Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.1% → 85.3%

Time: 26.1s

Alternatives: 16

Speedup: 2.2×

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: 56.1% 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: 85.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_3 := y \cdot t_2\\ t_4 := \mathsf{fma}\left(y, y + a, b\right)\\ t_5 := {t_4}^{2}\\ t_6 := \mathsf{fma}\left(y, t_4, c\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -16000000000000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{t_2} + \left(\frac{t}{t_3} + \mathsf{fma}\left(-1, c \cdot \left(\frac{27464.7644705}{y \cdot t_5} + \left(\frac{z}{t_5} + \frac{x}{\frac{t_5}{y}}\right)\right), \frac{27464.7644705}{t_4} + \frac{y}{\frac{t_4}{\mathsf{fma}\left(y, x, z\right)}}\right)\right)\\ \mathbf{elif}\;y \leq 27000000:\\ \;\;\;\;\frac{t + \left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)}{t_3 + i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+102}:\\ \;\;\;\;\frac{230661.510616}{t_6} + \left(\frac{\frac{t}{y}}{t_6} + \frac{y}{\frac{t_6}{\mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_2 (+ c (* y (+ b (* y (+ y a))))))
        (t_3 (* y t_2))
        (t_4 (fma y (+ y a) b))
        (t_5 (pow t_4 2.0))
        (t_6 (fma y t_4 c)))
   (if (<= y -1.55e+110)
     t_1
     (if (<= y -16000000000000.0)
       (+
        (* 230661.510616 (/ 1.0 t_2))
        (+
         (/ t t_3)
         (fma
          -1.0
          (* c (+ (/ 27464.7644705 (* y t_5)) (+ (/ z t_5) (/ x (/ t_5 y)))))
          (+ (/ 27464.7644705 t_4) (/ y (/ t_4 (fma y x z)))))))
       (if (<= y 27000000.0)
         (/
          (+
           t
           (+
            (* x (pow y 4.0))
            (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))))
          (+ t_3 i))
         (if (<= y 4.4e+102)
           (+
            (/ 230661.510616 t_6)
            (+
             (/ (/ t y) t_6)
             (/ y (/ t_6 (fma y (fma x y z) 27464.7644705)))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double t_2 = c + (y * (b + (y * (y + a))));
	double t_3 = y * t_2;
	double t_4 = fma(y, (y + a), b);
	double t_5 = pow(t_4, 2.0);
	double t_6 = fma(y, t_4, c);
	double tmp;
	if (y <= -1.55e+110) {
		tmp = t_1;
	} else if (y <= -16000000000000.0) {
		tmp = (230661.510616 * (1.0 / t_2)) + ((t / t_3) + fma(-1.0, (c * ((27464.7644705 / (y * t_5)) + ((z / t_5) + (x / (t_5 / y))))), ((27464.7644705 / t_4) + (y / (t_4 / fma(y, x, z))))));
	} else if (y <= 27000000.0) {
		tmp = (t + ((x * pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z))))))) / (t_3 + i);
	} else if (y <= 4.4e+102) {
		tmp = (230661.510616 / t_6) + (((t / y) / t_6) + (y / (t_6 / fma(y, fma(x, y, z), 27464.7644705))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_2 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_3 = Float64(y * t_2)
	t_4 = fma(y, Float64(y + a), b)
	t_5 = t_4 ^ 2.0
	t_6 = fma(y, t_4, c)
	tmp = 0.0
	if (y <= -1.55e+110)
		tmp = t_1;
	elseif (y <= -16000000000000.0)
		tmp = Float64(Float64(230661.510616 * Float64(1.0 / t_2)) + Float64(Float64(t / t_3) + fma(-1.0, Float64(c * Float64(Float64(27464.7644705 / Float64(y * t_5)) + Float64(Float64(z / t_5) + Float64(x / Float64(t_5 / y))))), Float64(Float64(27464.7644705 / t_4) + Float64(y / Float64(t_4 / fma(y, x, z)))))));
	elseif (y <= 27000000.0)
		tmp = Float64(Float64(t + Float64(Float64(x * (y ^ 4.0)) + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))))) / Float64(t_3 + i));
	elseif (y <= 4.4e+102)
		tmp = Float64(Float64(230661.510616 / t_6) + Float64(Float64(Float64(t / y) / t_6) + Float64(y / Float64(t_6 / fma(y, fma(x, y, z), 27464.7644705)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[Power[t$95$4, 2.0], $MachinePrecision]}, Block[{t$95$6 = N[(y * t$95$4 + c), $MachinePrecision]}, If[LessEqual[y, -1.55e+110], t$95$1, If[LessEqual[y, -16000000000000.0], N[(N[(230661.510616 * N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(t / t$95$3), $MachinePrecision] + N[(-1.0 * N[(c * N[(N[(27464.7644705 / N[(y * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t$95$5), $MachinePrecision] + N[(x / N[(t$95$5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 / t$95$4), $MachinePrecision] + N[(y / N[(t$95$4 / N[(y * x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 27000000.0], N[(N[(t + N[(N[(x * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$3 + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+102], N[(N[(230661.510616 / t$95$6), $MachinePrecision] + N[(N[(N[(t / y), $MachinePrecision] / t$95$6), $MachinePrecision] + N[(y / N[(t$95$6 / N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.55000000000000009e110 or 4.40000000000000015e102 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 78.5%

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

   if -1.55000000000000009e110 < y < -1.6e13

   1. Initial program 31.7%

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

   2. Taylor expanded in i around 0 26.2%

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

   3. Taylor expanded in t around 0 49.3%

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

   4. Taylor expanded in c around 0 77.1%

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

   6. Simplified 88.0%

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

   if -1.6e13 < y < 2.7e7

   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. Taylor expanded in x around 0 99.8%

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

   if 2.7e7 < y < 4.40000000000000015e102

   1. Initial program 25.1%

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

   2. Taylor expanded in i around 0 25.1%

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

   3. Taylor expanded in t around 0 53.6%

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

      1. associate-*r/ 53.6%

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

      2. metadata-eval 53.6%

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

      3. +-commutative 53.6%

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

      4. +-commutative 53.6%

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

      5. +-commutative 53.6%

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

      6. fma-udef 53.6%

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

      7. fma-udef 53.6%

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

   5. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{230661.510616}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \left(\frac{\frac{t}{y}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)}}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+110}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -16000000000000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \mathsf{fma}\left(-1, c \cdot \left(\frac{27464.7644705}{y \cdot {\left(\mathsf{fma}\left(y, y + a, b\right)\right)}^{2}} + \left(\frac{z}{{\left(\mathsf{fma}\left(y, y + a, b\right)\right)}^{2}} + \frac{x}{\frac{{\left(\mathsf{fma}\left(y, y + a, b\right)\right)}^{2}}{y}}\right)\right), \frac{27464.7644705}{\mathsf{fma}\left(y, y + a, b\right)} + \frac{y}{\frac{\mathsf{fma}\left(y, y + a, b\right)}{\mathsf{fma}\left(y, x, z\right)}}\right)\right)\\ \mathbf{elif}\;y \leq 27000000:\\ \;\;\;\;\frac{t + \left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+102}:\\ \;\;\;\;\frac{230661.510616}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \left(\frac{\frac{t}{y}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 2: 84.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\\ t_2 := b + y \cdot \left(y + a\right)\\ t_3 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_4 := c + y \cdot t_2\\ t_5 := y \cdot t_4\\ \mathbf{if}\;y \leq -1.28 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -16000000000000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{t_4} + \left(\frac{t}{t_5} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{t_2}\right)\\ \mathbf{elif}\;y \leq 1900000000:\\ \;\;\;\;\frac{t + \left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)}{t_5 + i}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{230661.510616}{t_1} + \left(\frac{\frac{t}{y}}{t_1} + \frac{y}{\frac{t_1}{\mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y (fma y (+ y a) b) c))
        (t_2 (+ b (* y (+ y a))))
        (t_3 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_4 (+ c (* y t_2)))
        (t_5 (* y t_4)))
   (if (<= y -1.28e+107)
     t_3
     (if (<= y -16000000000000.0)
       (+
        (* 230661.510616 (/ 1.0 t_4))
        (+ (/ t t_5) (/ (+ 27464.7644705 (* y (+ z (* y x)))) t_2)))
       (if (<= y 1900000000.0)
         (/
          (+
           t
           (+
            (* x (pow y 4.0))
            (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))))
          (+ t_5 i))
         (if (<= y 5.6e+102)
           (+
            (/ 230661.510616 t_1)
            (+
             (/ (/ t y) t_1)
             (/ y (/ t_1 (fma y (fma x y z) 27464.7644705)))))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, fma(y, (y + a), b), c);
	double t_2 = b + (y * (y + a));
	double t_3 = (x + (z / y)) - ((x * a) / y);
	double t_4 = c + (y * t_2);
	double t_5 = y * t_4;
	double tmp;
	if (y <= -1.28e+107) {
		tmp = t_3;
	} else if (y <= -16000000000000.0) {
		tmp = (230661.510616 * (1.0 / t_4)) + ((t / t_5) + ((27464.7644705 + (y * (z + (y * x)))) / t_2));
	} else if (y <= 1900000000.0) {
		tmp = (t + ((x * pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z))))))) / (t_5 + i);
	} else if (y <= 5.6e+102) {
		tmp = (230661.510616 / t_1) + (((t / y) / t_1) + (y / (t_1 / fma(y, fma(x, y, z), 27464.7644705))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, fma(y, Float64(y + a), b), c)
	t_2 = Float64(b + Float64(y * Float64(y + a)))
	t_3 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_4 = Float64(c + Float64(y * t_2))
	t_5 = Float64(y * t_4)
	tmp = 0.0
	if (y <= -1.28e+107)
		tmp = t_3;
	elseif (y <= -16000000000000.0)
		tmp = Float64(Float64(230661.510616 * Float64(1.0 / t_4)) + Float64(Float64(t / t_5) + Float64(Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))) / t_2)));
	elseif (y <= 1900000000.0)
		tmp = Float64(Float64(t + Float64(Float64(x * (y ^ 4.0)) + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))))) / Float64(t_5 + i));
	elseif (y <= 5.6e+102)
		tmp = Float64(Float64(230661.510616 / t_1) + Float64(Float64(Float64(t / y) / t_1) + Float64(y / Float64(t_1 / fma(y, fma(x, y, z), 27464.7644705)))));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * t$95$4), $MachinePrecision]}, If[LessEqual[y, -1.28e+107], t$95$3, If[LessEqual[y, -16000000000000.0], N[(N[(230661.510616 * N[(1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(t / t$95$5), $MachinePrecision] + N[(N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1900000000.0], N[(N[(t + N[(N[(x * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$5 + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+102], N[(N[(230661.510616 / t$95$1), $MachinePrecision] + N[(N[(N[(t / y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(y / N[(t$95$1 / N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2799999999999999e107 or 5.60000000000000037e102 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 78.5%

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

   if -1.2799999999999999e107 < y < -1.6e13

   1. Initial program 31.7%

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

   2. Taylor expanded in i around 0 26.2%

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

   3. Taylor expanded in t around 0 49.3%

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

   4. Taylor expanded in c around 0 77.0%

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

   if -1.6e13 < y < 1.9e9

   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. Taylor expanded in x around 0 99.8%

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

   if 1.9e9 < y < 5.60000000000000037e102

   1. Initial program 25.1%

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

   2. Taylor expanded in i around 0 25.1%

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

   3. Taylor expanded in t around 0 53.6%

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

      1. associate-*r/ 53.6%

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

      2. metadata-eval 53.6%

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

      3. +-commutative 53.6%

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

      4. +-commutative 53.6%

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

      5. +-commutative 53.6%

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

      6. fma-udef 53.6%

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

      7. fma-udef 53.6%

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

   5. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{230661.510616}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \left(\frac{\frac{t}{y}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)}}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+107}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -16000000000000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right)\\ \mathbf{elif}\;y \leq 1900000000:\\ \;\;\;\;\frac{t + \left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{230661.510616}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \left(\frac{\frac{t}{y}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 3: 83.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_3 := c + y \cdot t_1\\ t_4 := y \cdot t_3\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3300000000000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{t_3} + \left(\frac{t}{t_4} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{t_1}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{t + \left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)}{t_4 + i}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{{y}^{3}}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_3 (+ c (* y t_1)))
        (t_4 (* y t_3)))
   (if (<= y -7.5e+109)
     t_2
     (if (<= y -3300000000000.0)
       (+
        (* 230661.510616 (/ 1.0 t_3))
        (+ (/ t t_4) (/ (+ 27464.7644705 (* y (+ z (* y x)))) t_1)))
       (if (<= y 7.5e+15)
         (/
          (+
           t
           (+
            (* x (pow y 4.0))
            (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))))
          (+ t_4 i))
         (if (<= y 2.45e+89)
           (/ x (/ (fma y (fma y (+ y a) b) c) (pow y 3.0)))
           t_2))))))

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 = (x + (z / y)) - ((x * a) / y);
	double t_3 = c + (y * t_1);
	double t_4 = y * t_3;
	double tmp;
	if (y <= -7.5e+109) {
		tmp = t_2;
	} else if (y <= -3300000000000.0) {
		tmp = (230661.510616 * (1.0 / t_3)) + ((t / t_4) + ((27464.7644705 + (y * (z + (y * x)))) / t_1));
	} else if (y <= 7.5e+15) {
		tmp = (t + ((x * pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z))))))) / (t_4 + i);
	} else if (y <= 2.45e+89) {
		tmp = x / (fma(y, fma(y, (y + a), b), c) / pow(y, 3.0));
	} else {
		tmp = t_2;
	}
	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(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_3 = Float64(c + Float64(y * t_1))
	t_4 = Float64(y * t_3)
	tmp = 0.0
	if (y <= -7.5e+109)
		tmp = t_2;
	elseif (y <= -3300000000000.0)
		tmp = Float64(Float64(230661.510616 * Float64(1.0 / t_3)) + Float64(Float64(t / t_4) + Float64(Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))) / t_1)));
	elseif (y <= 7.5e+15)
		tmp = Float64(Float64(t + Float64(Float64(x * (y ^ 4.0)) + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))))) / Float64(t_4 + i));
	elseif (y <= 2.45e+89)
		tmp = Float64(x / Float64(fma(y, fma(y, Float64(y + a), b), c) / (y ^ 3.0)));
	else
		tmp = t_2;
	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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * t$95$3), $MachinePrecision]}, If[LessEqual[y, -7.5e+109], t$95$2, If[LessEqual[y, -3300000000000.0], N[(N[(230661.510616 * N[(1.0 / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(t / t$95$4), $MachinePrecision] + N[(N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+15], N[(N[(t + N[(N[(x * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$4 + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+89], N[(x / N[(N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.50000000000000018e109 or 2.44999999999999998e89 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 78.4%

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

   if -7.50000000000000018e109 < y < -3.3e12

   1. Initial program 31.7%

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

   2. Taylor expanded in i around 0 26.2%

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

   3. Taylor expanded in t around 0 49.3%

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

   4. Taylor expanded in c around 0 77.0%

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

   if -3.3e12 < y < 7.5e15

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 98.3%

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

   if 7.5e15 < y < 2.44999999999999998e89

   1. Initial program 26.9%

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

   2. Taylor expanded in i around 0 26.9%

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

   3. Taylor expanded in x around inf 35.9%

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

      1. associate-/l* 58.7%

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

      2. +-commutative 58.7%

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

      3. +-commutative 58.7%

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

      4. +-commutative 58.7%

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

      5. fma-udef 58.7%

         \[\leadsto \frac{x}{\frac{y \cdot \color{blue}{\mathsf{fma}\left(y, y + a, b\right)} + c}{{y}^{3}}} \]

      6. fma-udef 58.7%

         \[\leadsto \frac{x}{\frac{\color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}}{{y}^{3}}} \]

   5. Simplified 58.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{{y}^{3}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+109}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -3300000000000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{t + \left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{{y}^{3}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 4: 84.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_3 := c + y \cdot t_1\\ t_4 := y \cdot t_3\\ t_5 := 230661.510616 \cdot \frac{1}{t_3} + \left(\frac{t}{t_4} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{t_1}\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3300000000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{t + \left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)}{t_4 + i}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+104}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_3 (+ c (* y t_1)))
        (t_4 (* y t_3))
        (t_5
         (+
          (* 230661.510616 (/ 1.0 t_3))
          (+ (/ t t_4) (/ (+ 27464.7644705 (* y (+ z (* y x)))) t_1)))))
   (if (<= y -1e+107)
     t_2
     (if (<= y -3300000000000.0)
       t_5
       (if (<= y 3.8e+39)
         (/
          (+
           t
           (+
            (* x (pow y 4.0))
            (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))))
          (+ t_4 i))
         (if (<= y 6.6e+104) t_5 t_2))))))

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 = (x + (z / y)) - ((x * a) / y);
	double t_3 = c + (y * t_1);
	double t_4 = y * t_3;
	double t_5 = (230661.510616 * (1.0 / t_3)) + ((t / t_4) + ((27464.7644705 + (y * (z + (y * x)))) / t_1));
	double tmp;
	if (y <= -1e+107) {
		tmp = t_2;
	} else if (y <= -3300000000000.0) {
		tmp = t_5;
	} else if (y <= 3.8e+39) {
		tmp = (t + ((x * pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z))))))) / (t_4 + i);
	} else if (y <= 6.6e+104) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	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 = (x + (z / y)) - ((x * a) / y)
    t_3 = c + (y * t_1)
    t_4 = y * t_3
    t_5 = (230661.510616d0 * (1.0d0 / t_3)) + ((t / t_4) + ((27464.7644705d0 + (y * (z + (y * x)))) / t_1))
    if (y <= (-1d+107)) then
        tmp = t_2
    else if (y <= (-3300000000000.0d0)) then
        tmp = t_5
    else if (y <= 3.8d+39) then
        tmp = (t + ((x * (y ** 4.0d0)) + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z))))))) / (t_4 + i)
    else if (y <= 6.6d+104) then
        tmp = t_5
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double t_3 = c + (y * t_1);
	double t_4 = y * t_3;
	double t_5 = (230661.510616 * (1.0 / t_3)) + ((t / t_4) + ((27464.7644705 + (y * (z + (y * x)))) / t_1));
	double tmp;
	if (y <= -1e+107) {
		tmp = t_2;
	} else if (y <= -3300000000000.0) {
		tmp = t_5;
	} else if (y <= 3.8e+39) {
		tmp = (t + ((x * Math.pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z))))))) / (t_4 + i);
	} else if (y <= 6.6e+104) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b + (y * (y + a))
	t_2 = (x + (z / y)) - ((x * a) / y)
	t_3 = c + (y * t_1)
	t_4 = y * t_3
	t_5 = (230661.510616 * (1.0 / t_3)) + ((t / t_4) + ((27464.7644705 + (y * (z + (y * x)))) / t_1))
	tmp = 0
	if y <= -1e+107:
		tmp = t_2
	elif y <= -3300000000000.0:
		tmp = t_5
	elif y <= 3.8e+39:
		tmp = (t + ((x * math.pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z))))))) / (t_4 + i)
	elif y <= 6.6e+104:
		tmp = t_5
	else:
		tmp = t_2
	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(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_3 = Float64(c + Float64(y * t_1))
	t_4 = Float64(y * t_3)
	t_5 = Float64(Float64(230661.510616 * Float64(1.0 / t_3)) + Float64(Float64(t / t_4) + Float64(Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))) / t_1)))
	tmp = 0.0
	if (y <= -1e+107)
		tmp = t_2;
	elseif (y <= -3300000000000.0)
		tmp = t_5;
	elseif (y <= 3.8e+39)
		tmp = Float64(Float64(t + Float64(Float64(x * (y ^ 4.0)) + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))))) / Float64(t_4 + i));
	elseif (y <= 6.6e+104)
		tmp = t_5;
	else
		tmp = t_2;
	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 = (x + (z / y)) - ((x * a) / y);
	t_3 = c + (y * t_1);
	t_4 = y * t_3;
	t_5 = (230661.510616 * (1.0 / t_3)) + ((t / t_4) + ((27464.7644705 + (y * (z + (y * x)))) / t_1));
	tmp = 0.0;
	if (y <= -1e+107)
		tmp = t_2;
	elseif (y <= -3300000000000.0)
		tmp = t_5;
	elseif (y <= 3.8e+39)
		tmp = (t + ((x * (y ^ 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z))))))) / (t_4 + i);
	elseif (y <= 6.6e+104)
		tmp = t_5;
	else
		tmp = t_2;
	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[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(230661.510616 * N[(1.0 / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(t / t$95$4), $MachinePrecision] + N[(N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+107], t$95$2, If[LessEqual[y, -3300000000000.0], t$95$5, If[LessEqual[y, 3.8e+39], N[(N[(t + N[(N[(x * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$4 + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+104], t$95$5, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.9999999999999997e106 or 6.59999999999999969e104 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 78.5%

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

   if -9.9999999999999997e106 < y < -3.3e12 or 3.7999999999999998e39 < y < 6.59999999999999969e104

   1. Initial program 24.4%

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

   2. Taylor expanded in i around 0 21.5%

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

   3. Taylor expanded in t around 0 46.1%

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

   4. Taylor expanded in c around 0 75.7%

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

   if -3.3e12 < y < 3.7999999999999998e39

   1. Initial program 94.4%

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

   2. Taylor expanded in x around 0 94.4%

      \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+107}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -3300000000000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{t + \left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+104}:\\ \;\;\;\;230661.510616 \cdot \frac{1}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 5: 81.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{if}\;t_1 \leq 10^{+276}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))
   (if (<= t_1 1e+276) t_1 (- (+ x (/ z y)) (/ (* x a) 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)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	double tmp;
	if (t_1 <= 1e+276) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - ((x * a) / 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 = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    if (t_1 <= 1d+276) then
        tmp = t_1
    else
        tmp = (x + (z / y)) - ((x * a) / 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 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	double tmp;
	if (t_1 <= 1e+276) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - ((x * a) / 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)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	tmp = 0
	if t_1 <= 1e+276:
		tmp = t_1
	else:
		tmp = (x + (z / y)) - ((x * a) / 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(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i))
	tmp = 0.0
	if (t_1 <= 1e+276)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / 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)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	tmp = 0.0;
	if (t_1 <= 1e+276)
		tmp = t_1;
	else
		tmp = (x + (z / y)) - ((x * a) / 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[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+276], t$95$1, N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 1.0000000000000001e276

   1. Initial program 87.8%

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

   if 1.0000000000000001e276 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 2.3%

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

   2. Taylor expanded in y around inf 72.9%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i} \leq 10^{+276}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 6: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 27464.7644705 + y \cdot \left(z + y \cdot x\right)\\ t_2 := b + y \cdot \left(y + a\right)\\ t_3 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_4 := c + y \cdot t_2\\ t_5 := y \cdot t_4\\ t_6 := 230661.510616 \cdot \frac{1}{t_4} + \left(\frac{t}{t_5} + \frac{t_1}{t_2}\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -16000000000000:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot t_1\right)}{t_5 + i}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+105}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ 27464.7644705 (* y (+ z (* y x)))))
        (t_2 (+ b (* y (+ y a))))
        (t_3 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_4 (+ c (* y t_2)))
        (t_5 (* y t_4))
        (t_6 (+ (* 230661.510616 (/ 1.0 t_4)) (+ (/ t t_5) (/ t_1 t_2)))))
   (if (<= y -1.15e+107)
     t_3
     (if (<= y -16000000000000.0)
       t_6
       (if (<= y 3.8e+39)
         (/ (+ t (* y (+ 230661.510616 (* y t_1)))) (+ t_5 i))
         (if (<= y 1.1e+105) t_6 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 27464.7644705 + (y * (z + (y * x)));
	double t_2 = b + (y * (y + a));
	double t_3 = (x + (z / y)) - ((x * a) / y);
	double t_4 = c + (y * t_2);
	double t_5 = y * t_4;
	double t_6 = (230661.510616 * (1.0 / t_4)) + ((t / t_5) + (t_1 / t_2));
	double tmp;
	if (y <= -1.15e+107) {
		tmp = t_3;
	} else if (y <= -16000000000000.0) {
		tmp = t_6;
	} else if (y <= 3.8e+39) {
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / (t_5 + i);
	} else if (y <= 1.1e+105) {
		tmp = t_6;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = 27464.7644705d0 + (y * (z + (y * x)))
    t_2 = b + (y * (y + a))
    t_3 = (x + (z / y)) - ((x * a) / y)
    t_4 = c + (y * t_2)
    t_5 = y * t_4
    t_6 = (230661.510616d0 * (1.0d0 / t_4)) + ((t / t_5) + (t_1 / t_2))
    if (y <= (-1.15d+107)) then
        tmp = t_3
    else if (y <= (-16000000000000.0d0)) then
        tmp = t_6
    else if (y <= 3.8d+39) then
        tmp = (t + (y * (230661.510616d0 + (y * t_1)))) / (t_5 + i)
    else if (y <= 1.1d+105) then
        tmp = t_6
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 27464.7644705 + (y * (z + (y * x)));
	double t_2 = b + (y * (y + a));
	double t_3 = (x + (z / y)) - ((x * a) / y);
	double t_4 = c + (y * t_2);
	double t_5 = y * t_4;
	double t_6 = (230661.510616 * (1.0 / t_4)) + ((t / t_5) + (t_1 / t_2));
	double tmp;
	if (y <= -1.15e+107) {
		tmp = t_3;
	} else if (y <= -16000000000000.0) {
		tmp = t_6;
	} else if (y <= 3.8e+39) {
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / (t_5 + i);
	} else if (y <= 1.1e+105) {
		tmp = t_6;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 27464.7644705 + (y * (z + (y * x)))
	t_2 = b + (y * (y + a))
	t_3 = (x + (z / y)) - ((x * a) / y)
	t_4 = c + (y * t_2)
	t_5 = y * t_4
	t_6 = (230661.510616 * (1.0 / t_4)) + ((t / t_5) + (t_1 / t_2))
	tmp = 0
	if y <= -1.15e+107:
		tmp = t_3
	elif y <= -16000000000000.0:
		tmp = t_6
	elif y <= 3.8e+39:
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / (t_5 + i)
	elif y <= 1.1e+105:
		tmp = t_6
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))
	t_2 = Float64(b + Float64(y * Float64(y + a)))
	t_3 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_4 = Float64(c + Float64(y * t_2))
	t_5 = Float64(y * t_4)
	t_6 = Float64(Float64(230661.510616 * Float64(1.0 / t_4)) + Float64(Float64(t / t_5) + Float64(t_1 / t_2)))
	tmp = 0.0
	if (y <= -1.15e+107)
		tmp = t_3;
	elseif (y <= -16000000000000.0)
		tmp = t_6;
	elseif (y <= 3.8e+39)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * t_1)))) / Float64(t_5 + i));
	elseif (y <= 1.1e+105)
		tmp = t_6;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 27464.7644705 + (y * (z + (y * x)));
	t_2 = b + (y * (y + a));
	t_3 = (x + (z / y)) - ((x * a) / y);
	t_4 = c + (y * t_2);
	t_5 = y * t_4;
	t_6 = (230661.510616 * (1.0 / t_4)) + ((t / t_5) + (t_1 / t_2));
	tmp = 0.0;
	if (y <= -1.15e+107)
		tmp = t_3;
	elseif (y <= -16000000000000.0)
		tmp = t_6;
	elseif (y <= 3.8e+39)
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / (t_5 + i);
	elseif (y <= 1.1e+105)
		tmp = t_6;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(230661.510616 * N[(1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(t / t$95$5), $MachinePrecision] + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+107], t$95$3, If[LessEqual[y, -16000000000000.0], t$95$6, If[LessEqual[y, 3.8e+39], N[(N[(t + N[(y * N[(230661.510616 + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$5 + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+105], t$95$6, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e107 or 1.10000000000000003e105 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 78.5%

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

   if -1.15e107 < y < -1.6e13 or 3.7999999999999998e39 < y < 1.10000000000000003e105

   1. Initial program 24.4%

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

   2. Taylor expanded in i around 0 21.5%

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

   3. Taylor expanded in t around 0 46.1%

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

   4. Taylor expanded in c around 0 75.7%

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

   if -1.6e13 < y < 3.7999999999999998e39

   1. Initial program 94.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -16000000000000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+105}:\\ \;\;\;\;230661.510616 \cdot \frac{1}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 7: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 650000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot t_1 + i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.12e+54)
     t_2
     (if (<= y 650000.0)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
        (+ (* y t_1) i))
       (if (<= y 4.4e+39)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1)
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.12e+54) {
		tmp = t_2;
	} else if (y <= 650000.0) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i);
	} else if (y <= 4.4e+39) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else {
		tmp = t_2;
	}
	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 = c + (y * (b + (y * (y + a))))
    t_2 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.12d+54)) then
        tmp = t_2
    else if (y <= 650000.0d0) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * t_1) + i)
    else if (y <= 4.4d+39) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.12e+54) {
		tmp = t_2;
	} else if (y <= 650000.0) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i);
	} else if (y <= 4.4e+39) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.12e+54:
		tmp = t_2
	elif y <= 650000.0:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i)
	elif y <= 4.4e+39:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.12e+54)
		tmp = t_2;
	elseif (y <= 650000.0)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(Float64(y * t_1) + i));
	elseif (y <= 4.4e+39)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.12e+54)
		tmp = t_2;
	elseif (y <= 650000.0)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i);
	elseif (y <= 4.4e+39)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+54], t$95$2, If[LessEqual[y, 650000.0], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * t$95$1), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+39], 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], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e54 or 4.4000000000000003e39 < y

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 71.5%

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

   if -1.12e54 < y < 6.5e5

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0 94.6%

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

   if 6.5e5 < y < 4.4000000000000003e39

   1. Initial program 36.3%

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

   2. Taylor expanded in i around 0 36.3%

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

   3. Taylor expanded in t around 0 67.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+54}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 650000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 8: 75.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot t_2 + i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_2 (+ c (* y (+ b (* y (+ y a)))))))
   (if (<= y -1.9e+44)
     t_1
     (if (<= y 9.2e-16)
       (/ (+ t (* y 230661.510616)) (+ (* y t_2) i))
       (if (<= y 4.4e+39)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_2)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -1.9e+44) {
		tmp = t_1;
	} else if (y <= 9.2e-16) {
		tmp = (t + (y * 230661.510616)) / ((y * t_2) + i);
	} else if (y <= 4.4e+39) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_2;
	} else {
		tmp = t_1;
	}
	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 = (x + (z / y)) - ((x * a) / y)
    t_2 = c + (y * (b + (y * (y + a))))
    if (y <= (-1.9d+44)) then
        tmp = t_1
    else if (y <= 9.2d-16) then
        tmp = (t + (y * 230661.510616d0)) / ((y * t_2) + i)
    else if (y <= 4.4d+39) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -1.9e+44) {
		tmp = t_1;
	} else if (y <= 9.2e-16) {
		tmp = (t + (y * 230661.510616)) / ((y * t_2) + i);
	} else if (y <= 4.4e+39) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	t_2 = c + (y * (b + (y * (y + a))))
	tmp = 0
	if y <= -1.9e+44:
		tmp = t_1
	elif y <= 9.2e-16:
		tmp = (t + (y * 230661.510616)) / ((y * t_2) + i)
	elif y <= 4.4e+39:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_2 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	tmp = 0.0
	if (y <= -1.9e+44)
		tmp = t_1;
	elseif (y <= 9.2e-16)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * t_2) + i));
	elseif (y <= 4.4e+39)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	t_2 = c + (y * (b + (y * (y + a))));
	tmp = 0.0;
	if (y <= -1.9e+44)
		tmp = t_1;
	elseif (y <= 9.2e-16)
		tmp = (t + (y * 230661.510616)) / ((y * t_2) + i);
	elseif (y <= 4.4e+39)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+44], t$95$1, If[LessEqual[y, 9.2e-16], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * t$95$2), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+39], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000001e44 or 4.4000000000000003e39 < y

   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. Taylor expanded in y around inf 70.9%

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

   if -1.9000000000000001e44 < y < 9.1999999999999996e-16

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 88.0%

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

      1. *-commutative 88.0%

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

   4. Simplified 88.0%

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

   if 9.1999999999999996e-16 < y < 4.4000000000000003e39

   1. Initial program 45.3%

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

   2. Taylor expanded in i around 0 38.6%

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

   3. Taylor expanded in t around 0 65.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 9: 75.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot t_1 + i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.35e+40)
     t_2
     (if (<= y 4.4e-16)
       (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ (* y t_1) i))
       (if (<= y 4.4e+39)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1)
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.35e+40) {
		tmp = t_2;
	} else if (y <= 4.4e-16) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * t_1) + i);
	} else if (y <= 4.4e+39) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else {
		tmp = t_2;
	}
	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 = c + (y * (b + (y * (y + a))))
    t_2 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.35d+40)) then
        tmp = t_2
    else if (y <= 4.4d-16) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * t_1) + i)
    else if (y <= 4.4d+39) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.35e+40) {
		tmp = t_2;
	} else if (y <= 4.4e-16) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * t_1) + i);
	} else if (y <= 4.4e+39) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.35e+40:
		tmp = t_2
	elif y <= 4.4e-16:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * t_1) + i)
	elif y <= 4.4e+39:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.35e+40)
		tmp = t_2;
	elseif (y <= 4.4e-16)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * t_1) + i));
	elseif (y <= 4.4e+39)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.35e+40)
		tmp = t_2;
	elseif (y <= 4.4e-16)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * t_1) + i);
	elseif (y <= 4.4e+39)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+40], t$95$2, If[LessEqual[y, 4.4e-16], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * t$95$1), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+39], 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], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35000000000000005e40 or 4.4000000000000003e39 < y

   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. Taylor expanded in y around inf 69.7%

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

   if -1.35000000000000005e40 < y < 4.40000000000000001e-16

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 90.7%

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

      1. *-commutative 90.7%

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

   4. Simplified 90.7%

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

   if 4.40000000000000001e-16 < y < 4.4000000000000003e39

   1. Initial program 45.3%

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

   2. Taylor expanded in i around 0 38.6%

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

   3. Taylor expanded in t around 0 65.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+40}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 10: 74.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+43} \lor \neg \left(y \leq 1.4 \cdot 10^{+30}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.25e+43) (not (<= y 1.4e+30)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ (+ t (* y 230661.510616)) (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.25e+43) || !(y <= 1.4e+30)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.25d+43)) .or. (.not. (y <= 1.4d+30))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.25e+43) || !(y <= 1.4e+30)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.25e+43) or not (y <= 1.4e+30):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.25e+43) || !(y <= 1.4e+30))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.25e+43) || ~((y <= 1.4e+30)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.25e+43], N[Not[LessEqual[y, 1.4e+30]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2500000000000001e43 or 1.39999999999999992e30 < y

   1. Initial program 6.1%

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

   2. Taylor expanded in y around inf 68.5%

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

   if -1.2500000000000001e43 < y < 1.39999999999999992e30

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 82.3%

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

      1. *-commutative 82.3%

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

   4. Simplified 82.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+43} \lor \neg \left(y \leq 1.4 \cdot 10^{+30}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]

Alternative 11: 72.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+50} \lor \neg \left(y \leq 2.6 \cdot 10^{+28}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.5e+50) (not (<= y 2.6e+28)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.5e+50) || !(y <= 2.6e+28)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-6.5d+50)) .or. (.not. (y <= 2.6d+28))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.5e+50) || !(y <= 2.6e+28)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6.5e+50) or not (y <= 2.6e+28):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6.5e+50) || !(y <= 2.6e+28))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -6.5e+50) || ~((y <= 2.6e+28)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6.5e+50], N[Not[LessEqual[y, 2.6e+28]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000003e50 or 2.6000000000000002e28 < y

   1. Initial program 5.3%

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

   2. Taylor expanded in y around inf 69.1%

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

   if -6.5000000000000003e50 < y < 2.6000000000000002e28

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 81.8%

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

      1. *-commutative 81.8%

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

   4. Simplified 81.8%

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

   5. Taylor expanded in y around 0 79.3%

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

      1. *-commutative 79.3%

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

   7. Simplified 79.3%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+50} \lor \neg \left(y \leq 2.6 \cdot 10^{+28}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 12: 58.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+43} \lor \neg \left(y \leq 4.2 \cdot 10^{+25}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.35e+43) (not (<= y 4.2e+25)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ (+ t (* y 230661.510616)) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.35e+43) || !(y <= 4.2e+25)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.35d+43)) .or. (.not. (y <= 4.2d+25))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.35e+43) || !(y <= 4.2e+25)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.35e+43) or not (y <= 4.2e+25):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = (t + (y * 230661.510616)) / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.35e+43) || !(y <= 4.2e+25))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.35e+43) || ~((y <= 4.2e+25)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = (t + (y * 230661.510616)) / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.35e+43], N[Not[LessEqual[y, 4.2e+25]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3500000000000001e43 or 4.1999999999999998e25 < y

   1. Initial program 6.1%

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

   2. Taylor expanded in y around inf 67.9%

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

   if -1.3500000000000001e43 < y < 4.1999999999999998e25

   1. Initial program 93.2%

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

   2. Taylor expanded in y around 0 82.9%

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

      1. *-commutative 82.9%

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

   4. Simplified 82.9%

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

   5. Taylor expanded in i around inf 56.9%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+43} \lor \neg \left(y \leq 4.2 \cdot 10^{+25}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \]

Alternative 13: 69.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+44} \lor \neg \left(y \leq 1.8 \cdot 10^{+27}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8.5e+44) (not (<= y 1.8e+27)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ (+ t (* y 230661.510616)) (+ 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 <= -8.5e+44) || !(y <= 1.8e+27)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (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 <= (-8.5d+44)) .or. (.not. (y <= 1.8d+27))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / (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 <= -8.5e+44) || !(y <= 1.8e+27)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8.5e+44) or not (y <= 1.8e+27):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8.5e+44) || !(y <= 1.8e+27))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / 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 <= -8.5e+44) || ~((y <= 1.8e+27)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8.5e+44], N[Not[LessEqual[y, 1.8e+27]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5e44 or 1.79999999999999991e27 < y

   1. Initial program 5.3%

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

   2. Taylor expanded in y around inf 69.1%

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

   if -8.5e44 < y < 1.79999999999999991e27

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 81.8%

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

      1. *-commutative 81.8%

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

   4. Simplified 81.8%

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

   5. Taylor expanded in y around 0 71.9%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{c \cdot y} + i} \]
   6. Step-by-step derivation

      1. *-commutative 71.9%

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

   7. Simplified 71.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+44} \lor \neg \left(y \leq 1.8 \cdot 10^{+27}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \]

Alternative 14: 54.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+25}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.4e+34) x (if (<= y 1.75e+25) (/ (+ t (* y 230661.510616)) 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 <= -5.4e+34) {
		tmp = x;
	} else if (y <= 1.75e+25) {
		tmp = (t + (y * 230661.510616)) / 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 <= (-5.4d+34)) then
        tmp = x
    else if (y <= 1.75d+25) then
        tmp = (t + (y * 230661.510616d0)) / 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 <= -5.4e+34) {
		tmp = x;
	} else if (y <= 1.75e+25) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.4e+34:
		tmp = x
	elif y <= 1.75e+25:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.4e+34)
		tmp = x;
	elseif (y <= 1.75e+25)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / 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 <= -5.4e+34)
		tmp = x;
	elseif (y <= 1.75e+25)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.4e+34], x, If[LessEqual[y, 1.75e+25], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4000000000000001e34 or 1.75e25 < y

   1. Initial program 7.7%

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

   2. Taylor expanded in y around inf 49.9%

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

   if -5.4000000000000001e34 < y < 1.75e25

   1. Initial program 95.0%

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

   2. Taylor expanded in y around 0 85.7%

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

      1. *-commutative 85.7%

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

   4. Simplified 85.7%

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

   5. Taylor expanded in i around inf 58.9%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+25}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 50.7% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.5e+35) x (if (<= y 1.35e+25) (/ 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 <= -5.5e+35) {
		tmp = x;
	} else if (y <= 1.35e+25) {
		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 <= (-5.5d+35)) then
        tmp = x
    else if (y <= 1.35d+25) 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 <= -5.5e+35) {
		tmp = x;
	} else if (y <= 1.35e+25) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.5e+35:
		tmp = x
	elif y <= 1.35e+25:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.5e+35)
		tmp = x;
	elseif (y <= 1.35e+25)
		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 <= -5.5e+35)
		tmp = x;
	elseif (y <= 1.35e+25)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.5e+35], x, If[LessEqual[y, 1.35e+25], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000001e35 or 1.35e25 < y

   1. Initial program 7.7%

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

   2. Taylor expanded in y around inf 49.9%

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

   if -5.50000000000000001e35 < y < 1.35e25

   1. Initial program 95.0%

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

   2. Taylor expanded in y around 0 51.0%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 25.8% 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 55.4%

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

2. Taylor expanded in y around inf 24.7%

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

3. Final simplification 24.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023321 
(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)))