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

Percentage Accurate: 60.5% → 87.9%

Time: 11.7s

Alternatives: 7

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.5% 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: 87.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := t + \left(x + y\right)\\ t_3 := z \cdot \left(\mathsf{fma}\left(\frac{y + t}{t\_1}, \frac{a}{z}, b \cdot \frac{y}{z \cdot \left(0 - t\_1\right)}\right) + \frac{x + y}{t\_2}\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+37}:\\ \;\;\;\;a \cdot \left(\frac{y + t}{t\_2} - \frac{y \cdot \left(b - z\right) - z \cdot x}{t\_2 \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t)))
        (t_2 (+ t (+ x y)))
        (t_3
         (*
          z
          (+
           (fma (/ (+ y t) t_1) (/ a z) (* b (/ y (* z (- 0.0 t_1)))))
           (/ (+ x y) t_2)))))
   (if (<= z -2.5e-33)
     t_3
     (if (<= z 3.1e+37)
       (* a (- (/ (+ y t) t_2) (/ (- (* y (- b z)) (* z x)) (* t_2 a))))
       t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = t + (x + y);
	double t_3 = z * (fma(((y + t) / t_1), (a / z), (b * (y / (z * (0.0 - t_1))))) + ((x + y) / t_2));
	double tmp;
	if (z <= -2.5e-33) {
		tmp = t_3;
	} else if (z <= 3.1e+37) {
		tmp = a * (((y + t) / t_2) - (((y * (b - z)) - (z * x)) / (t_2 * a)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(t + Float64(x + y))
	t_3 = Float64(z * Float64(fma(Float64(Float64(y + t) / t_1), Float64(a / z), Float64(b * Float64(y / Float64(z * Float64(0.0 - t_1))))) + Float64(Float64(x + y) / t_2)))
	tmp = 0.0
	if (z <= -2.5e-33)
		tmp = t_3;
	elseif (z <= 3.1e+37)
		tmp = Float64(a * Float64(Float64(Float64(y + t) / t_2) - Float64(Float64(Float64(y * Float64(b - z)) - Float64(z * x)) / Float64(t_2 * a))));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision] * N[(a / z), $MachinePrecision] + N[(b * N[(y / N[(z * N[(0.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-33], t$95$3, If[LessEqual[z, 3.1e+37], N[(a * N[(N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision] - N[(N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] - N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t$95$2 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000014e-33 or 3.1000000000000002e37 < z

   1. Initial program 46.6%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)\right)\right)\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}}\right)\right)\right) \]

   5. Simplified 71.0%

      \[\leadsto \color{blue}{0 - z \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)} \]
   6. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \left(\frac{a \cdot \left(t + y\right)}{z \cdot \left(t + \left(y + x\right)\right)} - \color{blue}{\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}}\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \left(\frac{\left(t + y\right) \cdot a}{z \cdot \left(t + \left(y + x\right)\right)} - \frac{\color{blue}{y} \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \left(\frac{\left(t + y\right) \cdot a}{\left(t + \left(y + x\right)\right) \cdot z} - \frac{y \cdot \color{blue}{b}}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right) \]

      4. times-frac N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \left(\frac{t + y}{t + \left(y + x\right)} \cdot \frac{a}{z} - \frac{\color{blue}{y \cdot b}}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right) \]

      5. fmm-def N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \left(\mathsf{fma}\left(\frac{t + y}{t + \left(y + x\right)}, \color{blue}{\frac{a}{z}}, \mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\left(\frac{t + y}{t + \left(y + x\right)}\right), \color{blue}{\left(\frac{a}{z}\right)}, \left(\mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(t + y\right), \left(t + \left(y + x\right)\right)\right), \left(\frac{\color{blue}{a}}{z}\right), \left(\mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(y + t\right), \left(t + \left(y + x\right)\right)\right), \left(\frac{a}{z}\right), \left(\mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(t + \left(y + x\right)\right)\right), \left(\frac{a}{z}\right), \left(\mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\left(t + y\right) + x\right)\right), \left(\frac{a}{z}\right), \left(\mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(x + \left(t + y\right)\right)\right), \left(\frac{a}{z}\right), \left(\mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \mathsf{+.f64}\left(x, \left(t + y\right)\right)\right), \left(\frac{a}{z}\right), \left(\mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \mathsf{+.f64}\left(x, \left(y + t\right)\right)\right), \left(\frac{a}{z}\right), \left(\mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \left(\frac{a}{z}\right), \left(\mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{/.f64}\left(a, \color{blue}{z}\right), \left(\mathsf{neg}\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      16. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{/.f64}\left(a, z\right), \mathsf{neg.f64}\left(\left(\frac{y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{/.f64}\left(a, z\right), \mathsf{neg.f64}\left(\left(\frac{b \cdot y}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      18. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{/.f64}\left(a, z\right), \mathsf{neg.f64}\left(\left(b \cdot \frac{y}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{/.f64}\left(a, z\right), \mathsf{neg.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{y}{z \cdot \left(t + \left(y + x\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

      20. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{/.f64}\left(a, z\right), \mathsf{neg.f64}\left(\mathsf{*.f64}\left(b, \mathsf{/.f64}\left(y, \left(z \cdot \left(t + \left(y + x\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Applied egg-rr 92.2%

      \[\leadsto 0 - z \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \color{blue}{\mathsf{fma}\left(\frac{y + t}{x + \left(y + t\right)}, \frac{a}{z}, -b \cdot \frac{y}{z \cdot \left(x + \left(y + t\right)\right)}\right)}\right) \]

   if -2.50000000000000014e-33 < z < 3.1000000000000002e37

   1. Initial program 70.6%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(-1 \cdot \frac{t + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a\right)\right), \left(\color{blue}{-1 \cdot \frac{t + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(0 - a\right), \left(\color{blue}{-1 \cdot \frac{t + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \left(\color{blue}{-1 \cdot \frac{t + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \left(-1 \cdot \frac{t + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \left(-1 \cdot \frac{t + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\left(-1 \cdot \frac{t + y}{t + \left(x + y\right)}\right), \color{blue}{\left(\frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)}\right)\right) \]

   5. Simplified 85.0%

      \[\leadsto \color{blue}{\left(0 - a\right) \cdot \left(\frac{t + y}{-\left(t + \left(y + x\right)\right)} - \frac{z \cdot x + y \cdot \left(z - b\right)}{a \cdot \left(t + \left(y + x\right)\right)}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(\mathsf{fma}\left(\frac{y + t}{x + \left(y + t\right)}, \frac{a}{z}, b \cdot \frac{y}{z \cdot \left(0 - \left(x + \left(y + t\right)\right)\right)}\right) + \frac{x + y}{t + \left(x + y\right)}\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+37}:\\ \;\;\;\;a \cdot \left(\frac{y + t}{t + \left(x + y\right)} - \frac{y \cdot \left(b - z\right) - z \cdot x}{\left(t + \left(x + y\right)\right) \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\mathsf{fma}\left(\frac{y + t}{x + \left(y + t\right)}, \frac{a}{z}, b \cdot \frac{y}{z \cdot \left(0 - \left(x + \left(y + t\right)\right)\right)}\right) + \frac{x + y}{t + \left(x + y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+288}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t))))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 1e+288) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+288) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 1e+288) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	t_2 = (z + a) - b
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 1e+288:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+288)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 1e+288)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+288], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1e288 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.5%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 68.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 68.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e288

   1. Initial program 99.7%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+288}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(z \cdot x + y \cdot \left(z + a\right)\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(\frac{\frac{t \cdot a}{z}}{x + t} - \frac{-1}{\frac{t}{x} + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -8.2e+97)
     t_1
     (if (<= y -1.7e-144)
       (/ (- (+ (* z x) (* y (+ z a))) (* y b)) (+ x y))
       (if (<= y 1.7e-57)
         (* z (- (/ (/ (* t a) z) (+ x t)) (/ -1.0 (+ (/ t x) 1.0))))
         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 <= -8.2e+97) {
		tmp = t_1;
	} else if (y <= -1.7e-144) {
		tmp = (((z * x) + (y * (z + a))) - (y * b)) / (x + y);
	} else if (y <= 1.7e-57) {
		tmp = z * ((((t * a) / z) / (x + t)) - (-1.0 / ((t / x) + 1.0)));
	} 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 <= (-8.2d+97)) then
        tmp = t_1
    else if (y <= (-1.7d-144)) then
        tmp = (((z * x) + (y * (z + a))) - (y * b)) / (x + y)
    else if (y <= 1.7d-57) then
        tmp = z * ((((t * a) / z) / (x + t)) - ((-1.0d0) / ((t / x) + 1.0d0)))
    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 <= -8.2e+97) {
		tmp = t_1;
	} else if (y <= -1.7e-144) {
		tmp = (((z * x) + (y * (z + a))) - (y * b)) / (x + y);
	} else if (y <= 1.7e-57) {
		tmp = z * ((((t * a) / z) / (x + t)) - (-1.0 / ((t / x) + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -8.2e+97:
		tmp = t_1
	elif y <= -1.7e-144:
		tmp = (((z * x) + (y * (z + a))) - (y * b)) / (x + y)
	elif y <= 1.7e-57:
		tmp = z * ((((t * a) / z) / (x + t)) - (-1.0 / ((t / x) + 1.0)))
	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 <= -8.2e+97)
		tmp = t_1;
	elseif (y <= -1.7e-144)
		tmp = Float64(Float64(Float64(Float64(z * x) + Float64(y * Float64(z + a))) - Float64(y * b)) / Float64(x + y));
	elseif (y <= 1.7e-57)
		tmp = Float64(z * Float64(Float64(Float64(Float64(t * a) / z) / Float64(x + t)) - Float64(-1.0 / Float64(Float64(t / x) + 1.0))));
	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 <= -8.2e+97)
		tmp = t_1;
	elseif (y <= -1.7e-144)
		tmp = (((z * x) + (y * (z + a))) - (y * b)) / (x + y);
	elseif (y <= 1.7e-57)
		tmp = z * ((((t * a) / z) / (x + t)) - (-1.0 / ((t / x) + 1.0)));
	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, -8.2e+97], t$95$1, If[LessEqual[y, -1.7e-144], N[(N[(N[(N[(z * x), $MachinePrecision] + N[(y * N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-57], N[(z * N[(N[(N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision] - N[(-1.0 / N[(N[(t / x), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.19999999999999977e97 or 1.70000000000000008e-57 < y

   1. Initial program 40.3%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 77.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 77.6%

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

   if -8.19999999999999977e97 < y < -1.70000000000000009e-144

   1. Initial program 75.4%

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

   3. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right), \color{blue}{\left(x + y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot y + z \cdot \left(x + y\right)\right), \left(b \cdot y\right)\right), \left(\color{blue}{x} + y\right)\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot y + \left(x \cdot z + y \cdot z\right)\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot y + \left(y \cdot z + x \cdot z\right)\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\left(a \cdot y + y \cdot z\right) + x \cdot z\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\left(y \cdot a + y \cdot z\right) + x \cdot z\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      7. distribute-lft-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(y \cdot \left(a + z\right) + x \cdot z\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot z + y \cdot \left(a + z\right)\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(x \cdot z\right), \left(y \cdot \left(a + z\right)\right)\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(z \cdot x\right), \left(y \cdot \left(a + z\right)\right)\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(y \cdot \left(a + z\right)\right)\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \left(a + z\right)\right)\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, z\right)\right)\right), \left(b \cdot y\right)\right), \left(x + y\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, z\right)\right)\right), \left(y \cdot b\right)\right), \left(x + y\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, z\right)\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \left(x + y\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, z\right)\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \left(y + \color{blue}{x}\right)\right) \]

      17. +-lowering-+.f64 65.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, z\right)\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 65.2%

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

   if -1.70000000000000009e-144 < y < 1.70000000000000008e-57

   1. Initial program 71.9%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)\right)\right)\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}}\right)\right)\right) \]

   5. Simplified 78.4%

      \[\leadsto \color{blue}{0 - z \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \color{blue}{\left(x \cdot \left(1 + \left(\frac{t}{x} + \frac{y}{x}\right)\right)\right)}\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{*.f64}\left(x, \left(1 + \left(\frac{t}{x} + \frac{y}{x}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \color{blue}{\mathsf{*.f64}\left(y, b\right)}\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{*.f64}\left(x, \left(\left(1 + \frac{t}{x}\right) + \frac{y}{x}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(1 + \frac{t}{x}\right), \left(\frac{y}{x}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{t}{x}\right)\right), \left(\frac{y}{x}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(t, x\right)\right), \left(\frac{y}{x}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right) \]

      6. /-lowering-/.f64 78.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(y, x\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right) \]

   8. Simplified 78.4%

      \[\leadsto 0 - z \cdot \left(\frac{\left(-x\right) - y}{\color{blue}{x \cdot \left(\left(1 + \frac{t}{x}\right) + \frac{y}{x}\right)}} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right) \]

   9. Taylor expanded in y around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{1 + \frac{t}{x}} + \frac{a \cdot t}{z \cdot \left(t + x\right)}\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{1}{1 + \frac{t}{x}}\right), \color{blue}{\left(\frac{a \cdot t}{z \cdot \left(t + x\right)}\right)}\right)\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \left(1 + \frac{t}{x}\right)\right), \left(\frac{\color{blue}{a \cdot t}}{z \cdot \left(t + x\right)}\right)\right)\right) \]

       4. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \left(\frac{t}{x}\right)\right)\right), \left(\frac{a \cdot \color{blue}{t}}{z \cdot \left(t + x\right)}\right)\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(t, x\right)\right)\right), \left(\frac{a \cdot t}{z \cdot \left(t + x\right)}\right)\right)\right) \]

       6. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(t, x\right)\right)\right), \left(\frac{\frac{a \cdot t}{z}}{\color{blue}{t + x}}\right)\right)\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(t, x\right)\right)\right), \mathsf{/.f64}\left(\left(\frac{a \cdot t}{z}\right), \color{blue}{\left(t + x\right)}\right)\right)\right) \]

       8. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(t, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(a \cdot t\right), z\right), \left(\color{blue}{t} + x\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(t, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), z\right), \left(t + x\right)\right)\right)\right) \]

       10. +-lowering-+.f64 66.9%

           \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(t, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), z\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right)\right)\right) \]

   11. Simplified 66.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+97}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(z \cdot x + y \cdot \left(z + a\right)\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(\frac{\frac{t \cdot a}{z}}{x + t} - \frac{-1}{\frac{t}{x} + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+129}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+141}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.7e+129) z (if (<= x 6.8e+141) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.7e+129) {
		tmp = z;
	} else if (x <= 6.8e+141) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.7d+129)) then
        tmp = z
    else if (x <= 6.8d+141) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.7e+129) {
		tmp = z;
	} else if (x <= 6.8e+141) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.7e+129:
		tmp = z
	elif x <= 6.8e+141:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.7e+129)
		tmp = z;
	elseif (x <= 6.8e+141)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.7e+129)
		tmp = z;
	elseif (x <= 6.8e+141)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.7e+129], z, If[LessEqual[x, 6.8e+141], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000001e129 or 6.7999999999999996e141 < x

   1. Initial program 50.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{z} \]
   4. Step-by-step derivation

   5. Simplified 55.7%

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

   if -2.7000000000000001e129 < x < 6.7999999999999996e141

   1. Initial program 62.6%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 67.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 67.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+129}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+141}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{+126}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \frac{z - b}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.2e+126) (- (+ z a) b) (+ a (* y (/ (- z b) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.2e+126) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (y * ((z - b) / 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 <= 1.2d+126) then
        tmp = (z + a) - b
    else
        tmp = a + (y * ((z - b) / 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 <= 1.2e+126) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (y * ((z - b) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.2e+126:
		tmp = (z + a) - b
	else:
		tmp = a + (y * ((z - b) / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.2e+126)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(y * Float64(Float64(z - b) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.2e+126)
		tmp = (z + a) - b;
	else
		tmp = a + (y * ((z - b) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.2e+126], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(y * N[(N[(z - b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.20000000000000006e126

   1. Initial program 63.4%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 62.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 62.7%

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

   if 1.20000000000000006e126 < t

   1. Initial program 31.9%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot \left(t + y\right) + y \cdot z\right) - b \cdot y\right), \color{blue}{\left(t + y\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t + y\right) + \left(y \cdot z - b \cdot y\right)\right), \left(\color{blue}{t} + y\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(t + y\right)\right), \left(y \cdot z - b \cdot y\right)\right), \left(\color{blue}{t} + y\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(t + y\right)\right), \left(y \cdot z - b \cdot y\right)\right), \left(t + y\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \left(y \cdot z - b \cdot y\right)\right), \left(t + y\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \left(y \cdot z - y \cdot b\right)\right), \left(t + y\right)\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \left(y \cdot \left(z - b\right)\right)\right), \left(t + y\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, \left(z - b\right)\right)\right), \left(t + y\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, b\right)\right)\right), \left(t + y\right)\right) \]

      10. +-lowering-+.f64 24.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, b\right)\right)\right), \mathsf{+.f64}\left(t, \color{blue}{y}\right)\right) \]

   5. Simplified 24.2%

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

   6. Taylor expanded in t around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{y \cdot \left(z - b\right)}{t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(y \cdot \left(z - b\right)\right), \color{blue}{t}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - b\right)\right), t\right)\right) \]

      4. --lowering--.f64 50.6%

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, b\right)\right), t\right)\right) \]

   8. Simplified 50.6%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(a, \left(y \cdot \color{blue}{\frac{z - b}{t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(a, \left(\frac{z - b}{t} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{z - b}{t}\right), \color{blue}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - b\right), t\right), y\right)\right) \]

      5. --lowering--.f64 75.4%

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, b\right), t\right), y\right)\right) \]

   10. Applied egg-rr 75.4%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{+126}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \frac{z - b}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 44.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+46}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+85}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.6e+46) a (if (<= a 8.5e+85) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.6e+46) {
		tmp = a;
	} else if (a <= 8.5e+85) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.6d+46)) then
        tmp = a
    else if (a <= 8.5d+85) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.6e+46) {
		tmp = a;
	} else if (a <= 8.5e+85) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.6e+46:
		tmp = a
	elif a <= 8.5e+85:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.6e+46)
		tmp = a;
	elseif (a <= 8.5e+85)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.6e+46)
		tmp = a;
	elseif (a <= 8.5e+85)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.6e+46], a, If[LessEqual[a, 8.5e+85], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5999999999999999e46 or 8.4999999999999994e85 < a

   1. Initial program 45.7%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a} \]
   4. Step-by-step derivation

   5. Simplified 56.4%

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

   if -1.5999999999999999e46 < a < 8.4999999999999994e85

   1. Initial program 68.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{z} \]
   4. Step-by-step derivation

   5. Simplified 47.8%

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

Alternative 7: 33.0% 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 58.6%

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

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{a} \]
4. Step-by-step derivation

5. Simplified 32.8%

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

Developer Target 1: 82.8% 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 2024150 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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