Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.8% → 88.1%

Time: 33.4s

Alternatives: 14

Speedup: 1.9×

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: 56.8% 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: 88.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := \frac{{y}^{2}}{t\_1}\\ t_3 := x \cdot t\_1\\ t_4 := \frac{1}{t\_3}\\ t_5 := \frac{t}{x \cdot \left(t\_1 \cdot {y}^{2}\right)}\\ t_6 := y \cdot t\_1\\ t_7 := i + y \cdot \left(t\_6 + c\right)\\ t_8 := \frac{1}{x \cdot t\_6}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+124}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(230661.510616 \cdot t\_8 + \left(27464.7644705 \cdot t\_4 + \left(t\_5 + \left(\frac{y \cdot z}{t\_3} + t\_2\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{t\_7} + \left(\frac{x \cdot {y}^{4}}{t\_7} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{t\_7}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(230661.510616, t\_8, \mathsf{fma}\left(27464.7644705, t\_4, t\_5 + \left(t\_2 + \frac{y}{x} \cdot \frac{z}{t\_1}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (/ (pow y 2.0) t_1))
        (t_3 (* x t_1))
        (t_4 (/ 1.0 t_3))
        (t_5 (/ t (* x (* t_1 (pow y 2.0)))))
        (t_6 (* y t_1))
        (t_7 (+ i (* y (+ t_6 c))))
        (t_8 (/ 1.0 (* x t_6))))
   (if (<= y -1.65e+124)
     (- x (/ (* z (+ -1.0 (/ a y))) y))
     (if (<= y -1.6e+17)
       (*
        x
        (+
         (* 230661.510616 t_8)
         (+ (* 27464.7644705 t_4) (+ t_5 (+ (/ (* y z) t_3) t_2)))))
       (if (<= y 4.8e+15)
         (+
          (/ t t_7)
          (+
           (/ (* x (pow y 4.0)) t_7)
           (/ (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))) t_7)))
         (if (<= y 6.5e+139)
           (*
            x
            (fma
             230661.510616
             t_8
             (fma 27464.7644705 t_4 (+ t_5 (+ t_2 (* (/ y x) (/ z 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 = b + (y * (y + a));
	double t_2 = pow(y, 2.0) / t_1;
	double t_3 = x * t_1;
	double t_4 = 1.0 / t_3;
	double t_5 = t / (x * (t_1 * pow(y, 2.0)));
	double t_6 = y * t_1;
	double t_7 = i + (y * (t_6 + c));
	double t_8 = 1.0 / (x * t_6);
	double tmp;
	if (y <= -1.65e+124) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= -1.6e+17) {
		tmp = x * ((230661.510616 * t_8) + ((27464.7644705 * t_4) + (t_5 + (((y * z) / t_3) + t_2))));
	} else if (y <= 4.8e+15) {
		tmp = (t / t_7) + (((x * pow(y, 4.0)) / t_7) + ((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) / t_7));
	} else if (y <= 6.5e+139) {
		tmp = x * fma(230661.510616, t_8, fma(27464.7644705, t_4, (t_5 + (t_2 + ((y / x) * (z / 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(b + Float64(y * Float64(y + a)))
	t_2 = Float64((y ^ 2.0) / t_1)
	t_3 = Float64(x * t_1)
	t_4 = Float64(1.0 / t_3)
	t_5 = Float64(t / Float64(x * Float64(t_1 * (y ^ 2.0))))
	t_6 = Float64(y * t_1)
	t_7 = Float64(i + Float64(y * Float64(t_6 + c)))
	t_8 = Float64(1.0 / Float64(x * t_6))
	tmp = 0.0
	if (y <= -1.65e+124)
		tmp = Float64(x - Float64(Float64(z * Float64(-1.0 + Float64(a / y))) / y));
	elseif (y <= -1.6e+17)
		tmp = Float64(x * Float64(Float64(230661.510616 * t_8) + Float64(Float64(27464.7644705 * t_4) + Float64(t_5 + Float64(Float64(Float64(y * z) / t_3) + t_2)))));
	elseif (y <= 4.8e+15)
		tmp = Float64(Float64(t / t_7) + Float64(Float64(Float64(x * (y ^ 4.0)) / t_7) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))) / t_7)));
	elseif (y <= 6.5e+139)
		tmp = Float64(x * fma(230661.510616, t_8, fma(27464.7644705, t_4, Float64(t_5 + Float64(t_2 + Float64(Float64(y / x) * Float64(z / t_1)))))));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[y, 2.0], $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(1.0 / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t / N[(x * N[(t$95$1 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y * t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[(i + N[(y * N[(t$95$6 + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(1.0 / N[(x * t$95$6), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+124], N[(x - N[(N[(z * N[(-1.0 + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e+17], N[(x * N[(N[(230661.510616 * t$95$8), $MachinePrecision] + N[(N[(27464.7644705 * t$95$4), $MachinePrecision] + N[(t$95$5 + N[(N[(N[(y * z), $MachinePrecision] / t$95$3), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+15], N[(N[(t / t$95$7), $MachinePrecision] + N[(N[(N[(x * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] / t$95$7), $MachinePrecision] + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+139], N[(x * N[(230661.510616 * t$95$8 + N[(27464.7644705 * t$95$4 + N[(t$95$5 + N[(t$95$2 + N[(N[(y / x), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.65000000000000007e124

   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 60.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{27464.7644705 - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]

   4. Taylor expanded in z around inf 87.6%

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

   if -1.65000000000000007e124 < y < -1.6e17

   1. Initial program 45.1%

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

   3. Taylor expanded in x around inf 53.0%

      \[\leadsto \color{blue}{x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   4. Taylor expanded in i around 0 63.3%

      \[\leadsto \color{blue}{x \cdot \left(230661.510616 \cdot \frac{1}{x \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{t}{x \cdot \left(y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\frac{y \cdot \left(27464.7644705 + y \cdot z\right)}{x \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right)\right)\right)} \]

   5. Taylor expanded in c around 0 71.8%

      \[\leadsto \color{blue}{x \cdot \left(230661.510616 \cdot \frac{1}{x \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(27464.7644705 \cdot \frac{1}{x \cdot \left(b + y \cdot \left(a + y\right)\right)} + \left(\frac{t}{x \cdot \left({y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{y \cdot z}{x \cdot \left(b + y \cdot \left(a + y\right)\right)} + \frac{{y}^{2}}{b + y \cdot \left(a + y\right)}\right)\right)\right)\right)} \]

   if -1.6e17 < y < 4.8e15

   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 99.7%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   if 4.8e15 < y < 6.5000000000000003e139

   1. Initial program 17.0%

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

   3. Taylor expanded in x around inf 23.1%

      \[\leadsto \color{blue}{x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   4. Taylor expanded in i around 0 30.9%

      \[\leadsto \color{blue}{x \cdot \left(230661.510616 \cdot \frac{1}{x \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{t}{x \cdot \left(y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\frac{y \cdot \left(27464.7644705 + y \cdot z\right)}{x \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right)\right)\right)} \]

   5. Taylor expanded in c around 0 73.3%

      \[\leadsto \color{blue}{x \cdot \left(230661.510616 \cdot \frac{1}{x \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(27464.7644705 \cdot \frac{1}{x \cdot \left(b + y \cdot \left(a + y\right)\right)} + \left(\frac{t}{x \cdot \left({y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{y \cdot z}{x \cdot \left(b + y \cdot \left(a + y\right)\right)} + \frac{{y}^{2}}{b + y \cdot \left(a + y\right)}\right)\right)\right)\right)} \]
   6. Step-by-step derivation

      1. fma-define 73.3%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(230661.510616, \frac{1}{x \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, 27464.7644705 \cdot \frac{1}{x \cdot \left(b + y \cdot \left(a + y\right)\right)} + \left(\frac{t}{x \cdot \left({y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{y \cdot z}{x \cdot \left(b + y \cdot \left(a + y\right)\right)} + \frac{{y}^{2}}{b + y \cdot \left(a + y\right)}\right)\right)\right)} \]

      2. fma-define 73.3%

         \[\leadsto x \cdot \mathsf{fma}\left(230661.510616, \frac{1}{x \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, \color{blue}{\mathsf{fma}\left(27464.7644705, \frac{1}{x \cdot \left(b + y \cdot \left(a + y\right)\right)}, \frac{t}{x \cdot \left({y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{y \cdot z}{x \cdot \left(b + y \cdot \left(a + y\right)\right)} + \frac{{y}^{2}}{b + y \cdot \left(a + y\right)}\right)\right)}\right) \]

   7. Simplified 73.8%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(230661.510616, \frac{1}{x \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, \mathsf{fma}\left(27464.7644705, \frac{1}{x \cdot \left(b + y \cdot \left(a + y\right)\right)}, \frac{t}{x \cdot \left({y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{y}{x} \cdot \frac{z}{b + y \cdot \left(a + y\right)} + \frac{{y}^{2}}{b + y \cdot \left(a + y\right)}\right)\right)\right)} \]

   if 6.5000000000000003e139 < y

   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 89.3%

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

      1. associate--l+ 89.3%

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

      2. associate-/l* 92.6%

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

   5. Simplified 92.6%

      \[\leadsto \color{blue}{x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+124}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(230661.510616 \cdot \frac{1}{x \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(27464.7644705 \cdot \frac{1}{x \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{x \cdot \left(\left(b + y \cdot \left(y + a\right)\right) \cdot {y}^{2}\right)} + \left(\frac{y \cdot z}{x \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{{y}^{2}}{b + y \cdot \left(y + a\right)}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(230661.510616, \frac{1}{x \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}, \mathsf{fma}\left(27464.7644705, \frac{1}{x \cdot \left(b + y \cdot \left(y + a\right)\right)}, \frac{t}{x \cdot \left(\left(b + y \cdot \left(y + a\right)\right) \cdot {y}^{2}\right)} + \left(\frac{{y}^{2}}{b + y \cdot \left(y + a\right)} + \frac{y}{x} \cdot \frac{z}{b + y \cdot \left(y + a\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := y \cdot t\_1\\ t_3 := i + y \cdot \left(t\_2 + c\right)\\ t_4 := x \cdot t\_1\\ t_5 := x \cdot \left(230661.510616 \cdot \frac{1}{x \cdot t\_2} + \left(27464.7644705 \cdot \frac{1}{t\_4} + \left(\frac{t}{x \cdot \left(t\_1 \cdot {y}^{2}\right)} + \left(\frac{y \cdot z}{t\_4} + \frac{{y}^{2}}{t\_1}\right)\right)\right)\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+123}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+17}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{t}{t\_3} + \left(\frac{x \cdot {y}^{4}}{t\_3} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{t\_3}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+139}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (* y t_1))
        (t_3 (+ i (* y (+ t_2 c))))
        (t_4 (* x t_1))
        (t_5
         (*
          x
          (+
           (* 230661.510616 (/ 1.0 (* x t_2)))
           (+
            (* 27464.7644705 (/ 1.0 t_4))
            (+
             (/ t (* x (* t_1 (pow y 2.0))))
             (+ (/ (* y z) t_4) (/ (pow y 2.0) t_1))))))))
   (if (<= y -6.4e+123)
     (- x (/ (* z (+ -1.0 (/ a y))) y))
     (if (<= y -1.6e+17)
       t_5
       (if (<= y 8.5e+18)
         (+
          (/ t t_3)
          (+
           (/ (* x (pow y 4.0)) t_3)
           (/ (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))) t_3)))
         (if (<= y 9e+139) t_5 (+ 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 = b + (y * (y + a));
	double t_2 = y * t_1;
	double t_3 = i + (y * (t_2 + c));
	double t_4 = x * t_1;
	double t_5 = x * ((230661.510616 * (1.0 / (x * t_2))) + ((27464.7644705 * (1.0 / t_4)) + ((t / (x * (t_1 * pow(y, 2.0)))) + (((y * z) / t_4) + (pow(y, 2.0) / t_1)))));
	double tmp;
	if (y <= -6.4e+123) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= -1.6e+17) {
		tmp = t_5;
	} else if (y <= 8.5e+18) {
		tmp = (t / t_3) + (((x * pow(y, 4.0)) / t_3) + ((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) / t_3));
	} else if (y <= 9e+139) {
		tmp = t_5;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = b + (y * (y + a))
    t_2 = y * t_1
    t_3 = i + (y * (t_2 + c))
    t_4 = x * t_1
    t_5 = x * ((230661.510616d0 * (1.0d0 / (x * t_2))) + ((27464.7644705d0 * (1.0d0 / t_4)) + ((t / (x * (t_1 * (y ** 2.0d0)))) + (((y * z) / t_4) + ((y ** 2.0d0) / t_1)))))
    if (y <= (-6.4d+123)) then
        tmp = x - ((z * ((-1.0d0) + (a / y))) / y)
    else if (y <= (-1.6d+17)) then
        tmp = t_5
    else if (y <= 8.5d+18) then
        tmp = (t / t_3) + (((x * (y ** 4.0d0)) / t_3) + ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z))))) / t_3))
    else if (y <= 9d+139) then
        tmp = t_5
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = y * t_1;
	double t_3 = i + (y * (t_2 + c));
	double t_4 = x * t_1;
	double t_5 = x * ((230661.510616 * (1.0 / (x * t_2))) + ((27464.7644705 * (1.0 / t_4)) + ((t / (x * (t_1 * Math.pow(y, 2.0)))) + (((y * z) / t_4) + (Math.pow(y, 2.0) / t_1)))));
	double tmp;
	if (y <= -6.4e+123) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= -1.6e+17) {
		tmp = t_5;
	} else if (y <= 8.5e+18) {
		tmp = (t / t_3) + (((x * Math.pow(y, 4.0)) / t_3) + ((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) / t_3));
	} else if (y <= 9e+139) {
		tmp = t_5;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b + (y * (y + a))
	t_2 = y * t_1
	t_3 = i + (y * (t_2 + c))
	t_4 = x * t_1
	t_5 = x * ((230661.510616 * (1.0 / (x * t_2))) + ((27464.7644705 * (1.0 / t_4)) + ((t / (x * (t_1 * math.pow(y, 2.0)))) + (((y * z) / t_4) + (math.pow(y, 2.0) / t_1)))))
	tmp = 0
	if y <= -6.4e+123:
		tmp = x - ((z * (-1.0 + (a / y))) / y)
	elif y <= -1.6e+17:
		tmp = t_5
	elif y <= 8.5e+18:
		tmp = (t / t_3) + (((x * math.pow(y, 4.0)) / t_3) + ((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) / t_3))
	elif y <= 9e+139:
		tmp = t_5
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	t_2 = Float64(y * t_1)
	t_3 = Float64(i + Float64(y * Float64(t_2 + c)))
	t_4 = Float64(x * t_1)
	t_5 = Float64(x * Float64(Float64(230661.510616 * Float64(1.0 / Float64(x * t_2))) + Float64(Float64(27464.7644705 * Float64(1.0 / t_4)) + Float64(Float64(t / Float64(x * Float64(t_1 * (y ^ 2.0)))) + Float64(Float64(Float64(y * z) / t_4) + Float64((y ^ 2.0) / t_1))))))
	tmp = 0.0
	if (y <= -6.4e+123)
		tmp = Float64(x - Float64(Float64(z * Float64(-1.0 + Float64(a / y))) / y));
	elseif (y <= -1.6e+17)
		tmp = t_5;
	elseif (y <= 8.5e+18)
		tmp = Float64(Float64(t / t_3) + Float64(Float64(Float64(x * (y ^ 4.0)) / t_3) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))) / t_3)));
	elseif (y <= 9e+139)
		tmp = t_5;
	else
		tmp = Float64(x + Float64(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 = b + (y * (y + a));
	t_2 = y * t_1;
	t_3 = i + (y * (t_2 + c));
	t_4 = x * t_1;
	t_5 = x * ((230661.510616 * (1.0 / (x * t_2))) + ((27464.7644705 * (1.0 / t_4)) + ((t / (x * (t_1 * (y ^ 2.0)))) + (((y * z) / t_4) + ((y ^ 2.0) / t_1)))));
	tmp = 0.0;
	if (y <= -6.4e+123)
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	elseif (y <= -1.6e+17)
		tmp = t_5;
	elseif (y <= 8.5e+18)
		tmp = (t / t_3) + (((x * (y ^ 4.0)) / t_3) + ((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) / t_3));
	elseif (y <= 9e+139)
		tmp = t_5;
	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[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(i + N[(y * N[(t$95$2 + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(N[(230661.510616 * N[(1.0 / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(x * N[(t$95$1 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * z), $MachinePrecision] / t$95$4), $MachinePrecision] + N[(N[Power[y, 2.0], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+123], N[(x - N[(N[(z * N[(-1.0 + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e+17], t$95$5, If[LessEqual[y, 8.5e+18], N[(N[(t / t$95$3), $MachinePrecision] + N[(N[(N[(x * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+139], t$95$5, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.40000000000000009e123

   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 60.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{27464.7644705 - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]

   4. Taylor expanded in z around inf 87.6%

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

   if -6.40000000000000009e123 < y < -1.6e17 or 8.5e18 < y < 8.9999999999999999e139

   1. Initial program 29.7%

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

   3. Taylor expanded in x around inf 36.6%

      \[\leadsto \color{blue}{x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   4. Taylor expanded in i around 0 45.6%

      \[\leadsto \color{blue}{x \cdot \left(230661.510616 \cdot \frac{1}{x \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{t}{x \cdot \left(y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\frac{y \cdot \left(27464.7644705 + y \cdot z\right)}{x \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right)\right)\right)} \]

   5. Taylor expanded in c around 0 72.6%

      \[\leadsto \color{blue}{x \cdot \left(230661.510616 \cdot \frac{1}{x \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(27464.7644705 \cdot \frac{1}{x \cdot \left(b + y \cdot \left(a + y\right)\right)} + \left(\frac{t}{x \cdot \left({y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{y \cdot z}{x \cdot \left(b + y \cdot \left(a + y\right)\right)} + \frac{{y}^{2}}{b + y \cdot \left(a + y\right)}\right)\right)\right)\right)} \]

   if -1.6e17 < y < 8.5e18

   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 99.7%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   if 8.9999999999999999e139 < y

   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 89.3%

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

      1. associate--l+ 89.3%

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

      2. associate-/l* 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+123}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(230661.510616 \cdot \frac{1}{x \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(27464.7644705 \cdot \frac{1}{x \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{x \cdot \left(\left(b + y \cdot \left(y + a\right)\right) \cdot {y}^{2}\right)} + \left(\frac{y \cdot z}{x \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{{y}^{2}}{b + y \cdot \left(y + a\right)}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \left(230661.510616 \cdot \frac{1}{x \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(27464.7644705 \cdot \frac{1}{x \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{x \cdot \left(\left(b + y \cdot \left(y + a\right)\right) \cdot {y}^{2}\right)} + \left(\frac{y \cdot z}{x \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{{y}^{2}}{b + y \cdot \left(y + a\right)}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* y (+ (* y (+ b (* y (+ y a)))) c))))))
   (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 * (z + (y * x)))))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	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 * (z + (y * x)))))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	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 * (z + (y * x)))))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
	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(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(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 * (z + (y * x)))))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	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[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $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 88.6%

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

   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 75.8%

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

      1. associate--l+ 75.8%

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

      2. associate-/l* 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 86.5%

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

Alternative 4: 78.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\\ t_2 := \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t\_1}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+71}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-17}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t\_1}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ b (* y (+ y a)))) c))
        (t_2
         (/
          (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))
          t_1)))
   (if (<= y -4.6e+71)
     (- x (/ (* z (+ -1.0 (/ a y))) y))
     (if (<= y -1.7e+16)
       t_2
       (if (<= y 1.12e-17)
         (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y t_1)))
         (if (<= y 1.15e+64) t_2 (+ 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 = (y * (b + (y * (y + a)))) + c;
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double tmp;
	if (y <= -4.6e+71) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= -1.7e+16) {
		tmp = t_2;
	} else if (y <= 1.12e-17) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 1.15e+64) {
		tmp = t_2;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	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 = (y * (b + (y * (y + a)))) + c
    t_2 = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    if (y <= (-4.6d+71)) then
        tmp = x - ((z * ((-1.0d0) + (a / y))) / y)
    else if (y <= (-1.7d+16)) then
        tmp = t_2
    else if (y <= 1.12d-17) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * t_1))
    else if (y <= 1.15d+64) then
        tmp = t_2
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * (b + (y * (y + a)))) + c;
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double tmp;
	if (y <= -4.6e+71) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= -1.7e+16) {
		tmp = t_2;
	} else if (y <= 1.12e-17) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 1.15e+64) {
		tmp = t_2;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * (b + (y * (y + a)))) + c
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	tmp = 0
	if y <= -4.6e+71:
		tmp = x - ((z * (-1.0 + (a / y))) / y)
	elif y <= -1.7e+16:
		tmp = t_2
	elif y <= 1.12e-17:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1))
	elif y <= 1.15e+64:
		tmp = t_2
	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(y * Float64(b + Float64(y * Float64(y + a)))) + c)
	t_2 = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1)
	tmp = 0.0
	if (y <= -4.6e+71)
		tmp = Float64(x - Float64(Float64(z * Float64(-1.0 + Float64(a / y))) / y));
	elseif (y <= -1.7e+16)
		tmp = t_2;
	elseif (y <= 1.12e-17)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * t_1)));
	elseif (y <= 1.15e+64)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(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 = (y * (b + (y * (y + a)))) + c;
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	tmp = 0.0;
	if (y <= -4.6e+71)
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	elseif (y <= -1.7e+16)
		tmp = t_2;
	elseif (y <= 1.12e-17)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	elseif (y <= 1.15e+64)
		tmp = t_2;
	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[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[y, -4.6e+71], N[(x - N[(N[(z * N[(-1.0 + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e+16], t$95$2, If[LessEqual[y, 1.12e-17], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+64], t$95$2, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6000000000000005e71

   1. Initial program 4.4%

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

   3. Taylor expanded in y around -inf 58.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{27464.7644705 - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]

   4. Taylor expanded in z around inf 80.4%

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

   if -4.6000000000000005e71 < y < -1.7e16 or 1.12000000000000005e-17 < y < 1.15e64

   1. Initial program 56.9%

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

   3. Taylor expanded in t around 0 53.9%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in i around 0 64.9%

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

   if -1.7e16 < y < 1.12000000000000005e-17

   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 y around 0 90.2%

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

      1. *-commutative 90.2%

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

   5. Simplified 90.2%

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

   if 1.15e64 < y

   1. Initial program 2.6%

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

   3. Taylor expanded in y around inf 76.4%

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

      1. associate--l+ 76.4%

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

      2. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+71}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+16}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(b + y \cdot \left(y + a\right)\right) + c}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-17}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+64}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(b + y \cdot \left(y + a\right)\right) + c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\\ t_2 := \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t\_1}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+70}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-19}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t\_1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ b (* y (+ y a)))) c))
        (t_2
         (/
          (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))
          t_1)))
   (if (<= y -3.6e+70)
     (- x (/ (* z (+ -1.0 (/ a y))) y))
     (if (<= y -1.45e+16)
       t_2
       (if (<= y 2e-19)
         (/ (+ t (* y 230661.510616)) (+ i (* y t_1)))
         (if (<= y 2.6e+63) t_2 (+ 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 = (y * (b + (y * (y + a)))) + c;
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double tmp;
	if (y <= -3.6e+70) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= -1.45e+16) {
		tmp = t_2;
	} else if (y <= 2e-19) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 2.6e+63) {
		tmp = t_2;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	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 = (y * (b + (y * (y + a)))) + c
    t_2 = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    if (y <= (-3.6d+70)) then
        tmp = x - ((z * ((-1.0d0) + (a / y))) / y)
    else if (y <= (-1.45d+16)) then
        tmp = t_2
    else if (y <= 2d-19) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_1))
    else if (y <= 2.6d+63) then
        tmp = t_2
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * (b + (y * (y + a)))) + c;
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double tmp;
	if (y <= -3.6e+70) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= -1.45e+16) {
		tmp = t_2;
	} else if (y <= 2e-19) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 2.6e+63) {
		tmp = t_2;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * (b + (y * (y + a)))) + c
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	tmp = 0
	if y <= -3.6e+70:
		tmp = x - ((z * (-1.0 + (a / y))) / y)
	elif y <= -1.45e+16:
		tmp = t_2
	elif y <= 2e-19:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1))
	elif y <= 2.6e+63:
		tmp = t_2
	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(y * Float64(b + Float64(y * Float64(y + a)))) + c)
	t_2 = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1)
	tmp = 0.0
	if (y <= -3.6e+70)
		tmp = Float64(x - Float64(Float64(z * Float64(-1.0 + Float64(a / y))) / y));
	elseif (y <= -1.45e+16)
		tmp = t_2;
	elseif (y <= 2e-19)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_1)));
	elseif (y <= 2.6e+63)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(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 = (y * (b + (y * (y + a)))) + c;
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	tmp = 0.0;
	if (y <= -3.6e+70)
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	elseif (y <= -1.45e+16)
		tmp = t_2;
	elseif (y <= 2e-19)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	elseif (y <= 2.6e+63)
		tmp = t_2;
	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[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[y, -3.6e+70], N[(x - N[(N[(z * N[(-1.0 + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e+16], t$95$2, If[LessEqual[y, 2e-19], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+63], t$95$2, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6e70

   1. Initial program 4.4%

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

   3. Taylor expanded in y around -inf 58.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{27464.7644705 - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]

   4. Taylor expanded in z around inf 80.4%

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

   if -3.6e70 < y < -1.45e16 or 2e-19 < y < 2.6000000000000001e63

   1. Initial program 56.9%

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

   3. Taylor expanded in t around 0 53.9%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in i around 0 64.9%

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

   if -1.45e16 < y < 2e-19

   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 y around 0 89.6%

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

      1. *-commutative 89.6%

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

   5. Simplified 89.6%

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

   if 2.6000000000000001e63 < y

   1. Initial program 2.6%

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

   3. Taylor expanded in y around inf 76.4%

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

      1. associate--l+ 76.4%

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

      2. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+70}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(b + y \cdot \left(y + a\right)\right) + c}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-19}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(b + y \cdot \left(y + a\right)\right) + c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+70}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+16}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t\_1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ b (* y (+ y a)))) c)))
   (if (<= y -2.8e+70)
     (- x (/ (* z (+ -1.0 (/ a y))) y))
     (if (<= y -2.9e+16)
       (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1)
       (if (<= y 4e+27)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y 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 = (y * (b + (y * (y + a)))) + c;
	double tmp;
	if (y <= -2.8e+70) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= -2.9e+16) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else if (y <= 4e+27) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	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) :: tmp
    t_1 = (y * (b + (y * (y + a)))) + c
    if (y <= (-2.8d+70)) then
        tmp = x - ((z * ((-1.0d0) + (a / y))) / y)
    else if (y <= (-2.9d+16)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    else if (y <= 4d+27) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * t_1))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * (b + (y * (y + a)))) + c;
	double tmp;
	if (y <= -2.8e+70) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= -2.9e+16) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else if (y <= 4e+27) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * 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 = (y * (b + (y * (y + a)))) + c
	tmp = 0
	if y <= -2.8e+70:
		tmp = x - ((z * (-1.0 + (a / y))) / y)
	elif y <= -2.9e+16:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	elif y <= 4e+27:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * 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(y * Float64(b + Float64(y * Float64(y + a)))) + c)
	tmp = 0.0
	if (y <= -2.8e+70)
		tmp = Float64(x - Float64(Float64(z * Float64(-1.0 + Float64(a / y))) / y));
	elseif (y <= -2.9e+16)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1);
	elseif (y <= 4e+27)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * t_1)));
	else
		tmp = Float64(x + Float64(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 = (y * (b + (y * (y + a)))) + c;
	tmp = 0.0;
	if (y <= -2.8e+70)
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	elseif (y <= -2.9e+16)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	elseif (y <= 4e+27)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * 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[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, If[LessEqual[y, -2.8e+70], N[(x - N[(N[(z * N[(-1.0 + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e+16], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 4e+27], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7999999999999999e70

   1. Initial program 4.4%

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

   3. Taylor expanded in y around -inf 58.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{27464.7644705 - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]

   4. Taylor expanded in z around inf 80.4%

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

   if -2.7999999999999999e70 < y < -2.9e16

   1. Initial program 57.8%

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

   3. Taylor expanded in t around 0 57.8%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in i around 0 74.2%

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

   if -2.9e16 < y < 4.0000000000000001e27

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 94.2%

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

   if 4.0000000000000001e27 < y

   1. Initial program 8.0%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-/l* 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+70}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+16}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(b + y \cdot \left(y + a\right)\right) + c}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.7e+26)
   (- x (/ (* z (+ -1.0 (/ a y))) y))
   (if (<= y 4e+27)
     (/ (+ t (* y 230661.510616)) (+ i (* y (+ (* y (+ b (* y (+ y a)))) c))))
     (+ 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 tmp;
	if (y <= -3.7e+26) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= 4e+27) {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	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 <= (-3.7d+26)) then
        tmp = x - ((z * ((-1.0d0) + (a / y))) / y)
    else if (y <= 4d+27) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.7e+26) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= 4e+27) {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.7e+26:
		tmp = x - ((z * (-1.0 + (a / y))) / y)
	elif y <= 4e+27:
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.7e+26)
		tmp = Float64(x - Float64(Float64(z * Float64(-1.0 + Float64(a / y))) / y));
	elseif (y <= 4e+27)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c))));
	else
		tmp = Float64(x + Float64(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)
	tmp = 0.0;
	if (y <= -3.7e+26)
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	elseif (y <= 4e+27)
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.7e+26], N[(x - N[(N[(z * N[(-1.0 + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+27], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.69999999999999988e26

   1. Initial program 15.5%

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

   3. Taylor expanded in y around -inf 56.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{27464.7644705 - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]

   4. Taylor expanded in z around inf 73.0%

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

   if -3.69999999999999988e26 < y < 4.0000000000000001e27

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 83.7%

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

      1. *-commutative 83.7%

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

   5. Simplified 83.7%

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

   if 4.0000000000000001e27 < y

   1. Initial program 8.0%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-/l* 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.8e+25)
   (- x (/ (* z (+ -1.0 (/ a y))) y))
   (if (<= y 1.7e+23)
     (/ t (+ i (* y (+ (* y (+ b (* y (+ y a)))) c))))
     (+ 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 tmp;
	if (y <= -1.8e+25) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= 1.7e+23) {
		tmp = t / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	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+25)) then
        tmp = x - ((z * ((-1.0d0) + (a / y))) / y)
    else if (y <= 1.7d+23) then
        tmp = t / (i + (y * ((y * (b + (y * (y + a)))) + c)))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.8e+25) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= 1.7e+23) {
		tmp = t / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.8e+25:
		tmp = x - ((z * (-1.0 + (a / y))) / y)
	elif y <= 1.7e+23:
		tmp = t / (i + (y * ((y * (b + (y * (y + a)))) + c)))
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.8e+25)
		tmp = Float64(x - Float64(Float64(z * Float64(-1.0 + Float64(a / y))) / y));
	elseif (y <= 1.7e+23)
		tmp = Float64(t / Float64(i + Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c))));
	else
		tmp = Float64(x + Float64(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)
	tmp = 0.0;
	if (y <= -1.8e+25)
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	elseif (y <= 1.7e+23)
		tmp = t / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.8e+25], N[(x - N[(N[(z * N[(-1.0 + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+23], N[(t / N[(i + N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000008e25

   1. Initial program 15.5%

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

   3. Taylor expanded in y around -inf 56.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{27464.7644705 - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]

   4. Taylor expanded in z around inf 73.0%

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

   if -1.80000000000000008e25 < y < 1.69999999999999996e23

   1. Initial program 97.7%

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

   3. Taylor expanded in t around inf 72.2%

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

   if 1.69999999999999996e23 < y

   1. Initial program 8.0%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-/l* 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+29} \lor \neg \left(y \leq 1.36 \cdot 10^{+23}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.9e+29) (not (<= y 1.36e+23)))
   (+ 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 <= -3.9e+29) || !(y <= 1.36e+23)) {
		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 <= (-3.9d+29)) .or. (.not. (y <= 1.36d+23))) 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 <= -3.9e+29) || !(y <= 1.36e+23)) {
		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 <= -3.9e+29) or not (y <= 1.36e+23):
		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 <= -3.9e+29) || !(y <= 1.36e+23))
		tmp = Float64(x + Float64(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 <= -3.9e+29) || ~((y <= 1.36e+23)))
		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, -3.9e+29], N[Not[LessEqual[y, 1.36e+23]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $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 < -3.89999999999999968e29 or 1.36e23 < y

   1. Initial program 11.9%

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

   3. Taylor expanded in y around inf 67.1%

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

      1. associate--l+ 67.1%

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

      2. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   if -3.89999999999999968e29 < y < 1.36e23

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf 71.7%

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

   4. Taylor expanded in b around inf 70.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+29} \lor \neg \left(y \leq 1.36 \cdot 10^{+23}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+27} \lor \neg \left(y \leq 1.15 \cdot 10^{+27}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.45e+27) (not (<= y 1.15e+27)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t (+ i (* y c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.45e+27) || !(y <= 1.15e+27)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * c));
	}
	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 <= (-1.45d+27)) .or. (.not. (y <= 1.15d+27))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / (i + (y * c))
    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 <= -1.45e+27) || !(y <= 1.15e+27)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.45e+27) or not (y <= 1.15e+27):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.45e+27) || !(y <= 1.15e+27))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / Float64(i + Float64(y * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.45e+27) || ~((y <= 1.15e+27)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.45e+27], N[Not[LessEqual[y, 1.15e+27]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4500000000000001e27 or 1.15e27 < y

   1. Initial program 11.9%

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

   3. Taylor expanded in y around inf 67.1%

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

      1. associate--l+ 67.1%

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

      2. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   if -1.4500000000000001e27 < y < 1.15e27

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf 71.7%

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

   4. Taylor expanded in y around 0 66.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+27} \lor \neg \left(y \leq 1.15 \cdot 10^{+27}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.75 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.75e+24)
   (- x (/ (* z (+ -1.0 (/ a y))) y))
   (if (<= y 5.4e+22)
     (/ t (+ i (* y (+ c (* y b)))))
     (+ 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 tmp;
	if (y <= -4.75e+24) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= 5.4e+22) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	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 <= (-4.75d+24)) then
        tmp = x - ((z * ((-1.0d0) + (a / y))) / y)
    else if (y <= 5.4d+22) then
        tmp = t / (i + (y * (c + (y * b))))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.75e+24) {
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	} else if (y <= 5.4e+22) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.75e+24:
		tmp = x - ((z * (-1.0 + (a / y))) / y)
	elif y <= 5.4e+22:
		tmp = t / (i + (y * (c + (y * b))))
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.75e+24)
		tmp = Float64(x - Float64(Float64(z * Float64(-1.0 + Float64(a / y))) / y));
	elseif (y <= 5.4e+22)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(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)
	tmp = 0.0;
	if (y <= -4.75e+24)
		tmp = x - ((z * (-1.0 + (a / y))) / y);
	elseif (y <= 5.4e+22)
		tmp = t / (i + (y * (c + (y * b))));
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.75e+24], N[(x - N[(N[(z * N[(-1.0 + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+22], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7500000000000001e24

   1. Initial program 15.5%

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

   3. Taylor expanded in y around -inf 56.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{27464.7644705 - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]

   4. Taylor expanded in z around inf 73.0%

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

   if -4.7500000000000001e24 < y < 5.4000000000000004e22

   1. Initial program 97.7%

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

   3. Taylor expanded in t around inf 72.2%

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

   4. Taylor expanded in b around inf 70.8%

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

   if 5.4000000000000004e22 < y

   1. Initial program 8.0%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-/l* 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.75 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{z \cdot \left(-1 + \frac{a}{y}\right)}{y}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.8e+26) x (if (<= y 2.9e+26) (/ t (+ i (* y c))) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.8e+26) {
		tmp = x;
	} else if (y <= 2.9e+26) {
		tmp = t / (i + (y * c));
	} 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) :: tmp
    if (y <= (-4.8d+26)) then
        tmp = x
    else if (y <= 2.9d+26) then
        tmp = t / (i + (y * c))
    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 tmp;
	if (y <= -4.8e+26) {
		tmp = x;
	} else if (y <= 2.9e+26) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.8e+26:
		tmp = x
	elif y <= 2.9e+26:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.8e+26)
		tmp = x;
	elseif (y <= 2.9e+26)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.8e+26)
		tmp = x;
	elseif (y <= 2.9e+26)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.8e+26], x, If[LessEqual[y, 2.9e+26], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000009e26 or 2.9e26 < y

   1. Initial program 11.9%

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

   3. Taylor expanded in y around inf 54.3%

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

   if -4.80000000000000009e26 < y < 2.9e26

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf 71.7%

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

   4. Taylor expanded in y around 0 66.2%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.9e+28) x (if (<= y 2.3e+24) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.9e+28) {
		tmp = x;
	} else if (y <= 2.3e+24) {
		tmp = t / i;
	} 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) :: tmp
    if (y <= (-4.9d+28)) then
        tmp = x
    else if (y <= 2.3d+24) then
        tmp = t / i
    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 tmp;
	if (y <= -4.9e+28) {
		tmp = x;
	} else if (y <= 2.3e+24) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.9e+28:
		tmp = x
	elif y <= 2.3e+24:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.9e+28)
		tmp = x;
	elseif (y <= 2.3e+24)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.9e+28)
		tmp = x;
	elseif (y <= 2.3e+24)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.9e+28], x, If[LessEqual[y, 2.3e+24], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8999999999999996e28 or 2.2999999999999999e24 < y

   1. Initial program 11.9%

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

   3. Taylor expanded in y around inf 54.3%

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

   if -4.8999999999999996e28 < y < 2.2999999999999999e24

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 50.5%

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

Alternative 14: 25.5% 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 58.5%

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

3. Taylor expanded in y around inf 26.7%

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

Reproduce

herbie shell --seed 2024091 
(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)))