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

Percentage Accurate: 61.1% → 97.6%

Time: 13.6s

Alternatives: 12

Speedup: 1.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.1% 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: 97.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \left(x + t\right) + y\\ z \cdot \left(\frac{x}{t_2} + \frac{y}{t_2}\right) + \left(a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right) + \frac{-1}{\frac{t_2}{b} \cdot \frac{1}{y}}\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (+ (+ x t) y)))
   (+
    (* z (+ (/ x t_2) (/ y t_2)))
    (+ (* a (+ (/ y t_1) (/ t t_1))) (/ -1.0 (* (/ t_2 b) (/ 1.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = (x + t) + y;
	return (z * ((x / t_2) + (y / t_2))) + ((a * ((y / t_1) + (t / t_1))) + (-1.0 / ((t_2 / b) * (1.0 / 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
    real(8) :: t_1
    real(8) :: t_2
    t_1 = t + (x + y)
    t_2 = (x + t) + y
    code = (z * ((x / t_2) + (y / t_2))) + ((a * ((y / t_1) + (t / t_1))) + ((-1.0d0) / ((t_2 / b) * (1.0d0 / y))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = (x + t) + y;
	return (z * ((x / t_2) + (y / t_2))) + ((a * ((y / t_1) + (t / t_1))) + (-1.0 / ((t_2 / b) * (1.0 / y))));
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = (x + t) + y
	return (z * ((x / t_2) + (y / t_2))) + ((a * ((y / t_1) + (t / t_1))) + (-1.0 / ((t_2 / b) * (1.0 / y))))

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(x + t) + y)
	return Float64(Float64(z * Float64(Float64(x / t_2) + Float64(y / t_2))) + Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) + Float64(-1.0 / Float64(Float64(t_2 / b) * Float64(1.0 / y)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = (x + t) + y;
	tmp = (z * ((x / t_2) + (y / t_2))) + ((a * ((y / t_1) + (t / t_1))) + (-1.0 / ((t_2 / b) * (1.0 / y))));
end

Wolfram

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

Derivation

1. Initial program 58.0%

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

2. Taylor expanded in z around 0 71.4%

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

   1. associate--l+ 71.4%

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

   2. associate-+r+ 71.4%

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

   3. associate-+r+ 71.4%

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

   4. div-sub 71.4%

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

   5. *-commutative 71.4%

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

   6. associate-+r+ 71.4%

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

4. Simplified 71.4%

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

5. Taylor expanded in a around 0 87.2%

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

   1. +-commutative 87.2%

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

   2. +-commutative 87.2%

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

   3. +-commutative 87.2%

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

   4. +-commutative 87.2%

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

   5. mul-1-neg 87.2%

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

   6. unsub-neg 87.2%

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

   7. +-commutative 87.2%

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

7. Simplified 87.2%

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

   1. clear-num 87.2%

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

   2. inv-pow 87.2%

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

   3. associate-+r+ 87.2%

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

   4. +-commutative 87.2%

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

   5. associate-+r+ 87.2%

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

9. Applied egg-rr 87.2%

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

    1. unpow-1 87.2%

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

    2. associate-+r+ 87.2%

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

11. Simplified 87.2%

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

    1. associate-/r* 97.5%

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

    2. div-inv 97.5%

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

    3. associate-+l+ 97.5%

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

13. Applied egg-rr 97.5%

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

14. Final simplification 97.5%

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

Alternative 2: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := a \cdot \left(t + y\right)\\ t_3 := \frac{\left(t_2 + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{+304} \lor \neg \left(t_3 \leq 2 \cdot 10^{+261}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right) + \frac{t_2 - y \cdot b}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (* a (+ t y)))
        (t_3 (/ (- (+ t_2 (* z (+ x y))) (* y b)) t_1)))
   (if (or (<= t_3 -5e+304) (not (<= t_3 2e+261)))
     (- (+ z a) b)
     (+ (* z (+ (/ x t_1) (/ y t_1))) (/ (- t_2 (* y b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = a * (t + y);
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_3 <= -5e+304) || !(t_3 <= 2e+261)) {
		tmp = (z + a) - b;
	} else {
		tmp = (z * ((x / t_1) + (y / t_1))) + ((t_2 - (y * b)) / 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = a * (t + y)
    t_3 = ((t_2 + (z * (x + y))) - (y * b)) / t_1
    if ((t_3 <= (-5d+304)) .or. (.not. (t_3 <= 2d+261))) then
        tmp = (z + a) - b
    else
        tmp = (z * ((x / t_1) + (y / t_1))) + ((t_2 - (y * b)) / 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 = (x + t) + y;
	double t_2 = a * (t + y);
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_3 <= -5e+304) || !(t_3 <= 2e+261)) {
		tmp = (z + a) - b;
	} else {
		tmp = (z * ((x / t_1) + (y / t_1))) + ((t_2 - (y * b)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = a * (t + y)
	t_3 = ((t_2 + (z * (x + y))) - (y * b)) / t_1
	tmp = 0
	if (t_3 <= -5e+304) or not (t_3 <= 2e+261):
		tmp = (z + a) - b
	else:
		tmp = (z * ((x / t_1) + (y / t_1))) + ((t_2 - (y * b)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(a * Float64(t + y))
	t_3 = Float64(Float64(Float64(t_2 + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_3 <= -5e+304) || !(t_3 <= 2e+261))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))) + Float64(Float64(t_2 - Float64(y * b)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = a * (t + y);
	t_3 = ((t_2 + (z * (x + y))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_3 <= -5e+304) || ~((t_3 <= 2e+261)))
		tmp = (z + a) - b;
	else
		tmp = (z * ((x / t_1) + (y / t_1))) + ((t_2 - (y * b)) / t_1);
	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[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$3, -5e+304], N[Not[LessEqual[t$95$3, 2e+261]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $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)) < -4.9999999999999997e304 or 1.9999999999999999e261 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.8%

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

   2. Taylor expanded in y around inf 75.5%

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

   if -4.9999999999999997e304 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e261

   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. Taylor expanded in z around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-+r+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. div-sub 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-+r+ 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+304} \lor \neg \left(\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq 2 \cdot 10^{+261}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{\left(x + t\right) + y} + \frac{y}{\left(x + t\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array} \]

Alternative 3: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+304} \lor \neg \left(t_1 \leq 2 \cdot 10^{+261}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ t y)) (* z (+ x y))) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -5e+304) (not (<= t_1 2e+261))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e+304) || !(t_1 <= 2e+261)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / ((x + t) + y)
    if ((t_1 <= (-5d+304)) .or. (.not. (t_1 <= 2d+261))) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e+304) || !(t_1 <= 2e+261)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / ((x + t) + y)
	tmp = 0
	if (t_1 <= -5e+304) or not (t_1 <= 2e+261):
		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(a * Float64(t + y)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -5e+304) || !(t_1 <= 2e+261))
		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 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / ((x + t) + y);
	tmp = 0.0;
	if ((t_1 <= -5e+304) || ~((t_1 <= 2e+261)))
		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[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+304], N[Not[LessEqual[t$95$1, 2e+261]], $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)) < -4.9999999999999997e304 or 1.9999999999999999e261 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.8%

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

   2. Taylor expanded in y around inf 75.5%

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

   if -4.9999999999999997e304 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e261

   1. Initial program 99.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+304} \lor \neg \left(\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{\left(x + t\right) + y} \leq 2 \cdot 10^{+261}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array} \]

Alternative 4: 91.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \left(x + t\right) + y\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+210} \lor \neg \left(y \leq 2.15 \cdot 10^{+107}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_2} + \frac{y}{t_2}\right) + \left(a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right) - \frac{y \cdot b}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (+ (+ x t) y)))
   (if (or (<= y -4.1e+210) (not (<= y 2.15e+107)))
     (- (+ z a) b)
     (+
      (* z (+ (/ x t_2) (/ y t_2)))
      (- (* a (+ (/ y t_1) (/ t t_1))) (/ (* y b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = (x + t) + y;
	double tmp;
	if ((y <= -4.1e+210) || !(y <= 2.15e+107)) {
		tmp = (z + a) - b;
	} else {
		tmp = (z * ((x / t_2) + (y / t_2))) + ((a * ((y / t_1) + (t / t_1))) - ((y * b) / 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) :: t_2
    real(8) :: tmp
    t_1 = t + (x + y)
    t_2 = (x + t) + y
    if ((y <= (-4.1d+210)) .or. (.not. (y <= 2.15d+107))) then
        tmp = (z + a) - b
    else
        tmp = (z * ((x / t_2) + (y / t_2))) + ((a * ((y / t_1) + (t / t_1))) - ((y * b) / 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 = t + (x + y);
	double t_2 = (x + t) + y;
	double tmp;
	if ((y <= -4.1e+210) || !(y <= 2.15e+107)) {
		tmp = (z + a) - b;
	} else {
		tmp = (z * ((x / t_2) + (y / t_2))) + ((a * ((y / t_1) + (t / t_1))) - ((y * b) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = (x + t) + y
	tmp = 0
	if (y <= -4.1e+210) or not (y <= 2.15e+107):
		tmp = (z + a) - b
	else:
		tmp = (z * ((x / t_2) + (y / t_2))) + ((a * ((y / t_1) + (t / t_1))) - ((y * b) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(x + t) + y)
	tmp = 0.0
	if ((y <= -4.1e+210) || !(y <= 2.15e+107))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(z * Float64(Float64(x / t_2) + Float64(y / t_2))) + Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) - Float64(Float64(y * b) / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = (x + t) + y;
	tmp = 0.0;
	if ((y <= -4.1e+210) || ~((y <= 2.15e+107)))
		tmp = (z + a) - b;
	else
		tmp = (z * ((x / t_2) + (y / t_2))) + ((a * ((y / t_1) + (t / t_1))) - ((y * b) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, If[Or[LessEqual[y, -4.1e+210], N[Not[LessEqual[y, 2.15e+107]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.10000000000000001e210 or 2.15e107 < y

   1. Initial program 23.7%

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

   2. Taylor expanded in y around inf 86.9%

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

   if -4.10000000000000001e210 < y < 2.15e107

   1. Initial program 69.2%

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

   2. Taylor expanded in z around 0 81.3%

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

      1. associate--l+ 81.3%

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

      2. associate-+r+ 81.3%

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

      3. associate-+r+ 81.3%

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

      4. div-sub 81.3%

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

      5. *-commutative 81.3%

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

      6. associate-+r+ 81.3%

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

   4. Simplified 81.3%

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

   5. Taylor expanded in a around 0 95.5%

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

      1. +-commutative 95.5%

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

      2. +-commutative 95.5%

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

      3. +-commutative 95.5%

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

      4. +-commutative 95.5%

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

      5. mul-1-neg 95.5%

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

      6. unsub-neg 95.5%

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

      7. +-commutative 95.5%

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

   7. Simplified 95.5%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+210} \lor \neg \left(y \leq 2.15 \cdot 10^{+107}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{\left(x + t\right) + y} + \frac{y}{\left(x + t\right) + y}\right) + \left(a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{t + \left(x + y\right)}\right) - \frac{y \cdot b}{t + \left(x + y\right)}\right)\\ \end{array} \]

Alternative 5: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-149}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 10^{+61}:\\ \;\;\;\;\frac{y \cdot \left(a - b\right) + z \cdot \left(x + y\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -5.6e-13)
     t_1
     (if (<= y 1.2e-149)
       (/ (+ (* t a) (* z x)) (+ x t))
       (if (<= y 1e+61) (/ (+ (* y (- a b)) (* z (+ x y))) (+ x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5.6e-13) {
		tmp = t_1;
	} else if (y <= 1.2e-149) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (y <= 1e+61) {
		tmp = ((y * (a - b)) + (z * (x + y))) / (x + y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-5.6d-13)) then
        tmp = t_1
    else if (y <= 1.2d-149) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if (y <= 1d+61) then
        tmp = ((y * (a - b)) + (z * (x + y))) / (x + y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5.6e-13) {
		tmp = t_1;
	} else if (y <= 1.2e-149) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (y <= 1e+61) {
		tmp = ((y * (a - b)) + (z * (x + y))) / (x + y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -5.6e-13:
		tmp = t_1
	elif y <= 1.2e-149:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif y <= 1e+61:
		tmp = ((y * (a - b)) + (z * (x + y))) / (x + y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5.6e-13)
		tmp = t_1;
	elseif (y <= 1.2e-149)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif (y <= 1e+61)
		tmp = Float64(Float64(Float64(y * Float64(a - b)) + Float64(z * Float64(x + y))) / Float64(x + y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5.6e-13)
		tmp = t_1;
	elseif (y <= 1.2e-149)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif (y <= 1e+61)
		tmp = ((y * (a - b)) + (z * (x + y))) / (x + y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5.6e-13], t$95$1, If[LessEqual[y, 1.2e-149], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+61], N[(N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6000000000000004e-13 or 9.99999999999999949e60 < y

   1. Initial program 37.9%

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

   2. Taylor expanded in y around inf 77.0%

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

   if -5.6000000000000004e-13 < y < 1.2000000000000001e-149

   1. Initial program 78.1%

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

   2. Taylor expanded in y around 0 65.5%

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

   if 1.2000000000000001e-149 < y < 9.99999999999999949e60

   1. Initial program 75.9%

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

   2. Taylor expanded in t around 0 60.9%

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

      1. sub-neg 60.9%

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

      2. mul-1-neg 60.9%

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

      3. +-commutative 60.9%

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

      4. associate-+r+ 60.9%

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

      5. +-commutative 60.9%

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

      6. associate-*r* 60.9%

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

      7. distribute-rgt-in 60.9%

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

      8. mul-1-neg 60.9%

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

      9. +-commutative 60.9%

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

      10. +-commutative 60.9%

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

   4. Simplified 60.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-13}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-149}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 10^{+61}:\\ \;\;\;\;\frac{y \cdot \left(a - b\right) + z \cdot \left(x + y\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 6: 59.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+218}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+138}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{t_1}{t + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y)) (t_2 (- (+ z a) b)))
   (if (<= t -2.9e+218)
     a
     (if (<= t 5.2e+67)
       t_2
       (if (<= t 8.2e+138)
         (/ z (/ t_1 (+ x y)))
         (if (<= t 7.6e+161) t_2 (/ a (/ t_1 (+ t y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (z + a) - b;
	double tmp;
	if (t <= -2.9e+218) {
		tmp = a;
	} else if (t <= 5.2e+67) {
		tmp = t_2;
	} else if (t <= 8.2e+138) {
		tmp = z / (t_1 / (x + y));
	} else if (t <= 7.6e+161) {
		tmp = t_2;
	} else {
		tmp = a / (t_1 / (t + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (z + a) - b
    if (t <= (-2.9d+218)) then
        tmp = a
    else if (t <= 5.2d+67) then
        tmp = t_2
    else if (t <= 8.2d+138) then
        tmp = z / (t_1 / (x + y))
    else if (t <= 7.6d+161) then
        tmp = t_2
    else
        tmp = a / (t_1 / (t + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (z + a) - b;
	double tmp;
	if (t <= -2.9e+218) {
		tmp = a;
	} else if (t <= 5.2e+67) {
		tmp = t_2;
	} else if (t <= 8.2e+138) {
		tmp = z / (t_1 / (x + y));
	} else if (t <= 7.6e+161) {
		tmp = t_2;
	} else {
		tmp = a / (t_1 / (t + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (z + a) - b
	tmp = 0
	if t <= -2.9e+218:
		tmp = a
	elif t <= 5.2e+67:
		tmp = t_2
	elif t <= 8.2e+138:
		tmp = z / (t_1 / (x + y))
	elif t <= 7.6e+161:
		tmp = t_2
	else:
		tmp = a / (t_1 / (t + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -2.9e+218)
		tmp = a;
	elseif (t <= 5.2e+67)
		tmp = t_2;
	elseif (t <= 8.2e+138)
		tmp = Float64(z / Float64(t_1 / Float64(x + y)));
	elseif (t <= 7.6e+161)
		tmp = t_2;
	else
		tmp = Float64(a / Float64(t_1 / Float64(t + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (t <= -2.9e+218)
		tmp = a;
	elseif (t <= 5.2e+67)
		tmp = t_2;
	elseif (t <= 8.2e+138)
		tmp = z / (t_1 / (x + y));
	elseif (t <= 7.6e+161)
		tmp = t_2;
	else
		tmp = a / (t_1 / (t + y));
	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[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t, -2.9e+218], a, If[LessEqual[t, 5.2e+67], t$95$2, If[LessEqual[t, 8.2e+138], N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e+161], t$95$2, N[(a / N[(t$95$1 / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.8999999999999999e218

   1. Initial program 36.0%

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

   2. Taylor expanded in t around inf 77.3%

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

   if -2.8999999999999999e218 < t < 5.2000000000000001e67 or 8.19999999999999961e138 < t < 7.6000000000000005e161

   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. Taylor expanded in y around inf 69.6%

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

   if 5.2000000000000001e67 < t < 8.19999999999999961e138

   1. Initial program 65.1%

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

   2. Taylor expanded in z around inf 38.3%

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

      1. associate-/l* 59.1%

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

      2. associate-+r+ 59.1%

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

      3. +-commutative 59.1%

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

   4. Simplified 59.1%

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

   if 7.6000000000000005e161 < t

   1. Initial program 56.3%

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

   2. Taylor expanded in a around inf 37.5%

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

      1. associate-/l* 64.4%

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

      2. associate-+r+ 64.4%

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

   4. Simplified 64.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+218}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+67}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+138}:\\ \;\;\;\;\frac{z}{\frac{\left(x + t\right) + y}{x + y}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+161}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ \end{array} \]

Alternative 7: 63.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-24} \lor \neg \left(y \leq 6.5 \cdot 10^{-141}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.5e-24) (not (<= y 6.5e-141)))
   (- (+ z a) b)
   (/ (+ (* t a) (* z x)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e-24) || !(y <= 6.5e-141)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (z * x)) / (x + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8.5d-24)) .or. (.not. (y <= 6.5d-141))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) + (z * x)) / (x + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e-24) || !(y <= 6.5e-141)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (z * x)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.5e-24) or not (y <= 6.5e-141):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) + (z * x)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.5e-24) || !(y <= 6.5e-141))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.5e-24) || ~((y <= 6.5e-141)))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) + (z * x)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.5e-24], N[Not[LessEqual[y, 6.5e-141]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5000000000000002e-24 or 6.4999999999999995e-141 < y

   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. Taylor expanded in y around inf 71.1%

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

   if -8.5000000000000002e-24 < y < 6.4999999999999995e-141

   1. Initial program 78.5%

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

   2. Taylor expanded in y around 0 65.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-24} \lor \neg \left(y \leq 6.5 \cdot 10^{-141}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \end{array} \]

Alternative 8: 59.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+219}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+61}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.15e+219)
   a
   (if (<= t 6e+61) (- (+ z a) b) (/ a (/ (+ (+ x t) y) (+ t y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e+219) {
		tmp = a;
	} else if (t <= 6e+61) {
		tmp = (z + a) - b;
	} else {
		tmp = a / (((x + t) + y) / (t + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.15d+219)) then
        tmp = a
    else if (t <= 6d+61) then
        tmp = (z + a) - b
    else
        tmp = a / (((x + t) + y) / (t + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e+219) {
		tmp = a;
	} else if (t <= 6e+61) {
		tmp = (z + a) - b;
	} else {
		tmp = a / (((x + t) + y) / (t + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.15e+219:
		tmp = a
	elif t <= 6e+61:
		tmp = (z + a) - b
	else:
		tmp = a / (((x + t) + y) / (t + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.15e+219)
		tmp = a;
	elseif (t <= 6e+61)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a / Float64(Float64(Float64(x + t) + y) / Float64(t + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.15e+219)
		tmp = a;
	elseif (t <= 6e+61)
		tmp = (z + a) - b;
	else
		tmp = a / (((x + t) + y) / (t + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.15e+219], a, If[LessEqual[t, 6e+61], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a / N[(N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1499999999999999e219

   1. Initial program 36.0%

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

   2. Taylor expanded in t around inf 77.3%

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

   if -2.1499999999999999e219 < t < 6e61

   1. Initial program 60.4%

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

   2. Taylor expanded in y around inf 68.8%

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

   if 6e61 < t

   1. Initial program 56.2%

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

   2. Taylor expanded in a around inf 34.7%

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

      1. associate-/l* 58.9%

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

      2. associate-+r+ 58.9%

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

   4. Simplified 58.9%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+219}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+61}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{\left(x + t\right) + y}{t + y}}\\ \end{array} \]

Alternative 9: 57.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+218}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.25e+218) a (if (<= t 5.5e+61) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.25e+218) {
		tmp = a;
	} else if (t <= 5.5e+61) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.25d+218)) then
        tmp = a
    else if (t <= 5.5d+61) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.25e+218) {
		tmp = a;
	} else if (t <= 5.5e+61) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.25e+218:
		tmp = a
	elif t <= 5.5e+61:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.25e+218)
		tmp = a;
	elseif (t <= 5.5e+61)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.25e+218)
		tmp = a;
	elseif (t <= 5.5e+61)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.25e+218], a, If[LessEqual[t, 5.5e+61], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -2.25000000000000004e218 or 5.50000000000000036e61 < 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. Taylor expanded in t around inf 60.5%

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

   if -2.25000000000000004e218 < t < 5.50000000000000036e61

   1. Initial program 60.4%

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

   2. Taylor expanded in y around inf 68.8%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+218}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 10: 47.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+155}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 60:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.8e+155) a (if (<= a 60.0) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.8e+155) {
		tmp = a;
	} else if (a <= 60.0) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-7.8d+155)) then
        tmp = a
    else if (a <= 60.0d0) then
        tmp = z - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.8e+155) {
		tmp = a;
	} else if (a <= 60.0) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.8e+155:
		tmp = a
	elif a <= 60.0:
		tmp = z - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.8e+155)
		tmp = a;
	elseif (a <= 60.0)
		tmp = Float64(z - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7.8e+155)
		tmp = a;
	elseif (a <= 60.0)
		tmp = z - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.8e+155], a, If[LessEqual[a, 60.0], N[(z - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if a < -7.7999999999999996e155 or 60 < a

   1. Initial program 45.2%

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

   2. Taylor expanded in t around inf 59.3%

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

   if -7.7999999999999996e155 < a < 60

   1. Initial program 66.6%

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

   2. Taylor expanded in a around 0 49.7%

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

      1. +-commutative 49.7%

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

      2. *-commutative 49.7%

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

   4. Simplified 49.7%

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

   5. Taylor expanded in y around inf 50.8%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+155}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 60:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 11: 44.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+28}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-25}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.1e+28) a (if (<= a 5.8e-25) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.1e+28) {
		tmp = a;
	} else if (a <= 5.8e-25) {
		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 <= (-3.1d+28)) then
        tmp = a
    else if (a <= 5.8d-25) 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 <= -3.1e+28) {
		tmp = a;
	} else if (a <= 5.8e-25) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.1e+28:
		tmp = a
	elif a <= 5.8e-25:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.1e+28)
		tmp = a;
	elseif (a <= 5.8e-25)
		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 <= -3.1e+28)
		tmp = a;
	elseif (a <= 5.8e-25)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.1e+28], a, If[LessEqual[a, 5.8e-25], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1000000000000001e28 or 5.8000000000000001e-25 < a

   1. Initial program 47.6%

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

   2. Taylor expanded in t around inf 54.7%

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

   if -3.1000000000000001e28 < a < 5.8000000000000001e-25

   1. Initial program 68.9%

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

   2. Taylor expanded in x around inf 46.2%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+28}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-25}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 12: 32.7% 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 58.0%

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

2. Taylor expanded in t around inf 36.1%

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

3. Final simplification 36.1%

   \[\leadsto a \]

Developer target: 82.2% 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 2023331 
(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)))