Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.6% → 84.4%

Time: 22.2s

Alternatives: 15

Speedup: 1.6×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Initial Program: 55.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))))
          (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))
   (if (<= t_1 INFINITY) t_1 (- (+ x (/ z y)) (* a (/ x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (x + (z / y)) - (a * (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (x + (z / y)) - (a * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 93.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.0%

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

      1. associate-/l* 67.9%

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

   5. Simplified 67.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i} \leq \infty:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ t_2 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{t\_1}\\ t_3 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{t\_1 + i}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* y (+ c (* y (+ b (* y (+ y a)))))))
        (t_2
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))))
          t_1))
        (t_3 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -1.8e+78)
     t_3
     (if (<= y -7.5e-18)
       t_2
       (if (<= y 3.4e-16)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ t_1 i))
         (if (<= y 1.45e+76) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * (c + (y * (b + (y * (y + a)))));
	double t_2 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / t_1;
	double t_3 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -1.8e+78) {
		tmp = t_3;
	} else if (y <= -7.5e-18) {
		tmp = t_2;
	} else if (y <= 3.4e-16) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (t_1 + i);
	} else if (y <= 1.45e+76) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (c + (y * (b + (y * (y + a)))))
    t_2 = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))))) / t_1
    t_3 = (x + (z / y)) - (a * (x / y))
    if (y <= (-1.8d+78)) then
        tmp = t_3
    else if (y <= (-7.5d-18)) then
        tmp = t_2
    else if (y <= 3.4d-16) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (t_1 + i)
    else if (y <= 1.45d+76) 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 c, double i) {
	double t_1 = y * (c + (y * (b + (y * (y + a)))));
	double t_2 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / t_1;
	double t_3 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -1.8e+78) {
		tmp = t_3;
	} else if (y <= -7.5e-18) {
		tmp = t_2;
	} else if (y <= 3.4e-16) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (t_1 + i);
	} else if (y <= 1.45e+76) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = y * (c + (y * (b + (y * (y + a)))))
	t_2 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / t_1
	t_3 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -1.8e+78:
		tmp = t_3
	elif y <= -7.5e-18:
		tmp = t_2
	elif y <= 3.4e-16:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (t_1 + i)
	elif y <= 1.45e+76:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))
	t_2 = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))) / t_1)
	t_3 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -1.8e+78)
		tmp = t_3;
	elseif (y <= -7.5e-18)
		tmp = t_2;
	elseif (y <= 3.4e-16)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(t_1 + i));
	elseif (y <= 1.45e+76)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = y * (c + (y * (b + (y * (y + a)))));
	t_2 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / t_1;
	t_3 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -1.8e+78)
		tmp = t_3;
	elseif (y <= -7.5e-18)
		tmp = t_2;
	elseif (y <= 3.4e-16)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (t_1 + i);
	elseif (y <= 1.45e+76)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+78], t$95$3, If[LessEqual[y, -7.5e-18], t$95$2, If[LessEqual[y, 3.4e-16], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+76], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8000000000000001e78 or 1.4500000000000001e76 < y

   1. Initial program 0.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.7%

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

      1. associate-/l* 70.7%

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

   5. Simplified 70.7%

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

   if -1.8000000000000001e78 < y < -7.50000000000000015e-18 or 3.4e-16 < y < 1.4500000000000001e76

   1. Initial program 75.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 69.5%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   if -7.50000000000000015e-18 < y < 3.4e-16

   1. Initial program 99.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.3%

      \[\leadsto \frac{\left(\left(\color{blue}{y \cdot z} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+78}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+76}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+65} \lor \neg \left(y \leq 2.7 \cdot 10^{+47}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.2e+65) (not (<= y 2.7e+47)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.2e+65) || !(y <= 2.7e+47)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-5.2d+65)) .or. (.not. (y <= 2.7d+47))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.2e+65) || !(y <= 2.7e+47)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.2e+65) or not (y <= 2.7e+47):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.2e+65) || !(y <= 2.7e+47))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5.2e+65) || ~((y <= 2.7e+47)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.2e+65], N[Not[LessEqual[y, 2.7e+47]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.20000000000000005e65 or 2.69999999999999996e47 < y

   1. Initial program 6.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.4%

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

      1. associate-/l* 69.1%

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

   5. Simplified 69.1%

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

   if -5.20000000000000005e65 < y < 2.69999999999999996e47

   1. Initial program 94.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.7%

      \[\leadsto \frac{\left(\left(\color{blue}{y \cdot z} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+65} \lor \neg \left(y \leq 2.7 \cdot 10^{+47}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := \frac{t\_1}{i}\\ t_3 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -47000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-241}:\\ \;\;\;\;\frac{t\_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616)))
        (t_2 (/ t_1 i))
        (t_3 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -47000.0)
     t_3
     (if (<= y -2.6e-224)
       t_2
       (if (<= y -3.8e-241)
         (/ t_1 (* y c))
         (if (<= y 2.15e-26)
           t_2
           (if (<= y 5e+101) (* y (+ (/ x a) (/ z (* y a)))) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = t_1 / i;
	double t_3 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -47000.0) {
		tmp = t_3;
	} else if (y <= -2.6e-224) {
		tmp = t_2;
	} else if (y <= -3.8e-241) {
		tmp = t_1 / (y * c);
	} else if (y <= 2.15e-26) {
		tmp = t_2;
	} else if (y <= 5e+101) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = t_1 / i
    t_3 = (x + (z / y)) - (a * (x / y))
    if (y <= (-47000.0d0)) then
        tmp = t_3
    else if (y <= (-2.6d-224)) then
        tmp = t_2
    else if (y <= (-3.8d-241)) then
        tmp = t_1 / (y * c)
    else if (y <= 2.15d-26) then
        tmp = t_2
    else if (y <= 5d+101) then
        tmp = y * ((x / a) + (z / (y * a)))
    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 c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = t_1 / i;
	double t_3 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -47000.0) {
		tmp = t_3;
	} else if (y <= -2.6e-224) {
		tmp = t_2;
	} else if (y <= -3.8e-241) {
		tmp = t_1 / (y * c);
	} else if (y <= 2.15e-26) {
		tmp = t_2;
	} else if (y <= 5e+101) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = t_1 / i
	t_3 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -47000.0:
		tmp = t_3
	elif y <= -2.6e-224:
		tmp = t_2
	elif y <= -3.8e-241:
		tmp = t_1 / (y * c)
	elif y <= 2.15e-26:
		tmp = t_2
	elif y <= 5e+101:
		tmp = y * ((x / a) + (z / (y * a)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(t_1 / i)
	t_3 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -47000.0)
		tmp = t_3;
	elseif (y <= -2.6e-224)
		tmp = t_2;
	elseif (y <= -3.8e-241)
		tmp = Float64(t_1 / Float64(y * c));
	elseif (y <= 2.15e-26)
		tmp = t_2;
	elseif (y <= 5e+101)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(z / Float64(y * a))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = t_1 / i;
	t_3 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -47000.0)
		tmp = t_3;
	elseif (y <= -2.6e-224)
		tmp = t_2;
	elseif (y <= -3.8e-241)
		tmp = t_1 / (y * c);
	elseif (y <= 2.15e-26)
		tmp = t_2;
	elseif (y <= 5e+101)
		tmp = y * ((x / a) + (z / (y * a)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / i), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -47000.0], t$95$3, If[LessEqual[y, -2.6e-224], t$95$2, If[LessEqual[y, -3.8e-241], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e-26], t$95$2, If[LessEqual[y, 5e+101], N[(y * N[(N[(x / a), $MachinePrecision] + N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -47000 or 4.99999999999999989e101 < y

   1. Initial program 11.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.7%

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

      1. associate-/l* 64.2%

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

   5. Simplified 64.2%

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

   if -47000 < y < -2.6000000000000002e-224 or -3.7999999999999999e-241 < y < 2.14999999999999994e-26

   1. Initial program 99.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 93.9%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 93.9%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 93.9%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 92.3%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 92.3%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 92.3%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in y around 0 92.3%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
   10. Step-by-step derivation

       1. *-commutative 92.3%

          \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   11. Simplified 92.3%

       \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   12. Taylor expanded in i around inf 67.4%

       \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]

   if -2.6000000000000002e-224 < y < -3.7999999999999999e-241

   1. Initial program 98.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 98.8%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 98.8%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
   10. Step-by-step derivation

       1. *-commutative 98.8%

          \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   11. Simplified 98.8%

       \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   12. Taylor expanded in c around inf 98.8%

       \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{c \cdot y}} \]

   if 2.14999999999999994e-26 < y < 4.99999999999999989e101

   1. Initial program 68.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 22.9%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]

   4. Taylor expanded in y around inf 27.7%

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

      1. *-commutative 27.7%

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

   6. Simplified 27.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -47000:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-241}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := \frac{t\_1}{i}\\ t_3 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -180000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-241}:\\ \;\;\;\;\frac{t\_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616)))
        (t_2 (/ t_1 i))
        (t_3 (+ x (/ (- z (* x a)) y))))
   (if (<= y -180000000000.0)
     t_3
     (if (<= y -2.6e-224)
       t_2
       (if (<= y -3.8e-241)
         (/ t_1 (* y c))
         (if (<= y 3e-26)
           t_2
           (if (<= y 5.1e+101) (* y (+ (/ x a) (/ z (* y a)))) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = t_1 / i;
	double t_3 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -180000000000.0) {
		tmp = t_3;
	} else if (y <= -2.6e-224) {
		tmp = t_2;
	} else if (y <= -3.8e-241) {
		tmp = t_1 / (y * c);
	} else if (y <= 3e-26) {
		tmp = t_2;
	} else if (y <= 5.1e+101) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = t_1 / i
    t_3 = x + ((z - (x * a)) / y)
    if (y <= (-180000000000.0d0)) then
        tmp = t_3
    else if (y <= (-2.6d-224)) then
        tmp = t_2
    else if (y <= (-3.8d-241)) then
        tmp = t_1 / (y * c)
    else if (y <= 3d-26) then
        tmp = t_2
    else if (y <= 5.1d+101) then
        tmp = y * ((x / a) + (z / (y * a)))
    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 c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = t_1 / i;
	double t_3 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -180000000000.0) {
		tmp = t_3;
	} else if (y <= -2.6e-224) {
		tmp = t_2;
	} else if (y <= -3.8e-241) {
		tmp = t_1 / (y * c);
	} else if (y <= 3e-26) {
		tmp = t_2;
	} else if (y <= 5.1e+101) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = t_1 / i
	t_3 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -180000000000.0:
		tmp = t_3
	elif y <= -2.6e-224:
		tmp = t_2
	elif y <= -3.8e-241:
		tmp = t_1 / (y * c)
	elif y <= 3e-26:
		tmp = t_2
	elif y <= 5.1e+101:
		tmp = y * ((x / a) + (z / (y * a)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(t_1 / i)
	t_3 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -180000000000.0)
		tmp = t_3;
	elseif (y <= -2.6e-224)
		tmp = t_2;
	elseif (y <= -3.8e-241)
		tmp = Float64(t_1 / Float64(y * c));
	elseif (y <= 3e-26)
		tmp = t_2;
	elseif (y <= 5.1e+101)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(z / Float64(y * a))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = t_1 / i;
	t_3 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -180000000000.0)
		tmp = t_3;
	elseif (y <= -2.6e-224)
		tmp = t_2;
	elseif (y <= -3.8e-241)
		tmp = t_1 / (y * c);
	elseif (y <= 3e-26)
		tmp = t_2;
	elseif (y <= 5.1e+101)
		tmp = y * ((x / a) + (z / (y * a)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / i), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -180000000000.0], t$95$3, If[LessEqual[y, -2.6e-224], t$95$2, If[LessEqual[y, -3.8e-241], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-26], t$95$2, If[LessEqual[y, 5.1e+101], N[(y * N[(N[(x / a), $MachinePrecision] + N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.8e11 or 5.09999999999999995e101 < y

   1. Initial program 11.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

      3. sub-neg 60.7%

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

      4. mul-1-neg 60.7%

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

      5. mul-1-neg 60.7%

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

      6. remove-double-neg 60.7%

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

   5. Simplified 60.7%

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

   if -1.8e11 < y < -2.6000000000000002e-224 or -3.7999999999999999e-241 < y < 3.00000000000000012e-26

   1. Initial program 99.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 93.9%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 93.9%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 93.9%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 92.3%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 92.3%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 92.3%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in y around 0 92.3%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
   10. Step-by-step derivation

       1. *-commutative 92.3%

          \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   11. Simplified 92.3%

       \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   12. Taylor expanded in i around inf 67.4%

       \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]

   if -2.6000000000000002e-224 < y < -3.7999999999999999e-241

   1. Initial program 98.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 98.8%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 98.8%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
   10. Step-by-step derivation

       1. *-commutative 98.8%

          \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   11. Simplified 98.8%

       \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   12. Taylor expanded in c around inf 98.8%

       \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{c \cdot y}} \]

   if 3.00000000000000012e-26 < y < 5.09999999999999995e101

   1. Initial program 68.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 22.9%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]

   4. Taylor expanded in y around inf 27.7%

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

      1. *-commutative 27.7%

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

   6. Simplified 27.7%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -180000000000:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-241}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+53} \lor \neg \left(y \leq 1.35 \cdot 10^{+45}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8e+53) (not (<= y 1.35e+45)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8e+53) || !(y <= 1.35e+45)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-8d+53)) .or. (.not. (y <= 1.35d+45))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8e+53) || !(y <= 1.35e+45)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8e+53) or not (y <= 1.35e+45):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8e+53) || !(y <= 1.35e+45))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -8e+53) || ~((y <= 1.35e+45)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8e+53], N[Not[LessEqual[y, 1.35e+45]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999999e53 or 1.34999999999999992e45 < y

   1. Initial program 8.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 63.7%

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

      1. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   if -7.9999999999999999e53 < y < 1.34999999999999992e45

   1. Initial program 94.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.9%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 80.9%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 80.9%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+53} \lor \neg \left(y \leq 1.35 \cdot 10^{+45}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+23} \lor \neg \left(y \leq 1.4 \cdot 10^{+47}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.8e+23) (not (<= y 1.4e+47)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/ (+ t (* y 230661.510616)) (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.8e+23) || !(y <= 1.4e+47)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.8d+23)) .or. (.not. (y <= 1.4d+47))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * 230661.510616d0)) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.8e+23) || !(y <= 1.4e+47)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.8e+23) or not (y <= 1.4e+47):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.8e+23) || !(y <= 1.4e+47))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.8e+23) || ~((y <= 1.4e+47)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.8e+23], N[Not[LessEqual[y, 1.4e+47]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999999e23 or 1.39999999999999994e47 < y

   1. Initial program 11.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.0%

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

      1. associate-/l* 62.3%

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

   5. Simplified 62.3%

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

   if -1.7999999999999999e23 < y < 1.39999999999999994e47

   1. Initial program 98.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.4%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 84.4%

         \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 84.4%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+23} \lor \neg \left(y \leq 1.4 \cdot 10^{+47}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := \frac{t\_1}{i}\\ t_3 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -51000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-241}:\\ \;\;\;\;\frac{t\_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616)))
        (t_2 (/ t_1 i))
        (t_3 (+ x (/ (- z (* x a)) y))))
   (if (<= y -51000000000.0)
     t_3
     (if (<= y -2.6e-224)
       t_2
       (if (<= y -3.8e-241) (/ t_1 (* y c)) (if (<= y 4.6e-15) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = t_1 / i;
	double t_3 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -51000000000.0) {
		tmp = t_3;
	} else if (y <= -2.6e-224) {
		tmp = t_2;
	} else if (y <= -3.8e-241) {
		tmp = t_1 / (y * c);
	} else if (y <= 4.6e-15) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = t_1 / i
    t_3 = x + ((z - (x * a)) / y)
    if (y <= (-51000000000.0d0)) then
        tmp = t_3
    else if (y <= (-2.6d-224)) then
        tmp = t_2
    else if (y <= (-3.8d-241)) then
        tmp = t_1 / (y * c)
    else if (y <= 4.6d-15) 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 c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = t_1 / i;
	double t_3 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -51000000000.0) {
		tmp = t_3;
	} else if (y <= -2.6e-224) {
		tmp = t_2;
	} else if (y <= -3.8e-241) {
		tmp = t_1 / (y * c);
	} else if (y <= 4.6e-15) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = t_1 / i
	t_3 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -51000000000.0:
		tmp = t_3
	elif y <= -2.6e-224:
		tmp = t_2
	elif y <= -3.8e-241:
		tmp = t_1 / (y * c)
	elif y <= 4.6e-15:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(t_1 / i)
	t_3 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -51000000000.0)
		tmp = t_3;
	elseif (y <= -2.6e-224)
		tmp = t_2;
	elseif (y <= -3.8e-241)
		tmp = Float64(t_1 / Float64(y * c));
	elseif (y <= 4.6e-15)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = t_1 / i;
	t_3 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -51000000000.0)
		tmp = t_3;
	elseif (y <= -2.6e-224)
		tmp = t_2;
	elseif (y <= -3.8e-241)
		tmp = t_1 / (y * c);
	elseif (y <= 4.6e-15)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / i), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -51000000000.0], t$95$3, If[LessEqual[y, -2.6e-224], t$95$2, If[LessEqual[y, -3.8e-241], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-15], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.1e10 or 4.59999999999999981e-15 < y

   1. Initial program 22.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

      3. sub-neg 51.4%

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

      4. mul-1-neg 51.4%

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

      5. mul-1-neg 51.4%

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

      6. remove-double-neg 51.4%

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

   5. Simplified 51.4%

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

   if -5.1e10 < y < -2.6000000000000002e-224 or -3.7999999999999999e-241 < y < 4.59999999999999981e-15

   1. Initial program 99.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 91.7%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 91.7%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 91.7%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 90.2%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 90.2%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 90.2%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in y around 0 90.2%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
   10. Step-by-step derivation

       1. *-commutative 90.2%

          \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   11. Simplified 90.2%

       \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   12. Taylor expanded in i around inf 65.9%

       \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]

   if -2.6000000000000002e-224 < y < -3.7999999999999999e-241

   1. Initial program 98.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 98.8%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 98.8%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
   10. Step-by-step derivation

       1. *-commutative 98.8%

          \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   11. Simplified 98.8%

       \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   12. Taylor expanded in c around inf 98.8%

       \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{c \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -51000000000:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-241}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+51} \lor \neg \left(y \leq 6.5 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.1e+51) (not (<= y 6.5e+44)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.1e+51) || !(y <= 6.5e+44)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-4.1d+51)) .or. (.not. (y <= 6.5d+44))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * 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 c, double i) {
	double tmp;
	if ((y <= -4.1e+51) || !(y <= 6.5e+44)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.1e+51) or not (y <= 6.5e+44):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.1e+51) || !(y <= 6.5e+44))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.1e+51) || ~((y <= 6.5e+44)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.1e+51], N[Not[LessEqual[y, 6.5e+44]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.10000000000000011e51 or 6.50000000000000018e44 < y

   1. Initial program 9.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.5%

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

      1. associate-/l* 66.0%

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

   5. Simplified 66.0%

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

   if -4.10000000000000011e51 < y < 6.50000000000000018e44

   1. Initial program 95.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.3%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 81.3%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 81.3%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 78.1%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 78.1%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 78.1%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+51} \lor \neg \left(y \leq 6.5 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := \frac{t\_1}{i}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-241}:\\ \;\;\;\;\frac{t\_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-17}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))) (t_2 (/ t_1 i)))
   (if (<= y -1.55e+27)
     x
     (if (<= y -2.6e-224)
       t_2
       (if (<= y -3.8e-241) (/ t_1 (* y c)) (if (<= y 3.2e-17) t_2 x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = t_1 / i;
	double tmp;
	if (y <= -1.55e+27) {
		tmp = x;
	} else if (y <= -2.6e-224) {
		tmp = t_2;
	} else if (y <= -3.8e-241) {
		tmp = t_1 / (y * c);
	} else if (y <= 3.2e-17) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = t_1 / i
    if (y <= (-1.55d+27)) then
        tmp = x
    else if (y <= (-2.6d-224)) then
        tmp = t_2
    else if (y <= (-3.8d-241)) then
        tmp = t_1 / (y * c)
    else if (y <= 3.2d-17) then
        tmp = t_2
    else
        tmp = 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 c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = t_1 / i;
	double tmp;
	if (y <= -1.55e+27) {
		tmp = x;
	} else if (y <= -2.6e-224) {
		tmp = t_2;
	} else if (y <= -3.8e-241) {
		tmp = t_1 / (y * c);
	} else if (y <= 3.2e-17) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = t_1 / i
	tmp = 0
	if y <= -1.55e+27:
		tmp = x
	elif y <= -2.6e-224:
		tmp = t_2
	elif y <= -3.8e-241:
		tmp = t_1 / (y * c)
	elif y <= 3.2e-17:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(t_1 / i)
	tmp = 0.0
	if (y <= -1.55e+27)
		tmp = x;
	elseif (y <= -2.6e-224)
		tmp = t_2;
	elseif (y <= -3.8e-241)
		tmp = Float64(t_1 / Float64(y * c));
	elseif (y <= 3.2e-17)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = t_1 / i;
	tmp = 0.0;
	if (y <= -1.55e+27)
		tmp = x;
	elseif (y <= -2.6e-224)
		tmp = t_2;
	elseif (y <= -3.8e-241)
		tmp = t_1 / (y * c);
	elseif (y <= 3.2e-17)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / i), $MachinePrecision]}, If[LessEqual[y, -1.55e+27], x, If[LessEqual[y, -2.6e-224], t$95$2, If[LessEqual[y, -3.8e-241], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-17], t$95$2, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999998e27 or 3.2000000000000002e-17 < y

   1. Initial program 20.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 43.5%

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

   if -1.54999999999999998e27 < y < -2.6000000000000002e-224 or -3.7999999999999999e-241 < y < 3.2000000000000002e-17

   1. Initial program 99.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 89.6%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 89.6%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 89.6%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 88.2%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 88.2%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 88.2%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in y around 0 88.3%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
   10. Step-by-step derivation

       1. *-commutative 88.3%

          \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   11. Simplified 88.3%

       \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   12. Taylor expanded in i around inf 63.9%

       \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]

   if -2.6000000000000002e-224 < y < -3.7999999999999999e-241

   1. Initial program 98.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 98.8%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 98.8%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in y around 0 98.8%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
   10. Step-by-step derivation

       1. *-commutative 98.8%

          \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   11. Simplified 98.8%

       \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   12. Taylor expanded in c around inf 98.8%

       \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{c \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-241}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+22} \lor \neg \left(y \leq 4 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7.4e+22) (not (<= y 4e+44)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7.4e+22) || !(y <= 4e+44)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-7.4d+22)) .or. (.not. (y <= 4d+44))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * 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 c, double i) {
	double tmp;
	if ((y <= -7.4e+22) || !(y <= 4e+44)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7.4e+22) or not (y <= 4e+44):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7.4e+22) || !(y <= 4e+44))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -7.4e+22) || ~((y <= 4e+44)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7.4e+22], N[Not[LessEqual[y, 4e+44]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.3999999999999996e22 or 4.0000000000000004e44 < y

   1. Initial program 12.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 58.6%

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

      1. associate-/l* 61.8%

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

   5. Simplified 61.8%

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

   if -7.3999999999999996e22 < y < 4.0000000000000004e44

   1. Initial program 98.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.9%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 84.9%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 84.9%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 82.0%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 82.0%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 82.0%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in y around 0 82.0%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
   10. Step-by-step derivation

       1. *-commutative 82.0%

          \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   11. Simplified 82.0%

       \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+22} \lor \neg \left(y \leq 4 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+23} \lor \neg \left(y \leq 4 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.8e+23) (not (<= y 4e+44)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.8e+23) || !(y <= 4e+44)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.8d+23)) .or. (.not. (y <= 4d+44))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = t / (i + (y * (c + (y * 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 c, double i) {
	double tmp;
	if ((y <= -3.8e+23) || !(y <= 4e+44)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.8e+23) or not (y <= 4e+44):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.8e+23) || !(y <= 4e+44))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.8e+23) || ~((y <= 4e+44)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.8e+23], N[Not[LessEqual[y, 4e+44]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999975e23 or 4.0000000000000004e44 < y

   1. Initial program 12.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 58.6%

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

      1. associate-/l* 61.8%

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

   5. Simplified 61.8%

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

   if -3.79999999999999975e23 < y < 4.0000000000000004e44

   1. Initial program 98.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.9%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 84.9%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 84.9%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 82.0%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 82.0%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 82.0%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in t around inf 72.3%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+23} \lor \neg \left(y \leq 4 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+24} \lor \neg \left(y \leq 3.2 \cdot 10^{-17}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.3e+24) (not (<= y 3.2e-17)))
   x
   (/ (+ t (* y 230661.510616)) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.3e+24) || !(y <= 3.2e-17)) {
		tmp = x;
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.3d+24)) .or. (.not. (y <= 3.2d-17))) then
        tmp = x
    else
        tmp = (t + (y * 230661.510616d0)) / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.3e+24) || !(y <= 3.2e-17)) {
		tmp = x;
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.3e+24) or not (y <= 3.2e-17):
		tmp = x
	else:
		tmp = (t + (y * 230661.510616)) / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.3e+24) || !(y <= 3.2e-17))
		tmp = x;
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.3e+24) || ~((y <= 3.2e-17)))
		tmp = x;
	else
		tmp = (t + (y * 230661.510616)) / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.3e+24], N[Not[LessEqual[y, 3.2e-17]], $MachinePrecision]], x, N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2999999999999999e24 or 3.2000000000000002e-17 < y

   1. Initial program 20.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 43.5%

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

   if -3.2999999999999999e24 < y < 3.2000000000000002e-17

   1. Initial program 99.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 90.0%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 90.0%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 90.0%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0 88.6%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   7. Step-by-step derivation

      1. *-commutative 88.6%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   8. Simplified 88.6%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   9. Taylor expanded in y around 0 88.7%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(y \cdot b + c\right) \cdot y + i} \]
   10. Step-by-step derivation

       1. *-commutative 88.7%

          \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   11. Simplified 88.7%

       \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(y \cdot b + c\right) \cdot y + i} \]

   12. Taylor expanded in i around inf 61.7%

       \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+24} \lor \neg \left(y \leq 3.2 \cdot 10^{-17}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+39} \lor \neg \left(y \leq 3.8 \cdot 10^{-25}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -9.6e+39) (not (<= y 3.8e-25))) x (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9.6e+39) || !(y <= 3.8e-25)) {
		tmp = x;
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-9.6d+39)) .or. (.not. (y <= 3.8d-25))) then
        tmp = x
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9.6e+39) || !(y <= 3.8e-25)) {
		tmp = x;
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -9.6e+39) or not (y <= 3.8e-25):
		tmp = x
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -9.6e+39) || !(y <= 3.8e-25))
		tmp = x;
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -9.6e+39) || ~((y <= 3.8e-25)))
		tmp = x;
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -9.6e+39], N[Not[LessEqual[y, 3.8e-25]], $MachinePrecision]], x, N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.6000000000000004e39 or 3.7999999999999998e-25 < y

   1. Initial program 19.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 44.1%

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

   if -9.6000000000000004e39 < y < 3.7999999999999998e-25

   1. Initial program 98.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 57.7%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+39} \lor \neg \left(y \leq 3.8 \cdot 10^{-25}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.9% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := x

Derivation

1. Initial program 60.9%

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 22.6%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))