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

Percentage Accurate: 59.9% → 84.6%

Time: 19.7s

Alternatives: 18

Speedup: 1.1×

• could not determine a ground truth

  1. x = -4.359153857208301e+155
  2. y = -8.072193768155165e+268
  3. z = 1.742106880574046e+52
  4. t = -9.112859110944377e-242
  5. a = 6.43913091922976e+291
  6. b = -2.4554877200704147e+292

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.9% 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: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ t_2 := y + \left(t + x\right)\\ t_3 := \frac{y}{t\_2}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-263}:\\ \;\;\;\;a \cdot \left(t\_3 + \frac{t}{t\_2}\right) + \frac{\left(y + x\right) \cdot z - y \cdot b}{t\_2}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+100}:\\ \;\;\;\;z \cdot \left(t\_3 + \frac{x}{t\_2}\right) + \frac{a \cdot \left(y + t\right) - y \cdot b}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ y (+ t (+ y x))) (+ a (- z b))))
        (t_2 (+ y (+ t x)))
        (t_3 (/ y t_2)))
   (if (<= y -2.9e+94)
     t_1
     (if (<= y -9.5e-263)
       (+ (* a (+ t_3 (/ t t_2))) (/ (- (* (+ y x) z) (* y b)) t_2))
       (if (<= y 3.8e+100)
         (+ (* z (+ t_3 (/ x t_2))) (/ (- (* a (+ y t)) (* y b)) t_2))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / (t + (y + x))) * (a + (z - b));
	double t_2 = y + (t + x);
	double t_3 = y / t_2;
	double tmp;
	if (y <= -2.9e+94) {
		tmp = t_1;
	} else if (y <= -9.5e-263) {
		tmp = (a * (t_3 + (t / t_2))) + ((((y + x) * z) - (y * b)) / t_2);
	} else if (y <= 3.8e+100) {
		tmp = (z * (t_3 + (x / t_2))) + (((a * (y + t)) - (y * b)) / t_2);
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y / (t + (y + x))) * (a + (z - b))
    t_2 = y + (t + x)
    t_3 = y / t_2
    if (y <= (-2.9d+94)) then
        tmp = t_1
    else if (y <= (-9.5d-263)) then
        tmp = (a * (t_3 + (t / t_2))) + ((((y + x) * z) - (y * b)) / t_2)
    else if (y <= 3.8d+100) then
        tmp = (z * (t_3 + (x / t_2))) + (((a * (y + t)) - (y * b)) / t_2)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / (t + (y + x))) * (a + (z - b));
	double t_2 = y + (t + x);
	double t_3 = y / t_2;
	double tmp;
	if (y <= -2.9e+94) {
		tmp = t_1;
	} else if (y <= -9.5e-263) {
		tmp = (a * (t_3 + (t / t_2))) + ((((y + x) * z) - (y * b)) / t_2);
	} else if (y <= 3.8e+100) {
		tmp = (z * (t_3 + (x / t_2))) + (((a * (y + t)) - (y * b)) / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y / (t + (y + x))) * (a + (z - b))
	t_2 = y + (t + x)
	t_3 = y / t_2
	tmp = 0
	if y <= -2.9e+94:
		tmp = t_1
	elif y <= -9.5e-263:
		tmp = (a * (t_3 + (t / t_2))) + ((((y + x) * z) - (y * b)) / t_2)
	elif y <= 3.8e+100:
		tmp = (z * (t_3 + (x / t_2))) + (((a * (y + t)) - (y * b)) / t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y / Float64(t + Float64(y + x))) * Float64(a + Float64(z - b)))
	t_2 = Float64(y + Float64(t + x))
	t_3 = Float64(y / t_2)
	tmp = 0.0
	if (y <= -2.9e+94)
		tmp = t_1;
	elseif (y <= -9.5e-263)
		tmp = Float64(Float64(a * Float64(t_3 + Float64(t / t_2))) + Float64(Float64(Float64(Float64(y + x) * z) - Float64(y * b)) / t_2));
	elseif (y <= 3.8e+100)
		tmp = Float64(Float64(z * Float64(t_3 + Float64(x / t_2))) + Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y / (t + (y + x))) * (a + (z - b));
	t_2 = y + (t + x);
	t_3 = y / t_2;
	tmp = 0.0;
	if (y <= -2.9e+94)
		tmp = t_1;
	elseif (y <= -9.5e-263)
		tmp = (a * (t_3 + (t / t_2))) + ((((y + x) * z) - (y * b)) / t_2);
	elseif (y <= 3.8e+100)
		tmp = (z * (t_3 + (x / t_2))) + (((a * (y + t)) - (y * b)) / t_2);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$2), $MachinePrecision]}, If[LessEqual[y, -2.9e+94], t$95$1, If[LessEqual[y, -9.5e-263], N[(N[(a * N[(t$95$3 + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+100], N[(N[(z * N[(t$95$3 + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8999999999999998e94 or 3.79999999999999963e100 < y

   1. Initial program 33.0%

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

   3. Taylor expanded in y around inf 31.1%

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

      1. expm1-log1p-u 19.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)\right)} \]

      2. expm1-udef 9.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)} - 1} \]

      3. associate-/l* 32.9%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{\left(a + z\right) - b}}}\right)} - 1 \]

      4. +-commutative 32.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{\left(t + x\right)} + y}{\left(a + z\right) - b}}\right)} - 1 \]

      5. associate-+l+ 32.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{t + \left(x + y\right)}}{\left(a + z\right) - b}}\right)} - 1 \]

      6. associate--l+ 32.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{\color{blue}{a + \left(z - b\right)}}}\right)} - 1 \]

   5. Applied egg-rr 32.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 38.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)\right)} \]

      2. expm1-log1p 85.1%

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

      3. associate-/r/ 89.9%

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

      4. +-commutative 89.9%

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

   7. Simplified 89.9%

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

   if -2.8999999999999998e94 < y < -9.5000000000000005e-263

   1. Initial program 73.0%

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

   3. Taylor expanded in a around 0 88.6%

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

      1. associate--l+ 88.6%

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

      2. +-commutative 88.6%

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

      3. associate-+r+ 88.6%

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

      4. associate-+r+ 88.6%

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

      5. div-sub 88.6%

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

      6. +-commutative 88.6%

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

      7. *-commutative 88.6%

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

      8. associate-+r+ 88.6%

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

   5. Simplified 88.6%

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

   if -9.5000000000000005e-263 < y < 3.79999999999999963e100

   1. Initial program 77.5%

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

   3. Taylor expanded in z around 0 91.4%

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

      1. associate--l+ 91.4%

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

      2. associate-+r+ 91.4%

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

      3. associate-+r+ 91.4%

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

      4. div-sub 91.4%

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

      5. *-commutative 91.4%

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

      6. associate-+r+ 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-263}:\\ \;\;\;\;a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \frac{\left(y + x\right) \cdot z - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+100}:\\ \;\;\;\;z \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{x}{y + \left(t + x\right)}\right) + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{y}{t\_1}\\ t_3 := \left(y + x\right) \cdot z\\ t_4 := \frac{\left(t\_3 + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty \lor \neg \left(t\_4 \leq 4 \cdot 10^{+276}\right):\\ \;\;\;\;z \cdot \left(t\_2 + \frac{x}{t\_1}\right) + \frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t\_2 + \frac{t}{t\_1}\right) + \frac{t\_3 - y \cdot b}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (/ y t_1))
        (t_3 (* (+ y x) z))
        (t_4 (/ (- (+ t_3 (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 4e+276)))
     (+ (* z (+ t_2 (/ x t_1))) (/ a (/ (+ t (+ y x)) (+ y t))))
     (+ (* a (+ t_2 (/ t t_1))) (/ (- t_3 (* y b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = y / t_1;
	double t_3 = (y + x) * z;
	double t_4 = ((t_3 + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= 4e+276)) {
		tmp = (z * (t_2 + (x / t_1))) + (a / ((t + (y + x)) / (y + t)));
	} else {
		tmp = (a * (t_2 + (t / t_1))) + ((t_3 - (y * b)) / t_1);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = y / t_1;
	double t_3 = (y + x) * z;
	double t_4 = ((t_3 + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_4 <= -Double.POSITIVE_INFINITY) || !(t_4 <= 4e+276)) {
		tmp = (z * (t_2 + (x / t_1))) + (a / ((t + (y + x)) / (y + t)));
	} else {
		tmp = (a * (t_2 + (t / t_1))) + ((t_3 - (y * b)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = y / t_1
	t_3 = (y + x) * z
	t_4 = ((t_3 + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_4 <= -math.inf) or not (t_4 <= 4e+276):
		tmp = (z * (t_2 + (x / t_1))) + (a / ((t + (y + x)) / (y + t)))
	else:
		tmp = (a * (t_2 + (t / t_1))) + ((t_3 - (y * b)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(y / t_1)
	t_3 = Float64(Float64(y + x) * z)
	t_4 = Float64(Float64(Float64(t_3 + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= 4e+276))
		tmp = Float64(Float64(z * Float64(t_2 + Float64(x / t_1))) + Float64(a / Float64(Float64(t + Float64(y + x)) / Float64(y + t))));
	else
		tmp = Float64(Float64(a * Float64(t_2 + Float64(t / t_1))) + Float64(Float64(t_3 - Float64(y * b)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = y / t_1;
	t_3 = (y + x) * z;
	t_4 = ((t_3 + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_4 <= -Inf) || ~((t_4 <= 4e+276)))
		tmp = (z * (t_2 + (x / t_1))) + (a / ((t + (y + x)) / (y + t)));
	else
		tmp = (a * (t_2 + (t / t_1))) + ((t_3 - (y * b)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, 4e+276]], $MachinePrecision]], N[(N[(z * N[(t$95$2 + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(t$95$2 + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 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)) < -inf.0 or 4.0000000000000002e276 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in z around 0 35.9%

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

      1. associate--l+ 35.9%

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

      2. associate-+r+ 35.9%

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

      3. associate-+r+ 35.9%

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

      4. div-sub 35.9%

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

      5. *-commutative 35.9%

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

      6. associate-+r+ 35.9%

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

   5. Simplified 35.9%

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

   6. Taylor expanded in a around inf 36.9%

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

      1. associate-/l* 73.9%

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

      2. +-commutative 73.9%

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

      3. +-commutative 73.9%

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

   8. Simplified 73.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000002e276

   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. Taylor expanded in a around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. div-sub 99.8%

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

      6. +-commutative 99.8%

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

      7. *-commutative 99.8%

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

      8. associate-+r+ 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq 4 \cdot 10^{+276}\right):\\ \;\;\;\;z \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{x}{y + \left(t + x\right)}\right) + \frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \frac{\left(y + x\right) \cdot z - y \cdot b}{y + \left(t + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 4 \cdot 10^{+276}\right):\\ \;\;\;\;z \cdot \left(\frac{y}{t\_1} + \frac{x}{t\_1}\right) + \frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(a + z\right) - b\right)\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (/ (- (+ (* (+ y x) z) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 4e+276)))
     (+ (* z (+ (/ y t_1) (/ x t_1))) (/ a (/ (+ t (+ y x)) (+ y t))))
     (/ (+ (* t a) (+ (* x z) (* y (- (+ a z) b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 4e+276)) {
		tmp = (z * ((y / t_1) + (x / t_1))) + (a / ((t + (y + x)) / (y + t)));
	} else {
		tmp = ((t * a) + ((x * z) + (y * ((a + z) - b)))) / t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 4e+276)) {
		tmp = (z * ((y / t_1) + (x / t_1))) + (a / ((t + (y + x)) / (y + t)));
	} else {
		tmp = ((t * a) + ((x * z) + (y * ((a + z) - b)))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 4e+276):
		tmp = (z * ((y / t_1) + (x / t_1))) + (a / ((t + (y + x)) / (y + t)))
	else:
		tmp = ((t * a) + ((x * z) + (y * ((a + z) - b)))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(Float64(Float64(Float64(Float64(y + x) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 4e+276))
		tmp = Float64(Float64(z * Float64(Float64(y / t_1) + Float64(x / t_1))) + Float64(a / Float64(Float64(t + Float64(y + x)) / Float64(y + t))));
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * Float64(Float64(a + z) - b)))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 4e+276)))
		tmp = (z * ((y / t_1) + (x / t_1))) + (a / ((t + (y + x)) / (y + t)));
	else
		tmp = ((t * a) + ((x * z) + (y * ((a + z) - b)))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 4e+276]], $MachinePrecision]], N[(N[(z * N[(N[(y / t$95$1), $MachinePrecision] + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.0000000000000002e276 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in z around 0 35.9%

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

      1. associate--l+ 35.9%

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

      2. associate-+r+ 35.9%

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

      3. associate-+r+ 35.9%

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

      4. div-sub 35.9%

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

      5. *-commutative 35.9%

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

      6. associate-+r+ 35.9%

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

   5. Simplified 35.9%

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

   6. Taylor expanded in a around inf 36.9%

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

      1. associate-/l* 73.9%

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

      2. +-commutative 73.9%

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

      3. +-commutative 73.9%

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

   8. Simplified 73.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000002e276

   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. Taylor expanded in y around 0 99.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq 4 \cdot 10^{+276}\right):\\ \;\;\;\;z \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{x}{y + \left(t + x\right)}\right) + \frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(a + z\right) - b\right)\right)}{y + \left(t + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+271} \lor \neg \left(t\_2 \leq 4 \cdot 10^{+276}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot t\_3\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (/ (- (+ (* (+ y x) z) (* a (+ y t))) (* y b)) t_1))
        (t_3 (- (+ a z) b)))
   (if (or (<= t_2 -5e+271) (not (<= t_2 4e+276)))
     t_3
     (/ (+ (* t a) (+ (* x z) (* y t_3))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (a + z) - b;
	double tmp;
	if ((t_2 <= -5e+271) || !(t_2 <= 4e+276)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / 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 = y + (t + x)
    t_2 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / t_1
    t_3 = (a + z) - b
    if ((t_2 <= (-5d+271)) .or. (.not. (t_2 <= 4d+276))) then
        tmp = t_3
    else
        tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (a + z) - b;
	double tmp;
	if ((t_2 <= -5e+271) || !(t_2 <= 4e+276)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / t_1
	t_3 = (a + z) - b
	tmp = 0
	if (t_2 <= -5e+271) or not (t_2 <= 4e+276):
		tmp = t_3
	else:
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(Float64(Float64(Float64(Float64(y + x) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if ((t_2 <= -5e+271) || !(t_2 <= 4e+276))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * t_3))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = ((((y + x) * z) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = (a + z) - b;
	tmp = 0.0;
	if ((t_2 <= -5e+271) || ~((t_2 <= 4e+276)))
		tmp = t_3;
	else
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+271], N[Not[LessEqual[t$95$2, 4e+276]], $MachinePrecision]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.0000000000000003e271 or 4.0000000000000002e276 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 10.6%

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

   3. Taylor expanded in y around inf 71.6%

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

   if -5.0000000000000003e271 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000002e276

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq -5 \cdot 10^{+271} \lor \neg \left(\frac{\left(\left(y + x\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq 4 \cdot 10^{+276}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(a + z\right) - b\right)\right)}{y + \left(t + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}\\ t_2 := \frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (- (* a (+ y t)) (* y b)) (+ y (+ t x)))))
        (t_2 (* (/ y (+ t (+ y x))) (+ a (- z b)))))
   (if (<= y -6e+36)
     t_2
     (if (<= y -2.2e-197)
       t_1
       (if (<= y 8.6e-239)
         (/ (+ (* t a) (* x z)) (+ t x))
         (if (<= y 2.15e+27) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (((a * (y + t)) - (y * b)) / (y + (t + x)));
	double t_2 = (y / (t + (y + x))) * (a + (z - b));
	double tmp;
	if (y <= -6e+36) {
		tmp = t_2;
	} else if (y <= -2.2e-197) {
		tmp = t_1;
	} else if (y <= 8.6e-239) {
		tmp = ((t * a) + (x * z)) / (t + x);
	} else if (y <= 2.15e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + (((a * (y + t)) - (y * b)) / (y + (t + x)))
    t_2 = (y / (t + (y + x))) * (a + (z - b))
    if (y <= (-6d+36)) then
        tmp = t_2
    else if (y <= (-2.2d-197)) then
        tmp = t_1
    else if (y <= 8.6d-239) then
        tmp = ((t * a) + (x * z)) / (t + x)
    else if (y <= 2.15d+27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (((a * (y + t)) - (y * b)) / (y + (t + x)));
	double t_2 = (y / (t + (y + x))) * (a + (z - b));
	double tmp;
	if (y <= -6e+36) {
		tmp = t_2;
	} else if (y <= -2.2e-197) {
		tmp = t_1;
	} else if (y <= 8.6e-239) {
		tmp = ((t * a) + (x * z)) / (t + x);
	} else if (y <= 2.15e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (((a * (y + t)) - (y * b)) / (y + (t + x)))
	t_2 = (y / (t + (y + x))) * (a + (z - b))
	tmp = 0
	if y <= -6e+36:
		tmp = t_2
	elif y <= -2.2e-197:
		tmp = t_1
	elif y <= 8.6e-239:
		tmp = ((t * a) + (x * z)) / (t + x)
	elif y <= 2.15e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / Float64(y + Float64(t + x))))
	t_2 = Float64(Float64(y / Float64(t + Float64(y + x))) * Float64(a + Float64(z - b)))
	tmp = 0.0
	if (y <= -6e+36)
		tmp = t_2;
	elseif (y <= -2.2e-197)
		tmp = t_1;
	elseif (y <= 8.6e-239)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(t + x));
	elseif (y <= 2.15e+27)
		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 + (((a * (y + t)) - (y * b)) / (y + (t + x)));
	t_2 = (y / (t + (y + x))) * (a + (z - b));
	tmp = 0.0;
	if (y <= -6e+36)
		tmp = t_2;
	elseif (y <= -2.2e-197)
		tmp = t_1;
	elseif (y <= 8.6e-239)
		tmp = ((t * a) + (x * z)) / (t + x);
	elseif (y <= 2.15e+27)
		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[(z + N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+36], t$95$2, If[LessEqual[y, -2.2e-197], t$95$1, If[LessEqual[y, 8.6e-239], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+27], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6e36 or 2.15000000000000004e27 < y

   1. Initial program 38.6%

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

   3. Taylor expanded in y around inf 34.6%

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

      1. expm1-log1p-u 22.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)\right)} \]

      2. expm1-udef 11.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)} - 1} \]

      3. associate-/l* 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{\left(a + z\right) - b}}}\right)} - 1 \]

      4. +-commutative 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{\left(t + x\right)} + y}{\left(a + z\right) - b}}\right)} - 1 \]

      5. associate-+l+ 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{t + \left(x + y\right)}}{\left(a + z\right) - b}}\right)} - 1 \]

      6. associate--l+ 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{\color{blue}{a + \left(z - b\right)}}}\right)} - 1 \]

   5. Applied egg-rr 32.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 39.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)\right)} \]

      2. expm1-log1p 81.2%

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

      3. associate-/r/ 85.0%

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

      4. +-commutative 85.0%

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

   7. Simplified 85.0%

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

   if -6e36 < y < -2.2e-197 or 8.6000000000000001e-239 < y < 2.15000000000000004e27

   1. Initial program 77.0%

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

   3. Taylor expanded in z around 0 89.0%

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

      1. associate--l+ 89.0%

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

      2. associate-+r+ 89.0%

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

      3. associate-+r+ 89.0%

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

      4. div-sub 89.0%

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

      5. *-commutative 89.0%

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

      6. associate-+r+ 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in x around inf 72.9%

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

   if -2.2e-197 < y < 8.6000000000000001e-239

   1. Initial program 83.3%

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

   3. Taylor expanded in y around 0 77.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-197}:\\ \;\;\;\;z + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+27}:\\ \;\;\;\;z + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ t_2 := a \cdot \left(y + t\right)\\ t_3 := y + \left(t + x\right)\\ t_4 := z + \frac{t\_2 - y \cdot b}{t\_3}\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-182}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{\left(y + x\right) \cdot z + t\_2}{t\_3}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+27}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ y (+ t (+ y x))) (+ a (- z b))))
        (t_2 (* a (+ y t)))
        (t_3 (+ y (+ t x)))
        (t_4 (+ z (/ (- t_2 (* y b)) t_3))))
   (if (<= y -2.55e+36)
     t_1
     (if (<= y -3.5e-182)
       t_4
       (if (<= y 4.6e-110)
         (/ (+ (* (+ y x) z) t_2) t_3)
         (if (<= y 5.4e+27) t_4 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / (t + (y + x))) * (a + (z - b));
	double t_2 = a * (y + t);
	double t_3 = y + (t + x);
	double t_4 = z + ((t_2 - (y * b)) / t_3);
	double tmp;
	if (y <= -2.55e+36) {
		tmp = t_1;
	} else if (y <= -3.5e-182) {
		tmp = t_4;
	} else if (y <= 4.6e-110) {
		tmp = (((y + x) * z) + t_2) / t_3;
	} else if (y <= 5.4e+27) {
		tmp = t_4;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y / (t + (y + x))) * (a + (z - b))
    t_2 = a * (y + t)
    t_3 = y + (t + x)
    t_4 = z + ((t_2 - (y * b)) / t_3)
    if (y <= (-2.55d+36)) then
        tmp = t_1
    else if (y <= (-3.5d-182)) then
        tmp = t_4
    else if (y <= 4.6d-110) then
        tmp = (((y + x) * z) + t_2) / t_3
    else if (y <= 5.4d+27) then
        tmp = t_4
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / (t + (y + x))) * (a + (z - b));
	double t_2 = a * (y + t);
	double t_3 = y + (t + x);
	double t_4 = z + ((t_2 - (y * b)) / t_3);
	double tmp;
	if (y <= -2.55e+36) {
		tmp = t_1;
	} else if (y <= -3.5e-182) {
		tmp = t_4;
	} else if (y <= 4.6e-110) {
		tmp = (((y + x) * z) + t_2) / t_3;
	} else if (y <= 5.4e+27) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y / (t + (y + x))) * (a + (z - b))
	t_2 = a * (y + t)
	t_3 = y + (t + x)
	t_4 = z + ((t_2 - (y * b)) / t_3)
	tmp = 0
	if y <= -2.55e+36:
		tmp = t_1
	elif y <= -3.5e-182:
		tmp = t_4
	elif y <= 4.6e-110:
		tmp = (((y + x) * z) + t_2) / t_3
	elif y <= 5.4e+27:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y / Float64(t + Float64(y + x))) * Float64(a + Float64(z - b)))
	t_2 = Float64(a * Float64(y + t))
	t_3 = Float64(y + Float64(t + x))
	t_4 = Float64(z + Float64(Float64(t_2 - Float64(y * b)) / t_3))
	tmp = 0.0
	if (y <= -2.55e+36)
		tmp = t_1;
	elseif (y <= -3.5e-182)
		tmp = t_4;
	elseif (y <= 4.6e-110)
		tmp = Float64(Float64(Float64(Float64(y + x) * z) + t_2) / t_3);
	elseif (y <= 5.4e+27)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y / (t + (y + x))) * (a + (z - b));
	t_2 = a * (y + t);
	t_3 = y + (t + x);
	t_4 = z + ((t_2 - (y * b)) / t_3);
	tmp = 0.0;
	if (y <= -2.55e+36)
		tmp = t_1;
	elseif (y <= -3.5e-182)
		tmp = t_4;
	elseif (y <= 4.6e-110)
		tmp = (((y + x) * z) + t_2) / t_3;
	elseif (y <= 5.4e+27)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z + N[(N[(t$95$2 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+36], t$95$1, If[LessEqual[y, -3.5e-182], t$95$4, If[LessEqual[y, 4.6e-110], N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[y, 5.4e+27], t$95$4, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.54999999999999986e36 or 5.3999999999999995e27 < y

   1. Initial program 38.6%

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

   3. Taylor expanded in y around inf 34.6%

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

      1. expm1-log1p-u 22.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)\right)} \]

      2. expm1-udef 11.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)} - 1} \]

      3. associate-/l* 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{\left(a + z\right) - b}}}\right)} - 1 \]

      4. +-commutative 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{\left(t + x\right)} + y}{\left(a + z\right) - b}}\right)} - 1 \]

      5. associate-+l+ 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{t + \left(x + y\right)}}{\left(a + z\right) - b}}\right)} - 1 \]

      6. associate--l+ 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{\color{blue}{a + \left(z - b\right)}}}\right)} - 1 \]

   5. Applied egg-rr 32.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 39.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)\right)} \]

      2. expm1-log1p 81.2%

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

      3. associate-/r/ 85.0%

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

      4. +-commutative 85.0%

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

   7. Simplified 85.0%

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

   if -2.54999999999999986e36 < y < -3.49999999999999983e-182 or 4.6000000000000003e-110 < y < 5.3999999999999995e27

   1. Initial program 77.7%

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

   3. Taylor expanded in z around 0 89.4%

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

      1. associate--l+ 89.4%

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

      2. associate-+r+ 89.4%

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

      3. associate-+r+ 89.4%

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

      4. div-sub 89.4%

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

      5. *-commutative 89.4%

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

      6. associate-+r+ 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in x around inf 77.7%

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

   if -3.49999999999999983e-182 < y < 4.6000000000000003e-110

   1. Initial program 79.7%

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

   3. Taylor expanded in b around 0 72.4%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-182}:\\ \;\;\;\;z + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{\left(y + x\right) \cdot z + a \cdot \left(y + t\right)}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+27}:\\ \;\;\;\;z + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ t_2 := y + \left(t + x\right)\\ t_3 := z + \frac{a \cdot \left(y + t\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-161}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-280}:\\ \;\;\;\;a + z \cdot \left(\frac{y}{t\_2} + \frac{x}{t\_2}\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+27}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ y (+ t (+ y x))) (+ a (- z b))))
        (t_2 (+ y (+ t x)))
        (t_3 (+ z (/ (- (* a (+ y t)) (* y b)) t_2))))
   (if (<= y -6e+36)
     t_1
     (if (<= y -1.2e-161)
       t_3
       (if (<= y 2.6e-280)
         (+ a (* z (+ (/ y t_2) (/ x t_2))))
         (if (<= y 2.15e+27) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / (t + (y + x))) * (a + (z - b));
	double t_2 = y + (t + x);
	double t_3 = z + (((a * (y + t)) - (y * b)) / t_2);
	double tmp;
	if (y <= -6e+36) {
		tmp = t_1;
	} else if (y <= -1.2e-161) {
		tmp = t_3;
	} else if (y <= 2.6e-280) {
		tmp = a + (z * ((y / t_2) + (x / t_2)));
	} else if (y <= 2.15e+27) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y / (t + (y + x))) * (a + (z - b))
    t_2 = y + (t + x)
    t_3 = z + (((a * (y + t)) - (y * b)) / t_2)
    if (y <= (-6d+36)) then
        tmp = t_1
    else if (y <= (-1.2d-161)) then
        tmp = t_3
    else if (y <= 2.6d-280) then
        tmp = a + (z * ((y / t_2) + (x / t_2)))
    else if (y <= 2.15d+27) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / (t + (y + x))) * (a + (z - b));
	double t_2 = y + (t + x);
	double t_3 = z + (((a * (y + t)) - (y * b)) / t_2);
	double tmp;
	if (y <= -6e+36) {
		tmp = t_1;
	} else if (y <= -1.2e-161) {
		tmp = t_3;
	} else if (y <= 2.6e-280) {
		tmp = a + (z * ((y / t_2) + (x / t_2)));
	} else if (y <= 2.15e+27) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y / (t + (y + x))) * (a + (z - b))
	t_2 = y + (t + x)
	t_3 = z + (((a * (y + t)) - (y * b)) / t_2)
	tmp = 0
	if y <= -6e+36:
		tmp = t_1
	elif y <= -1.2e-161:
		tmp = t_3
	elif y <= 2.6e-280:
		tmp = a + (z * ((y / t_2) + (x / t_2)))
	elif y <= 2.15e+27:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y / Float64(t + Float64(y + x))) * Float64(a + Float64(z - b)))
	t_2 = Float64(y + Float64(t + x))
	t_3 = Float64(z + Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_2))
	tmp = 0.0
	if (y <= -6e+36)
		tmp = t_1;
	elseif (y <= -1.2e-161)
		tmp = t_3;
	elseif (y <= 2.6e-280)
		tmp = Float64(a + Float64(z * Float64(Float64(y / t_2) + Float64(x / t_2))));
	elseif (y <= 2.15e+27)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y / (t + (y + x))) * (a + (z - b));
	t_2 = y + (t + x);
	t_3 = z + (((a * (y + t)) - (y * b)) / t_2);
	tmp = 0.0;
	if (y <= -6e+36)
		tmp = t_1;
	elseif (y <= -1.2e-161)
		tmp = t_3;
	elseif (y <= 2.6e-280)
		tmp = a + (z * ((y / t_2) + (x / t_2)));
	elseif (y <= 2.15e+27)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z + N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+36], t$95$1, If[LessEqual[y, -1.2e-161], t$95$3, If[LessEqual[y, 2.6e-280], N[(a + N[(z * N[(N[(y / t$95$2), $MachinePrecision] + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+27], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6e36 or 2.15000000000000004e27 < y

   1. Initial program 38.6%

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

   3. Taylor expanded in y around inf 34.6%

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

      1. expm1-log1p-u 22.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)\right)} \]

      2. expm1-udef 11.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)} - 1} \]

      3. associate-/l* 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{\left(a + z\right) - b}}}\right)} - 1 \]

      4. +-commutative 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{\left(t + x\right)} + y}{\left(a + z\right) - b}}\right)} - 1 \]

      5. associate-+l+ 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{t + \left(x + y\right)}}{\left(a + z\right) - b}}\right)} - 1 \]

      6. associate--l+ 32.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{\color{blue}{a + \left(z - b\right)}}}\right)} - 1 \]

   5. Applied egg-rr 32.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 39.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)\right)} \]

      2. expm1-log1p 81.2%

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

      3. associate-/r/ 85.0%

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

      4. +-commutative 85.0%

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

   7. Simplified 85.0%

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

   if -6e36 < y < -1.19999999999999999e-161 or 2.6e-280 < y < 2.15000000000000004e27

   1. Initial program 80.8%

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

   3. Taylor expanded in z around 0 91.4%

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

      1. associate--l+ 91.4%

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

      2. associate-+r+ 91.4%

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

      3. associate-+r+ 91.4%

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

      4. div-sub 91.4%

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

      5. *-commutative 91.4%

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

      6. associate-+r+ 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in x around inf 79.2%

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

   if -1.19999999999999999e-161 < y < 2.6e-280

   1. Initial program 74.1%

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

   3. Taylor expanded in z around 0 86.0%

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

      1. associate--l+ 86.0%

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

      2. associate-+r+ 86.0%

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

      3. associate-+r+ 86.0%

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

      4. div-sub 86.0%

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

      5. *-commutative 86.0%

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

      6. associate-+r+ 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in t around inf 78.5%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-161}:\\ \;\;\;\;z + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-280}:\\ \;\;\;\;a + z \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{x}{y + \left(t + x\right)}\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+27}:\\ \;\;\;\;z + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \frac{y}{t\_1} \cdot \left(a + \left(z - b\right)\right)\\ t_3 := z + \frac{a}{\frac{t\_1}{y + t}}\\ \mathbf{if}\;a \leq -1.26 \cdot 10^{-64}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-195}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-186}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x)))
        (t_2 (* (/ y t_1) (+ a (- z b))))
        (t_3 (+ z (/ a (/ t_1 (+ y t))))))
   (if (<= a -1.26e-64)
     t_3
     (if (<= a 1.15e-195)
       t_2
       (if (<= a 5.9e-186)
         (/ (+ (* t a) (* x z)) (+ t x))
         (if (<= a 2e-52) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (y / t_1) * (a + (z - b));
	double t_3 = z + (a / (t_1 / (y + t)));
	double tmp;
	if (a <= -1.26e-64) {
		tmp = t_3;
	} else if (a <= 1.15e-195) {
		tmp = t_2;
	} else if (a <= 5.9e-186) {
		tmp = ((t * a) + (x * z)) / (t + x);
	} else if (a <= 2e-52) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t + (y + x)
    t_2 = (y / t_1) * (a + (z - b))
    t_3 = z + (a / (t_1 / (y + t)))
    if (a <= (-1.26d-64)) then
        tmp = t_3
    else if (a <= 1.15d-195) then
        tmp = t_2
    else if (a <= 5.9d-186) then
        tmp = ((t * a) + (x * z)) / (t + x)
    else if (a <= 2d-52) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (y / t_1) * (a + (z - b));
	double t_3 = z + (a / (t_1 / (y + t)));
	double tmp;
	if (a <= -1.26e-64) {
		tmp = t_3;
	} else if (a <= 1.15e-195) {
		tmp = t_2;
	} else if (a <= 5.9e-186) {
		tmp = ((t * a) + (x * z)) / (t + x);
	} else if (a <= 2e-52) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	t_2 = (y / t_1) * (a + (z - b))
	t_3 = z + (a / (t_1 / (y + t)))
	tmp = 0
	if a <= -1.26e-64:
		tmp = t_3
	elif a <= 1.15e-195:
		tmp = t_2
	elif a <= 5.9e-186:
		tmp = ((t * a) + (x * z)) / (t + x)
	elif a <= 2e-52:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(Float64(y / t_1) * Float64(a + Float64(z - b)))
	t_3 = Float64(z + Float64(a / Float64(t_1 / Float64(y + t))))
	tmp = 0.0
	if (a <= -1.26e-64)
		tmp = t_3;
	elseif (a <= 1.15e-195)
		tmp = t_2;
	elseif (a <= 5.9e-186)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(t + x));
	elseif (a <= 2e-52)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	t_2 = (y / t_1) * (a + (z - b));
	t_3 = z + (a / (t_1 / (y + t)));
	tmp = 0.0;
	if (a <= -1.26e-64)
		tmp = t_3;
	elseif (a <= 1.15e-195)
		tmp = t_2;
	elseif (a <= 5.9e-186)
		tmp = ((t * a) + (x * z)) / (t + x);
	elseif (a <= 2e-52)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / t$95$1), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.26e-64], t$95$3, If[LessEqual[a, 1.15e-195], t$95$2, If[LessEqual[a, 5.9e-186], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-52], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2599999999999999e-64 or 2e-52 < a

   1. Initial program 57.1%

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

   3. Taylor expanded in z around 0 63.7%

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

      1. associate--l+ 63.7%

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

      2. associate-+r+ 63.7%

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

      3. associate-+r+ 63.7%

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

      4. div-sub 63.7%

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

      5. *-commutative 63.7%

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

      6. associate-+r+ 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in a around inf 59.1%

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

      1. associate-/l* 88.4%

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

      2. +-commutative 88.4%

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

      3. +-commutative 88.4%

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

   8. Simplified 88.4%

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

   9. Taylor expanded in x around inf 78.7%

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

   if -1.2599999999999999e-64 < a < 1.1500000000000001e-195 or 5.8999999999999999e-186 < a < 2e-52

   1. Initial program 58.8%

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

   3. Taylor expanded in y around inf 48.2%

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

      1. expm1-log1p-u 33.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)\right)} \]

      2. expm1-udef 16.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)} - 1} \]

      3. associate-/l* 25.9%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{\left(a + z\right) - b}}}\right)} - 1 \]

      4. +-commutative 25.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{\left(t + x\right)} + y}{\left(a + z\right) - b}}\right)} - 1 \]

      5. associate-+l+ 25.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{t + \left(x + y\right)}}{\left(a + z\right) - b}}\right)} - 1 \]

      6. associate--l+ 25.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{\color{blue}{a + \left(z - b\right)}}}\right)} - 1 \]

   5. Applied egg-rr 25.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 39.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)\right)} \]

      2. expm1-log1p 69.7%

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

      3. associate-/r/ 77.6%

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

      4. +-commutative 77.6%

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

   7. Simplified 77.6%

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

   if 1.1500000000000001e-195 < a < 5.8999999999999999e-186

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.26 \cdot 10^{-64}:\\ \;\;\;\;z + \frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-195}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-186}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-52}:\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + \frac{a}{\frac{t + \left(y + x\right)}{y + t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-147} \lor \neg \left(y \leq 2.1 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.4e-147) (not (<= y 2.1e-114)))
   (* (/ y (+ t (+ y x))) (+ a (- z b)))
   (/ (+ (* t a) (* x z)) (+ t x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.4e-147) || !(y <= 2.1e-114)) {
		tmp = (y / (t + (y + x))) * (a + (z - b));
	} else {
		tmp = ((t * a) + (x * z)) / (t + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.4d-147)) .or. (.not. (y <= 2.1d-114))) then
        tmp = (y / (t + (y + x))) * (a + (z - b))
    else
        tmp = ((t * a) + (x * z)) / (t + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.4e-147) || !(y <= 2.1e-114)) {
		tmp = (y / (t + (y + x))) * (a + (z - b));
	} else {
		tmp = ((t * a) + (x * z)) / (t + x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.4e-147) or not (y <= 2.1e-114):
		tmp = (y / (t + (y + x))) * (a + (z - b))
	else:
		tmp = ((t * a) + (x * z)) / (t + x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.4e-147) || !(y <= 2.1e-114))
		tmp = Float64(Float64(y / Float64(t + Float64(y + x))) * Float64(a + Float64(z - b)));
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(t + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.4e-147) || ~((y <= 2.1e-114)))
		tmp = (y / (t + (y + x))) * (a + (z - b));
	else
		tmp = ((t * a) + (x * z)) / (t + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.4e-147], N[Not[LessEqual[y, 2.1e-114]], $MachinePrecision]], N[(N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999998e-147 or 2.09999999999999993e-114 < y

   1. Initial program 50.8%

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

   3. Taylor expanded in y around inf 40.3%

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

      1. expm1-log1p-u 25.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)\right)} \]

      2. expm1-udef 16.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{\left(x + t\right) + y}\right)} - 1} \]

      3. associate-/l* 30.6%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{\left(a + z\right) - b}}}\right)} - 1 \]

      4. +-commutative 30.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{\left(t + x\right)} + y}{\left(a + z\right) - b}}\right)} - 1 \]

      5. associate-+l+ 30.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{t + \left(x + y\right)}}{\left(a + z\right) - b}}\right)} - 1 \]

      6. associate--l+ 30.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{\color{blue}{a + \left(z - b\right)}}}\right)} - 1 \]

   5. Applied egg-rr 30.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 37.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t + \left(x + y\right)}{a + \left(z - b\right)}}\right)\right)} \]

      2. expm1-log1p 71.9%

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

      3. associate-/r/ 76.7%

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

      4. +-commutative 76.7%

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

   7. Simplified 76.7%

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

   if -2.39999999999999998e-147 < y < 2.09999999999999993e-114

   1. Initial program 76.2%

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

   3. Taylor expanded in y around 0 62.8%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-147} \lor \neg \left(y \leq 2.1 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{y}{t + \left(y + x\right)} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+89} \lor \neg \left(x \leq 3.1 \cdot 10^{+201}\right):\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -2.25e+89) (not (<= x 3.1e+201)))
   (+ z (* y (- (/ a x) (/ b x))))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.25e+89) || !(x <= 3.1e+201)) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-2.25d+89)) .or. (.not. (x <= 3.1d+201))) then
        tmp = z + (y * ((a / x) - (b / x)))
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.25e+89) || !(x <= 3.1e+201)) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.25e+89) or not (x <= 3.1e+201):
		tmp = z + (y * ((a / x) - (b / x)))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -2.25e+89) || !(x <= 3.1e+201))
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -2.25e+89) || ~((x <= 3.1e+201)))
		tmp = z + (y * ((a / x) - (b / x)));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -2.25e+89], N[Not[LessEqual[x, 3.1e+201]], $MachinePrecision]], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e89 or 3.0999999999999998e201 < x

   1. Initial program 47.7%

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

   3. Taylor expanded in x around inf 49.2%

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

      1. associate--r+ 49.2%

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

      2. sub-neg 49.2%

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

      3. mul-1-neg 49.2%

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

      4. associate-+r+ 49.2%

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

      5. +-commutative 49.2%

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

      6. associate--l+ 53.4%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in y around inf 70.6%

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

   if -2.25e89 < x < 3.0999999999999998e201

   1. Initial program 62.7%

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

   3. Taylor expanded in y around inf 63.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+89} \lor \neg \left(x \leq 3.1 \cdot 10^{+201}\right):\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-145} \lor \neg \left(y \leq 9 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{y}{\frac{y + x}{a + \left(z - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.6e-145) (not (<= y 9e-33)))
   (/ y (/ (+ y x) (+ a (- z b))))
   (/ (+ (* t a) (* x z)) (+ t x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e-145) || !(y <= 9e-33)) {
		tmp = y / ((y + x) / (a + (z - b)));
	} else {
		tmp = ((t * a) + (x * z)) / (t + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.6d-145)) .or. (.not. (y <= 9d-33))) then
        tmp = y / ((y + x) / (a + (z - b)))
    else
        tmp = ((t * a) + (x * z)) / (t + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e-145) || !(y <= 9e-33)) {
		tmp = y / ((y + x) / (a + (z - b)));
	} else {
		tmp = ((t * a) + (x * z)) / (t + x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.6e-145) or not (y <= 9e-33):
		tmp = y / ((y + x) / (a + (z - b)))
	else:
		tmp = ((t * a) + (x * z)) / (t + x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.6e-145) || !(y <= 9e-33))
		tmp = Float64(y / Float64(Float64(y + x) / Float64(a + Float64(z - b))));
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(t + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.6e-145) || ~((y <= 9e-33)))
		tmp = y / ((y + x) / (a + (z - b)));
	else
		tmp = ((t * a) + (x * z)) / (t + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.6e-145], N[Not[LessEqual[y, 9e-33]], $MachinePrecision]], N[(y / N[(N[(y + x), $MachinePrecision] / N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e-145 or 8.99999999999999982e-33 < y

   1. Initial program 47.4%

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

   3. Taylor expanded in y around inf 39.3%

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

   4. Taylor expanded in t around 0 36.0%

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

      1. associate-+r- 36.0%

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

      2. associate-/l* 69.9%

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

      3. +-commutative 69.9%

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

   6. Simplified 69.9%

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

   if -3.6e-145 < y < 8.99999999999999982e-33

   1. Initial program 78.0%

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

   3. Taylor expanded in y around 0 60.0%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-145} \lor \neg \left(y \leq 9 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{y}{\frac{y + x}{a + \left(z - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+98} \lor \neg \left(x \leq 1.56 \cdot 10^{+205}\right):\\ \;\;\;\;z + \left(y + t\right) \cdot \frac{a}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.65e+98) (not (<= x 1.56e+205)))
   (+ z (* (+ y t) (/ a x)))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.65e+98) || !(x <= 1.56e+205)) {
		tmp = z + ((y + t) * (a / x));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.65d+98)) .or. (.not. (x <= 1.56d+205))) then
        tmp = z + ((y + t) * (a / x))
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.65e+98) || !(x <= 1.56e+205)) {
		tmp = z + ((y + t) * (a / x));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.65e+98) or not (x <= 1.56e+205):
		tmp = z + ((y + t) * (a / x))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.65e+98) || !(x <= 1.56e+205))
		tmp = Float64(z + Float64(Float64(y + t) * Float64(a / x)));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.65e+98) || ~((x <= 1.56e+205)))
		tmp = z + ((y + t) * (a / x));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.65e+98], N[Not[LessEqual[x, 1.56e+205]], $MachinePrecision]], N[(z + N[(N[(y + t), $MachinePrecision] * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65000000000000014e98 or 1.56000000000000007e205 < x

   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. Add Preprocessing

   3. Taylor expanded in x around inf 50.5%

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

      1. associate--r+ 50.5%

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

      2. sub-neg 50.5%

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

      3. mul-1-neg 50.5%

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

      4. associate-+r+ 50.5%

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

      5. +-commutative 50.5%

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

      6. associate--l+ 54.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in a around -inf 54.6%

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

      1. associate-*l/ 63.1%

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

      2. *-commutative 63.1%

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

      3. +-commutative 63.1%

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

   8. Simplified 63.1%

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

   if -1.65000000000000014e98 < x < 1.56000000000000007e205

   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 62.8%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+98} \lor \neg \left(x \leq 1.56 \cdot 10^{+205}\right):\\ \;\;\;\;z + \left(y + t\right) \cdot \frac{a}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+99} \lor \neg \left(x \leq 7 \cdot 10^{+205}\right):\\ \;\;\;\;z + \frac{y \cdot a}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -2.05e+99) (not (<= x 7e+205)))
   (+ z (/ (* y a) x))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.05e+99) || !(x <= 7e+205)) {
		tmp = z + ((y * a) / x);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-2.05d+99)) .or. (.not. (x <= 7d+205))) then
        tmp = z + ((y * a) / x)
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.05e+99) || !(x <= 7e+205)) {
		tmp = z + ((y * a) / x);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.05e+99) or not (x <= 7e+205):
		tmp = z + ((y * a) / x)
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -2.05e+99) || !(x <= 7e+205))
		tmp = Float64(z + Float64(Float64(y * a) / x));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -2.05e+99) || ~((x <= 7e+205)))
		tmp = z + ((y * a) / x);
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -2.05e+99], N[Not[LessEqual[x, 7e+205]], $MachinePrecision]], N[(z + N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0499999999999999e99 or 6.9999999999999996e205 < x

   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. Add Preprocessing

   3. Taylor expanded in x around inf 50.5%

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

      1. associate--r+ 50.5%

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

      2. sub-neg 50.5%

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

      3. mul-1-neg 50.5%

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

      4. associate-+r+ 50.5%

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

      5. +-commutative 50.5%

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

      6. associate--l+ 54.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in a around -inf 54.6%

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

      1. associate-*l/ 63.1%

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

      2. *-commutative 63.1%

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

      3. +-commutative 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in y around inf 54.2%

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

   if -2.0499999999999999e99 < x < 6.9999999999999996e205

   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 62.8%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+99} \lor \neg \left(x \leq 7 \cdot 10^{+205}\right):\\ \;\;\;\;z + \frac{y \cdot a}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+95} \lor \neg \left(x \leq 5.8 \cdot 10^{+204}\right):\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -6.2e+95) (not (<= x 5.8e+204)))
   (+ z (* y (/ a x)))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -6.2e+95) || !(x <= 5.8e+204)) {
		tmp = z + (y * (a / x));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-6.2d+95)) .or. (.not. (x <= 5.8d+204))) then
        tmp = z + (y * (a / x))
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -6.2e+95) || !(x <= 5.8e+204)) {
		tmp = z + (y * (a / x));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -6.2e+95) or not (x <= 5.8e+204):
		tmp = z + (y * (a / x))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -6.2e+95) || !(x <= 5.8e+204))
		tmp = Float64(z + Float64(y * Float64(a / x)));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -6.2e+95) || ~((x <= 5.8e+204)))
		tmp = z + (y * (a / x));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -6.2e+95], N[Not[LessEqual[x, 5.8e+204]], $MachinePrecision]], N[(z + N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2000000000000006e95 or 5.80000000000000007e204 < x

   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. Add Preprocessing

   3. Taylor expanded in x around inf 50.5%

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

      1. associate--r+ 50.5%

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

      2. sub-neg 50.5%

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

      3. mul-1-neg 50.5%

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

      4. associate-+r+ 50.5%

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

      5. +-commutative 50.5%

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

      6. associate--l+ 54.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in a around -inf 54.6%

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

      1. associate-*l/ 63.1%

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

      2. *-commutative 63.1%

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

      3. +-commutative 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in t around 0 54.2%

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

       1. +-commutative 54.2%

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

       2. associate-/l* 58.5%

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

   11. Simplified 58.5%

       \[\leadsto \color{blue}{\frac{a}{\frac{x}{y}} + z} \]
   12. Step-by-step derivation

       1. associate-/r/ 58.5%

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

   13. Applied egg-rr 58.5%

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

   if -6.2000000000000006e95 < x < 5.80000000000000007e204

   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 62.8%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+95} \lor \neg \left(x \leq 5.8 \cdot 10^{+204}\right):\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+97}:\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+204}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + \frac{a}{\frac{x}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.9e+97)
   (+ z (* y (/ a x)))
   (if (<= x 2e+204) (- (+ a z) b) (+ z (/ a (/ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.9e+97) {
		tmp = z + (y * (a / x));
	} else if (x <= 2e+204) {
		tmp = (a + z) - b;
	} else {
		tmp = z + (a / (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.9d+97)) then
        tmp = z + (y * (a / x))
    else if (x <= 2d+204) then
        tmp = (a + z) - b
    else
        tmp = z + (a / (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.9e+97) {
		tmp = z + (y * (a / x));
	} else if (x <= 2e+204) {
		tmp = (a + z) - b;
	} else {
		tmp = z + (a / (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.9e+97:
		tmp = z + (y * (a / x))
	elif x <= 2e+204:
		tmp = (a + z) - b
	else:
		tmp = z + (a / (x / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.9e+97)
		tmp = Float64(z + Float64(y * Float64(a / x)));
	elseif (x <= 2e+204)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z + Float64(a / Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.9e+97)
		tmp = z + (y * (a / x));
	elseif (x <= 2e+204)
		tmp = (a + z) - b;
	else
		tmp = z + (a / (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.9e+97], N[(z + N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+204], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(a / N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.89999999999999987e97

   1. Initial program 44.0%

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

   3. Taylor expanded in x around inf 46.3%

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

      1. associate--r+ 46.3%

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

      2. sub-neg 46.3%

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

      3. mul-1-neg 46.3%

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

      4. associate-+r+ 46.3%

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

      5. +-commutative 46.3%

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

      6. associate--l+ 50.1%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in a around -inf 49.8%

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

      1. associate-*l/ 59.1%

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

      2. *-commutative 59.1%

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

      3. +-commutative 59.1%

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

   8. Simplified 59.1%

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

   9. Taylor expanded in t around 0 49.7%

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

       1. +-commutative 49.7%

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

       2. associate-/l* 55.4%

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

   11. Simplified 55.4%

       \[\leadsto \color{blue}{\frac{a}{\frac{x}{y}} + z} \]
   12. Step-by-step derivation

       1. associate-/r/ 55.4%

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

   13. Applied egg-rr 55.4%

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

   if -2.89999999999999987e97 < x < 1.99999999999999998e204

   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 62.8%

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

   if 1.99999999999999998e204 < x

   1. Initial program 58.9%

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

   3. Taylor expanded in x around inf 64.1%

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

      1. associate--r+ 64.1%

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

      2. sub-neg 64.1%

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

      3. mul-1-neg 64.1%

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

      4. associate-+r+ 64.1%

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

      5. +-commutative 64.1%

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

      6. associate--l+ 70.1%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in a around -inf 70.1%

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

      1. associate-*l/ 76.1%

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

      2. *-commutative 76.1%

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

      3. +-commutative 76.1%

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

   8. Simplified 76.1%

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

   9. Taylor expanded in y around 0 65.8%

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

       1. +-commutative 65.8%

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

       2. associate-/l* 71.8%

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

   11. Simplified 71.8%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+97}:\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+204}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + \frac{a}{\frac{x}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+167}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+209}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.4e+167) z (if (<= x 5.4e+209) (- (+ a z) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.4e+167) {
		tmp = z;
	} else if (x <= 5.4e+209) {
		tmp = (a + z) - 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 <= (-3.4d+167)) then
        tmp = z
    else if (x <= 5.4d+209) then
        tmp = (a + z) - 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 <= -3.4e+167) {
		tmp = z;
	} else if (x <= 5.4e+209) {
		tmp = (a + z) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.4e+167:
		tmp = z
	elif x <= 5.4e+209:
		tmp = (a + z) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.4e+167)
		tmp = z;
	elseif (x <= 5.4e+209)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.4e+167)
		tmp = z;
	elseif (x <= 5.4e+209)
		tmp = (a + z) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.4e+167], z, If[LessEqual[x, 5.4e+209], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4e167 or 5.4e209 < x

   1. Initial program 48.7%

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

   3. Taylor expanded in x around inf 59.0%

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

   if -3.4e167 < x < 5.4e209

   1. Initial program 61.1%

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

   3. Taylor expanded in y around inf 60.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+167}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+209}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -510000:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -510000.0) a (if (<= a 2.1e+44) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -510000.0) {
		tmp = a;
	} else if (a <= 2.1e+44) {
		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 <= (-510000.0d0)) then
        tmp = a
    else if (a <= 2.1d+44) 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 <= -510000.0) {
		tmp = a;
	} else if (a <= 2.1e+44) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -510000.0:
		tmp = a
	elif a <= 2.1e+44:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -510000.0)
		tmp = a;
	elseif (a <= 2.1e+44)
		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 <= -510000.0)
		tmp = a;
	elseif (a <= 2.1e+44)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -510000.0], a, If[LessEqual[a, 2.1e+44], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -5.1e5 or 2.09999999999999987e44 < a

   1. Initial program 53.1%

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

   3. Taylor expanded in t around inf 54.5%

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

   if -5.1e5 < a < 2.09999999999999987e44

   1. Initial program 62.9%

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

   3. Taylor expanded in x around inf 41.2%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -510000:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.5% 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 29.7%

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

4. Final simplification 29.7%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 81.7% 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 2024031 
(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)))