

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

   7. Taylor expanded in x around inf 62.6%

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

      1. associate-/l* 70.1%

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

   9. Simplified 70.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+160}:\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+98}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+59}:\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+164}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{+59}:\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -4.2e+164)
     (- a (* y (/ b t)))
     (if (<= t -1.35e+98)
       t_1
       (if (<= t -5.6e+59)
         (+ a (* y (/ z t)))
         (if (<= t 1.85e+123) t_1 (+ a (* x (/ z t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -4.2e+164) {
		tmp = a - (y * (b / t));
	} else if (t <= -1.35e+98) {
		tmp = t_1;
	} else if (t <= -5.6e+59) {
		tmp = a + (y * (z / t));
	} else if (t <= 1.85e+123) {
		tmp = t_1;
	} else {
		tmp = a + (x * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-4.2d+164)) then
        tmp = a - (y * (b / t))
    else if (t <= (-1.35d+98)) then
        tmp = t_1
    else if (t <= (-5.6d+59)) then
        tmp = a + (y * (z / t))
    else if (t <= 1.85d+123) then
        tmp = t_1
    else
        tmp = a + (x * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -4.2e+164) {
		tmp = a - (y * (b / t));
	} else if (t <= -1.35e+98) {
		tmp = t_1;
	} else if (t <= -5.6e+59) {
		tmp = a + (y * (z / t));
	} else if (t <= 1.85e+123) {
		tmp = t_1;
	} else {
		tmp = a + (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -4.2e+164:
		tmp = a - (y * (b / t))
	elif t <= -1.35e+98:
		tmp = t_1
	elif t <= -5.6e+59:
		tmp = a + (y * (z / t))
	elif t <= 1.85e+123:
		tmp = t_1
	else:
		tmp = a + (x * (z / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -4.2e+164)
		tmp = Float64(a - Float64(y * Float64(b / t)));
	elseif (t <= -1.35e+98)
		tmp = t_1;
	elseif (t <= -5.6e+59)
		tmp = Float64(a + Float64(y * Float64(z / t)));
	elseif (t <= 1.85e+123)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -4.2e+164)
		tmp = a - (y * (b / t));
	elseif (t <= -1.35e+98)
		tmp = t_1;
	elseif (t <= -5.6e+59)
		tmp = a + (y * (z / t));
	elseif (t <= 1.85e+123)
		tmp = t_1;
	else
		tmp = a + (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t, -4.2e+164], N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e+98], t$95$1, If[LessEqual[t, -5.6e+59], N[(a + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+123], t$95$1, N[(a + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.1999999999999998e164

   1. Initial program 51.1%

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

   3. Taylor expanded in t around inf 71.5%

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

      1. associate--l+ 71.5%

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

      2. associate-/l* 71.7%

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

      3. associate-/l* 78.4%

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

      4. +-commutative 78.4%

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

      5. associate-/l* 85.3%

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

      6. +-commutative 85.3%

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

      7. associate-/l* 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in b around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-/l* 77.2%

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

      4. distribute-rgt-neg-in 77.2%

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

      5. distribute-neg-frac2 77.2%

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

   8. Simplified 77.2%

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

   if -4.1999999999999998e164 < t < -1.35e98 or -5.5999999999999996e59 < t < 1.84999999999999998e123

   1. Initial program 59.5%

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

   3. Taylor expanded in y around inf 61.7%

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

   if -1.35e98 < t < -5.5999999999999996e59

   1. Initial program 83.0%

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

   3. Taylor expanded in t around inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. associate-/l* 81.6%

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

      3. associate-/l* 81.7%

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

      4. +-commutative 81.7%

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

      5. associate-/l* 81.8%

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

      6. +-commutative 81.8%

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

      7. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in z around -inf 72.3%

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

   7. Taylor expanded in x around 0 65.1%

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

      1. associate-/l* 65.1%

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

   9. Simplified 65.1%

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

   if 1.84999999999999998e123 < t

   1. Initial program 52.0%

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

   3. Taylor expanded in t around inf 53.7%

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

      1. associate--l+ 56.2%

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

      2. associate-/l* 56.3%

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

      3. associate-/l* 66.4%

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

      4. +-commutative 66.4%

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

      5. associate-/l* 74.2%

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

      6. +-commutative 74.2%

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

      7. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in z around -inf 61.1%

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

   7. Taylor expanded in x around inf 62.6%

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

      1. associate-/l* 70.1%

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

   9. Simplified 70.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+164}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+98}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{+59}:\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 10^{-12}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -9.6e-36)
     t_1
     (if (<= y 2.5e-43)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 1e-12) (* z (/ (+ x y) (+ y (+ x t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -9.6e-36) {
		tmp = t_1;
	} else if (y <= 2.5e-43) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1e-12) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-9.6d-36)) then
        tmp = t_1
    else if (y <= 2.5d-43) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 1d-12) then
        tmp = z * ((x + y) / (y + (x + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -9.6e-36) {
		tmp = t_1;
	} else if (y <= 2.5e-43) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1e-12) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -9.6e-36:
		tmp = t_1
	elif y <= 2.5e-43:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 1e-12:
		tmp = z * ((x + y) / (y + (x + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -9.6e-36)
		tmp = t_1;
	elseif (y <= 2.5e-43)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 1e-12)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -9.6e-36)
		tmp = t_1;
	elseif (y <= 2.5e-43)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 1e-12)
		tmp = z * ((x + y) / (y + (x + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -9.6e-36], t$95$1, If[LessEqual[y, 2.5e-43], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-12], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.6e-36 or 9.9999999999999998e-13 < y

   1. Initial program 43.3%

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

   3. Taylor expanded in y around inf 69.4%

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

   if -9.6e-36 < y < 2.50000000000000009e-43

   1. Initial program 76.0%

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

   3. Taylor expanded in y around 0 63.1%

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

   if 2.50000000000000009e-43 < y < 9.9999999999999998e-13

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 55.0%

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

      1. associate-/l* 82.3%

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

      2. +-commutative 82.3%

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

      3. +-commutative 82.3%

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

      4. +-commutative 82.3%

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

      5. associate-+l+ 82.3%

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

      6. +-commutative 82.3%

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

   5. Simplified 82.3%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-36}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 10^{-12}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+57} \lor \neg \left(t \leq 3.6 \cdot 10^{+132}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.2e+57) (not (<= t 3.6e+132)))
   (* a (/ t (+ x t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e+57) || !(t <= 3.6e+132)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.2d+57)) .or. (.not. (t <= 3.6d+132))) then
        tmp = a * (t / (x + t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e+57) || !(t <= 3.6e+132)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.2e+57) or not (t <= 3.6e+132):
		tmp = a * (t / (x + t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.2e+57) || !(t <= 3.6e+132))
		tmp = Float64(a * Float64(t / Float64(x + t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.2e+57) || ~((t <= 3.6e+132)))
		tmp = a * (t / (x + t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.2e+57], N[Not[LessEqual[t, 3.6e+132]], $MachinePrecision]], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.20000000000000002e57 or 3.60000000000000016e132 < t

   1. Initial program 54.0%

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

   3. Taylor expanded in a around inf 34.0%

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

      1. associate-/l* 61.6%

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

      2. +-commutative 61.6%

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

      3. +-commutative 61.6%

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

      4. associate-+l+ 61.6%

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

      5. +-commutative 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in y around 0 35.1%

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

      1. associate-/l* 61.6%

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

   8. Simplified 61.6%

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

   if -1.20000000000000002e57 < t < 3.60000000000000016e132

   1. Initial program 61.1%

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

   3. Taylor expanded in y around inf 60.6%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+57} \lor \neg \left(t \leq 3.6 \cdot 10^{+132}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.55e+54)
   (* a (/ t (+ x t)))
   (if (<= t 3.4e+123) (- (+ z a) b) (+ a (* x (/ z t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.55e+54) {
		tmp = a * (t / (x + t));
	} else if (t <= 3.4e+123) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (x * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.55d+54)) then
        tmp = a * (t / (x + t))
    else if (t <= 3.4d+123) then
        tmp = (z + a) - b
    else
        tmp = a + (x * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.55e+54) {
		tmp = a * (t / (x + t));
	} else if (t <= 3.4e+123) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.55e+54:
		tmp = a * (t / (x + t))
	elif t <= 3.4e+123:
		tmp = (z + a) - b
	else:
		tmp = a + (x * (z / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.55e+54)
		tmp = Float64(a * Float64(t / Float64(x + t)));
	elseif (t <= 3.4e+123)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.55e+54)
		tmp = a * (t / (x + t));
	elseif (t <= 3.4e+123)
		tmp = (z + a) - b;
	else
		tmp = a + (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.55e+54], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+123], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55e54

   1. Initial program 55.1%

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

   3. Taylor expanded in a around inf 33.0%

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

      1. associate-/l* 61.2%

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

      2. +-commutative 61.2%

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

      3. +-commutative 61.2%

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

      4. associate-+l+ 61.2%

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

      5. +-commutative 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in y around 0 33.0%

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

      1. associate-/l* 61.2%

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

   8. Simplified 61.2%

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

   if -1.55e54 < t < 3.40000000000000001e123

   1. Initial program 61.3%

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

   3. Taylor expanded in y around inf 61.3%

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

   if 3.40000000000000001e123 < t

   1. Initial program 52.0%

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

   3. Taylor expanded in t around inf 53.7%

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

      1. associate--l+ 56.2%

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

      2. associate-/l* 56.3%

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

      3. associate-/l* 66.4%

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

      4. +-commutative 66.4%

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

      5. associate-/l* 74.2%

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

      6. +-commutative 74.2%

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

      7. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in z around -inf 61.1%

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

   7. Taylor expanded in x around inf 62.6%

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

      1. associate-/l* 70.1%

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

   9. Simplified 70.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+154}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+71}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.2e+154) z (if (<= x 1.45e+71) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.2e+154) {
		tmp = z;
	} else if (x <= 1.45e+71) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.2d+154)) then
        tmp = z
    else if (x <= 1.45d+71) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.2e+154) {
		tmp = z;
	} else if (x <= 1.45e+71) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.2e+154:
		tmp = z
	elif x <= 1.45e+71:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.2e+154)
		tmp = z;
	elseif (x <= 1.45e+71)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.2e+154)
		tmp = z;
	elseif (x <= 1.45e+71)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.2e+154], z, If[LessEqual[x, 1.45e+71], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2000000000000003e154 or 1.45000000000000004e71 < x

   1. Initial program 47.0%

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

   3. Taylor expanded in x around inf 56.9%

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

   if -6.2000000000000003e154 < x < 1.45000000000000004e71

   1. Initial program 64.3%

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

   3. Taylor expanded in t around inf 45.6%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+154}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+71}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+164}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.3e+164) a (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.3e+164) {
		tmp = a;
	} 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 (t <= (-3.3d+164)) then
        tmp = a
    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 (t <= -3.3e+164) {
		tmp = a;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.3e+164:
		tmp = a
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.3e+164)
		tmp = a;
	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 (t <= -3.3e+164)
		tmp = a;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.3e+164], a, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.29999999999999995e164

   1. Initial program 51.1%

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

   3. Taylor expanded in t around inf 70.4%

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

   if -3.29999999999999995e164 < t

   1. Initial program 59.4%

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

   3. Taylor expanded in y around inf 56.3%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+164}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.6% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.5%

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

3. Taylor expanded in t around inf 34.5%

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

4. Final simplification 34.5%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.5% 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 2024040 
(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)))