Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.9% → 87.5%

Time: 24.1s

Alternatives: 18

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: 55.9% 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: 87.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, y + a, b\right)\\ t_2 := \frac{27464.7644705}{t_1} + \left(\frac{230661.510616}{y \cdot t_1} + \left(\frac{t}{t_1 \cdot {y}^{2}} + \frac{y}{\frac{t_1}{\mathsf{fma}\left(y, x, z\right)}}\right)\right)\\ t_3 := \left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1250000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y (+ y a) b))
        (t_2
         (+
          (/ 27464.7644705 t_1)
          (+
           (/ 230661.510616 (* y t_1))
           (+ (/ t (* t_1 (pow y 2.0))) (/ y (/ t_1 (fma y x z)))))))
        (t_3 (- (+ (/ z y) x) (/ a (/ y x)))))
   (if (<= y -3.6e+126)
     t_3
     (if (<= y -1250000.0)
       t_2
       (if (<= y 9.2e+35)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))
         (if (<= y 6.8e+123) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, (y + a), b);
	double t_2 = (27464.7644705 / t_1) + ((230661.510616 / (y * t_1)) + ((t / (t_1 * pow(y, 2.0))) + (y / (t_1 / fma(y, x, z)))));
	double t_3 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -3.6e+126) {
		tmp = t_3;
	} else if (y <= -1250000.0) {
		tmp = t_2;
	} else if (y <= 9.2e+35) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 6.8e+123) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, Float64(y + a), b)
	t_2 = Float64(Float64(27464.7644705 / t_1) + Float64(Float64(230661.510616 / Float64(y * t_1)) + Float64(Float64(t / Float64(t_1 * (y ^ 2.0))) + Float64(y / Float64(t_1 / fma(y, x, z))))))
	t_3 = Float64(Float64(Float64(z / y) + x) - Float64(a / Float64(y / x)))
	tmp = 0.0
	if (y <= -3.6e+126)
		tmp = t_3;
	elseif (y <= -1250000.0)
		tmp = t_2;
	elseif (y <= 9.2e+35)
		tmp = 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));
	elseif (y <= 6.8e+123)
		tmp = t_2;
	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 + a), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27464.7644705 / t$95$1), $MachinePrecision] + N[(N[(230661.510616 / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(t$95$1 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t$95$1 / N[(y * x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+126], t$95$3, If[LessEqual[y, -1250000.0], t$95$2, If[LessEqual[y, 9.2e+35], 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[y, 6.8e+123], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e126 or 6.80000000000000002e123 < y

   1. Initial program 0.0%

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

   2. Taylor expanded in i around 0 0.0%

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

   3. Taylor expanded in c around 0 0.0%

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

   4. Taylor expanded in y around inf 82.6%

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

      1. +-commutative 82.6%

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

      2. associate-/l* 91.9%

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

   6. Simplified 91.9%

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

   if -3.6e126 < y < -1.25e6 or 9.1999999999999993e35 < y < 6.80000000000000002e123

   1. Initial program 29.0%

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

   2. Taylor expanded in i around 0 27.0%

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

   3. Taylor expanded in c around 0 26.9%

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

   4. Taylor expanded in t around inf 62.2%

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

      1. associate-*r/ 62.2%

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

      2. metadata-eval 62.2%

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

      3. +-commutative 62.2%

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

      4. +-commutative 62.2%

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

      5. fma-udef 62.2%

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

      6. associate-*r/ 62.2%

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

      7. metadata-eval 62.2%

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

      8. +-commutative 62.2%

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

      9. +-commutative 62.2%

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

      10. fma-udef 62.2%

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

   6. Simplified 77.2%

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

   if -1.25e6 < y < 9.1999999999999993e35

   1. Initial program 96.8%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+126}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1250000:\\ \;\;\;\;\frac{27464.7644705}{\mathsf{fma}\left(y, y + a, b\right)} + \left(\frac{230661.510616}{y \cdot \mathsf{fma}\left(y, y + a, b\right)} + \left(\frac{t}{\mathsf{fma}\left(y, y + a, b\right) \cdot {y}^{2}} + \frac{y}{\frac{\mathsf{fma}\left(y, y + a, b\right)}{\mathsf{fma}\left(y, x, z\right)}}\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+123}:\\ \;\;\;\;\frac{27464.7644705}{\mathsf{fma}\left(y, y + a, b\right)} + \left(\frac{230661.510616}{y \cdot \mathsf{fma}\left(y, y + a, b\right)} + \left(\frac{t}{\mathsf{fma}\left(y, y + a, b\right) \cdot {y}^{2}} + \frac{y}{\frac{\mathsf{fma}\left(y, y + a, b\right)}{\mathsf{fma}\left(y, x, z\right)}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 2: 84.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 27464.7644705 + y \cdot \left(z + y \cdot x\right)\\ t_2 := b + y \cdot \left(y + a\right)\\ t_3 := \left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ t_4 := y \cdot t_2\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1250000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{t_4} + \left(\frac{t}{{y}^{2} \cdot t_2} + \frac{t_1}{t_2}\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot t_1\right)}{y \cdot \left(c + t_4\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (- (+ (/ z y) x) (/ a (/ y x))))
        (t_4 (* y t_2)))
   (if (<= y -3.1e+97)
     t_3
     (if (<= y -1250000.0)
       (+
        (* 230661.510616 (/ 1.0 t_4))
        (+ (/ t (* (pow y 2.0) t_2)) (/ t_1 t_2)))
       (if (<= y 1.6e+52)
         (/ (+ t (* y (+ 230661.510616 (* y t_1)))) (+ (* y (+ c t_4)) i))
         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 = ((z / y) + x) - (a / (y / x));
	double t_4 = y * t_2;
	double tmp;
	if (y <= -3.1e+97) {
		tmp = t_3;
	} else if (y <= -1250000.0) {
		tmp = (230661.510616 * (1.0 / t_4)) + ((t / (pow(y, 2.0) * t_2)) + (t_1 / t_2));
	} else if (y <= 1.6e+52) {
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / ((y * (c + t_4)) + i);
	} 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) :: tmp
    t_1 = 27464.7644705d0 + (y * (z + (y * x)))
    t_2 = b + (y * (y + a))
    t_3 = ((z / y) + x) - (a / (y / x))
    t_4 = y * t_2
    if (y <= (-3.1d+97)) then
        tmp = t_3
    else if (y <= (-1250000.0d0)) then
        tmp = (230661.510616d0 * (1.0d0 / t_4)) + ((t / ((y ** 2.0d0) * t_2)) + (t_1 / t_2))
    else if (y <= 1.6d+52) then
        tmp = (t + (y * (230661.510616d0 + (y * t_1)))) / ((y * (c + t_4)) + i)
    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 = ((z / y) + x) - (a / (y / x));
	double t_4 = y * t_2;
	double tmp;
	if (y <= -3.1e+97) {
		tmp = t_3;
	} else if (y <= -1250000.0) {
		tmp = (230661.510616 * (1.0 / t_4)) + ((t / (Math.pow(y, 2.0) * t_2)) + (t_1 / t_2));
	} else if (y <= 1.6e+52) {
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / ((y * (c + t_4)) + i);
	} 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 = ((z / y) + x) - (a / (y / x))
	t_4 = y * t_2
	tmp = 0
	if y <= -3.1e+97:
		tmp = t_3
	elif y <= -1250000.0:
		tmp = (230661.510616 * (1.0 / t_4)) + ((t / (math.pow(y, 2.0) * t_2)) + (t_1 / t_2))
	elif y <= 1.6e+52:
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / ((y * (c + t_4)) + i)
	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(Float64(z / y) + x) - Float64(a / Float64(y / x)))
	t_4 = Float64(y * t_2)
	tmp = 0.0
	if (y <= -3.1e+97)
		tmp = t_3;
	elseif (y <= -1250000.0)
		tmp = Float64(Float64(230661.510616 * Float64(1.0 / t_4)) + Float64(Float64(t / Float64((y ^ 2.0) * t_2)) + Float64(t_1 / t_2)));
	elseif (y <= 1.6e+52)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * t_1)))) / Float64(Float64(y * Float64(c + t_4)) + i));
	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 = ((z / y) + x) - (a / (y / x));
	t_4 = y * t_2;
	tmp = 0.0;
	if (y <= -3.1e+97)
		tmp = t_3;
	elseif (y <= -1250000.0)
		tmp = (230661.510616 * (1.0 / t_4)) + ((t / ((y ^ 2.0) * t_2)) + (t_1 / t_2));
	elseif (y <= 1.6e+52)
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / ((y * (c + t_4)) + i);
	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[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * t$95$2), $MachinePrecision]}, If[LessEqual[y, -3.1e+97], t$95$3, If[LessEqual[y, -1250000.0], N[(N[(230661.510616 * N[(1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(N[Power[y, 2.0], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+52], N[(N[(t + N[(y * N[(230661.510616 + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + t$95$4), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999981e97 or 1.6e52 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in i around 0 1.2%

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

   3. Taylor expanded in c around 0 1.2%

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

   4. Taylor expanded in y around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. associate-/l* 81.9%

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

   6. Simplified 81.9%

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

   if -3.09999999999999981e97 < y < -1.25e6

   1. Initial program 42.1%

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

   2. Taylor expanded in i around 0 38.8%

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

   3. Taylor expanded in c around 0 38.6%

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

   4. Taylor expanded in t around 0 77.7%

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

   if -1.25e6 < y < 1.6e52

   1. Initial program 96.1%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+97}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1250000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{{y}^{2} \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 3: 84.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := \left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ t_3 := y \cdot t_1\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1250000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{t_3} + \left(\frac{y \cdot z}{t_1} + \frac{27464.7644705 + x \cdot {y}^{2}}{t_1}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + t_3\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (- (+ (/ z y) x) (/ a (/ y x))))
        (t_3 (* y t_1)))
   (if (<= y -3.8e+98)
     t_2
     (if (<= y -1250000.0)
       (+
        (* 230661.510616 (/ 1.0 t_3))
        (+ (/ (* y z) t_1) (/ (+ 27464.7644705 (* x (pow y 2.0))) t_1)))
       (if (<= y 2.7e+51)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ (* y (+ c t_3)) i))
         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 = ((z / y) + x) - (a / (y / x));
	double t_3 = y * t_1;
	double tmp;
	if (y <= -3.8e+98) {
		tmp = t_2;
	} else if (y <= -1250000.0) {
		tmp = (230661.510616 * (1.0 / t_3)) + (((y * z) / t_1) + ((27464.7644705 + (x * pow(y, 2.0))) / t_1));
	} else if (y <= 2.7e+51) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + t_3)) + i);
	} 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) :: tmp
    t_1 = b + (y * (y + a))
    t_2 = ((z / y) + x) - (a / (y / x))
    t_3 = y * t_1
    if (y <= (-3.8d+98)) then
        tmp = t_2
    else if (y <= (-1250000.0d0)) then
        tmp = (230661.510616d0 * (1.0d0 / t_3)) + (((y * z) / t_1) + ((27464.7644705d0 + (x * (y ** 2.0d0))) / t_1))
    else if (y <= 2.7d+51) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / ((y * (c + t_3)) + i)
    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 = ((z / y) + x) - (a / (y / x));
	double t_3 = y * t_1;
	double tmp;
	if (y <= -3.8e+98) {
		tmp = t_2;
	} else if (y <= -1250000.0) {
		tmp = (230661.510616 * (1.0 / t_3)) + (((y * z) / t_1) + ((27464.7644705 + (x * Math.pow(y, 2.0))) / t_1));
	} else if (y <= 2.7e+51) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + t_3)) + i);
	} 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 = ((z / y) + x) - (a / (y / x))
	t_3 = y * t_1
	tmp = 0
	if y <= -3.8e+98:
		tmp = t_2
	elif y <= -1250000.0:
		tmp = (230661.510616 * (1.0 / t_3)) + (((y * z) / t_1) + ((27464.7644705 + (x * math.pow(y, 2.0))) / t_1))
	elif y <= 2.7e+51:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + t_3)) + i)
	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(Float64(z / y) + x) - Float64(a / Float64(y / x)))
	t_3 = Float64(y * t_1)
	tmp = 0.0
	if (y <= -3.8e+98)
		tmp = t_2;
	elseif (y <= -1250000.0)
		tmp = Float64(Float64(230661.510616 * Float64(1.0 / t_3)) + Float64(Float64(Float64(y * z) / t_1) + Float64(Float64(27464.7644705 + Float64(x * (y ^ 2.0))) / t_1)));
	elseif (y <= 2.7e+51)
		tmp = 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 + t_3)) + i));
	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 = ((z / y) + x) - (a / (y / x));
	t_3 = y * t_1;
	tmp = 0.0;
	if (y <= -3.8e+98)
		tmp = t_2;
	elseif (y <= -1250000.0)
		tmp = (230661.510616 * (1.0 / t_3)) + (((y * z) / t_1) + ((27464.7644705 + (x * (y ^ 2.0))) / t_1));
	elseif (y <= 2.7e+51)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + t_3)) + i);
	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[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * t$95$1), $MachinePrecision]}, If[LessEqual[y, -3.8e+98], t$95$2, If[LessEqual[y, -1250000.0], N[(N[(230661.510616 * N[(1.0 / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(27464.7644705 + N[(x * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+51], 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 + t$95$3), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999999e98 or 2.69999999999999992e51 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in i around 0 1.2%

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

   3. Taylor expanded in c around 0 1.2%

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

   4. Taylor expanded in y around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. associate-/l* 81.9%

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

   6. Simplified 81.9%

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

   if -3.7999999999999999e98 < y < -1.25e6

   1. Initial program 42.1%

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

   2. Taylor expanded in i around 0 38.8%

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

   3. Taylor expanded in c around 0 38.6%

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

   4. Taylor expanded in t around 0 51.5%

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

   5. Taylor expanded in z around 0 74.5%

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

   if -1.25e6 < y < 2.69999999999999992e51

   1. Initial program 96.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+98}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1250000:\\ \;\;\;\;230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{y \cdot z}{b + y \cdot \left(y + a\right)} + \frac{27464.7644705 + x \cdot {y}^{2}}{b + y \cdot \left(y + a\right)}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 4: 84.4% accurate, 0.5× speedup

Math

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

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 INFINITY) t_1 (- (+ (/ z y) x) (/ a (/ y x))))))

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = ((z / y) + x) - (a / (y / x));
	}
	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 <= math.inf:
		tmp = t_1
	else:
		tmp = ((z / y) + x) - (a / (y / x))
	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 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(a / Float64(y / x)));
	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 <= Inf)
		tmp = t_1;
	else
		tmp = ((z / y) + x) - (a / (y / x));
	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, Infinity], t$95$1, N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.2%

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

   if +inf.0 < (/.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 0.0%

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

   2. Taylor expanded in i around 0 0.0%

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

   3. Taylor expanded in c around 0 0.0%

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

   4. Taylor expanded in y around inf 70.1%

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

      1. +-commutative 70.1%

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

      2. associate-/l* 76.9%

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

   6. Simplified 76.9%

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

4. Final simplification 85.2%

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

Alternative 5: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-6}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot t_1 + i}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2 (- (+ (/ z y) x) (/ a (/ y x)))))
   (if (<= y -2.6e+97)
     t_2
     (if (<= y -1.1e-6)
       (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1)
       (if (<= y 1.2e+58)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ (* y t_1) i))
         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 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -2.6e+97) {
		tmp = t_2;
	} else if (y <= -1.1e-6) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else if (y <= 1.2e+58) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i);
	} 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 = ((z / y) + x) - (a / (y / x))
    if (y <= (-2.6d+97)) then
        tmp = t_2
    else if (y <= (-1.1d-6)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    else if (y <= 1.2d+58) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * t_1) + i)
    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 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -2.6e+97) {
		tmp = t_2;
	} else if (y <= -1.1e-6) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else if (y <= 1.2e+58) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i);
	} 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 = ((z / y) + x) - (a / (y / x))
	tmp = 0
	if y <= -2.6e+97:
		tmp = t_2
	elif y <= -1.1e-6:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	elif y <= 1.2e+58:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i)
	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(Float64(z / y) + x) - Float64(a / Float64(y / x)))
	tmp = 0.0
	if (y <= -2.6e+97)
		tmp = t_2;
	elseif (y <= -1.1e-6)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1);
	elseif (y <= 1.2e+58)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(Float64(y * t_1) + i));
	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 = ((z / y) + x) - (a / (y / x));
	tmp = 0.0;
	if (y <= -2.6e+97)
		tmp = t_2;
	elseif (y <= -1.1e-6)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	elseif (y <= 1.2e+58)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i);
	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[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+97], t$95$2, If[LessEqual[y, -1.1e-6], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 1.2e+58], 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], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e97 or 1.2e58 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in i around 0 1.2%

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

   3. Taylor expanded in c around 0 1.2%

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

   4. Taylor expanded in y around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   if -2.6e97 < y < -1.1000000000000001e-6

   1. Initial program 53.0%

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

   2. Taylor expanded in i around 0 47.7%

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

   3. Taylor expanded in t around 0 55.4%

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

   if -1.1000000000000001e-6 < y < 1.2e58

   1. Initial program 95.2%

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

   2. Taylor expanded in x around 0 89.3%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-6}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 6: 77.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ t_3 := \left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-25}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot t_1 + i}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1))
        (t_3 (- (+ (/ z y) x) (/ a (/ y x)))))
   (if (<= y -2.6e+97)
     t_3
     (if (<= y -2.9e-8)
       t_2
       (if (<= y 8e-25)
         (/ (+ t (* y 230661.510616)) (+ (* y t_1) i))
         (if (<= y 1.25e+64) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -2.6e+97) {
		tmp = t_3;
	} else if (y <= -2.9e-8) {
		tmp = t_2;
	} else if (y <= 8e-25) {
		tmp = (t + (y * 230661.510616)) / ((y * t_1) + i);
	} else if (y <= 1.25e+64) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (y * (b + (y * (y + a))))
    t_2 = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    t_3 = ((z / y) + x) - (a / (y / x))
    if (y <= (-2.6d+97)) then
        tmp = t_3
    else if (y <= (-2.9d-8)) then
        tmp = t_2
    else if (y <= 8d-25) then
        tmp = (t + (y * 230661.510616d0)) / ((y * t_1) + i)
    else if (y <= 1.25d+64) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -2.6e+97) {
		tmp = t_3;
	} else if (y <= -2.9e-8) {
		tmp = t_2;
	} else if (y <= 8e-25) {
		tmp = (t + (y * 230661.510616)) / ((y * t_1) + i);
	} else if (y <= 1.25e+64) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	t_3 = ((z / y) + x) - (a / (y / x))
	tmp = 0
	if y <= -2.6e+97:
		tmp = t_3
	elif y <= -2.9e-8:
		tmp = t_2
	elif y <= 8e-25:
		tmp = (t + (y * 230661.510616)) / ((y * t_1) + i)
	elif y <= 1.25e+64:
		tmp = t_2
	else:
		tmp = t_3
	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(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1)
	t_3 = Float64(Float64(Float64(z / y) + x) - Float64(a / Float64(y / x)))
	tmp = 0.0
	if (y <= -2.6e+97)
		tmp = t_3;
	elseif (y <= -2.9e-8)
		tmp = t_2;
	elseif (y <= 8e-25)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * t_1) + i));
	elseif (y <= 1.25e+64)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	t_3 = ((z / y) + x) - (a / (y / x));
	tmp = 0.0;
	if (y <= -2.6e+97)
		tmp = t_3;
	elseif (y <= -2.9e-8)
		tmp = t_2;
	elseif (y <= 8e-25)
		tmp = (t + (y * 230661.510616)) / ((y * t_1) + i);
	elseif (y <= 1.25e+64)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+97], t$95$3, If[LessEqual[y, -2.9e-8], t$95$2, If[LessEqual[y, 8e-25], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * t$95$1), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+64], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e97 or 1.25e64 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in i around 0 1.2%

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

   3. Taylor expanded in c around 0 1.2%

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

   4. Taylor expanded in y around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   if -2.6e97 < y < -2.9000000000000002e-8 or 8.00000000000000031e-25 < y < 1.25e64

   1. Initial program 56.9%

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

   2. Taylor expanded in i around 0 49.8%

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

   3. Taylor expanded in t around 0 56.3%

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

   if -2.9000000000000002e-8 < y < 8.00000000000000031e-25

   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 y around 0 90.7%

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

      1. *-commutative 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-25}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+64}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 7: 76.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ t_3 := \left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -0.235:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + t_1\right) + i}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* y (+ b (* y (+ y a)))))
        (t_2
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1))
        (t_3 (- (+ (/ z y) x) (/ a (/ y x)))))
   (if (<= y -2.6e+97)
     t_3
     (if (<= y -0.235)
       t_2
       (if (<= y 6.8e-13)
         (/ (+ t (* y 230661.510616)) (+ (* y (+ c t_1)) i))
         (if (<= y 1.75e+63) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * (b + (y * (y + a)));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -2.6e+97) {
		tmp = t_3;
	} else if (y <= -0.235) {
		tmp = t_2;
	} else if (y <= 6.8e-13) {
		tmp = (t + (y * 230661.510616)) / ((y * (c + t_1)) + i);
	} else if (y <= 1.75e+63) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (b + (y * (y + a)))
    t_2 = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    t_3 = ((z / y) + x) - (a / (y / x))
    if (y <= (-2.6d+97)) then
        tmp = t_3
    else if (y <= (-0.235d0)) then
        tmp = t_2
    else if (y <= 6.8d-13) then
        tmp = (t + (y * 230661.510616d0)) / ((y * (c + t_1)) + i)
    else if (y <= 1.75d+63) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * (b + (y * (y + a)));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -2.6e+97) {
		tmp = t_3;
	} else if (y <= -0.235) {
		tmp = t_2;
	} else if (y <= 6.8e-13) {
		tmp = (t + (y * 230661.510616)) / ((y * (c + t_1)) + i);
	} else if (y <= 1.75e+63) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = y * (b + (y * (y + a)))
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	t_3 = ((z / y) + x) - (a / (y / x))
	tmp = 0
	if y <= -2.6e+97:
		tmp = t_3
	elif y <= -0.235:
		tmp = t_2
	elif y <= 6.8e-13:
		tmp = (t + (y * 230661.510616)) / ((y * (c + t_1)) + i)
	elif y <= 1.75e+63:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(y * Float64(b + Float64(y * Float64(y + a))))
	t_2 = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1)
	t_3 = Float64(Float64(Float64(z / y) + x) - Float64(a / Float64(y / x)))
	tmp = 0.0
	if (y <= -2.6e+97)
		tmp = t_3;
	elseif (y <= -0.235)
		tmp = t_2;
	elseif (y <= 6.8e-13)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(c + t_1)) + i));
	elseif (y <= 1.75e+63)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = y * (b + (y * (y + a)));
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	t_3 = ((z / y) + x) - (a / (y / x));
	tmp = 0.0;
	if (y <= -2.6e+97)
		tmp = t_3;
	elseif (y <= -0.235)
		tmp = t_2;
	elseif (y <= 6.8e-13)
		tmp = (t + (y * 230661.510616)) / ((y * (c + t_1)) + i);
	elseif (y <= 1.75e+63)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+97], t$95$3, If[LessEqual[y, -0.235], t$95$2, If[LessEqual[y, 6.8e-13], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + t$95$1), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+63], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e97 or 1.75000000000000015e63 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in i around 0 1.2%

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

   3. Taylor expanded in c around 0 1.2%

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

   4. Taylor expanded in y around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   if -2.6e97 < y < -0.23499999999999999 or 6.80000000000000031e-13 < y < 1.75000000000000015e63

   1. Initial program 52.6%

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

   2. Taylor expanded in i around 0 46.7%

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

   3. Taylor expanded in c around 0 41.2%

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

   4. Taylor expanded in t around 0 50.5%

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

   if -0.23499999999999999 < y < 6.80000000000000031e-13

   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 y around 0 88.6%

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

      1. *-commutative 88.6%

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

   4. Simplified 88.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -0.235:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+63}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 8: 75.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := \left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -400000:\\ \;\;\;\;\frac{y \cdot z}{t_1}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot t_1\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a)))) (t_2 (- (+ (/ z y) x) (/ a (/ y x)))))
   (if (<= y -1.85e+58)
     t_2
     (if (<= y -400000.0)
       (/ (* y z) t_1)
       (if (<= y 2.3e+53)
         (/ (+ t (* y 230661.510616)) (+ (* y (+ c (* y t_1))) i))
         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 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -1.85e+58) {
		tmp = t_2;
	} else if (y <= -400000.0) {
		tmp = (y * z) / t_1;
	} else if (y <= 2.3e+53) {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * t_1))) + i);
	} 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 = b + (y * (y + a))
    t_2 = ((z / y) + x) - (a / (y / x))
    if (y <= (-1.85d+58)) then
        tmp = t_2
    else if (y <= (-400000.0d0)) then
        tmp = (y * z) / t_1
    else if (y <= 2.3d+53) then
        tmp = (t + (y * 230661.510616d0)) / ((y * (c + (y * t_1))) + i)
    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 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -1.85e+58) {
		tmp = t_2;
	} else if (y <= -400000.0) {
		tmp = (y * z) / t_1;
	} else if (y <= 2.3e+53) {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * t_1))) + i);
	} 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 = ((z / y) + x) - (a / (y / x))
	tmp = 0
	if y <= -1.85e+58:
		tmp = t_2
	elif y <= -400000.0:
		tmp = (y * z) / t_1
	elif y <= 2.3e+53:
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * t_1))) + i)
	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(Float64(z / y) + x) - Float64(a / Float64(y / x)))
	tmp = 0.0
	if (y <= -1.85e+58)
		tmp = t_2;
	elseif (y <= -400000.0)
		tmp = Float64(Float64(y * z) / t_1);
	elseif (y <= 2.3e+53)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(c + Float64(y * t_1))) + i));
	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 = ((z / y) + x) - (a / (y / x));
	tmp = 0.0;
	if (y <= -1.85e+58)
		tmp = t_2;
	elseif (y <= -400000.0)
		tmp = (y * z) / t_1;
	elseif (y <= 2.3e+53)
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * t_1))) + i);
	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[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+58], t$95$2, If[LessEqual[y, -400000.0], N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.3e+53], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8500000000000001e58 or 2.3000000000000002e53 < y

   1. Initial program 5.2%

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

   2. Taylor expanded in i around 0 5.2%

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

   3. Taylor expanded in c around 0 5.2%

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

   4. Taylor expanded in y around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-/l* 77.2%

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

   6. Simplified 77.2%

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

   if -1.8500000000000001e58 < y < -4e5

   1. Initial program 46.5%

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

   2. Taylor expanded in i around 0 41.0%

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

   3. Taylor expanded in c around 0 40.7%

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

   4. Taylor expanded in z around inf 34.1%

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

   if -4e5 < y < 2.3000000000000002e53

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0 78.0%

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

      1. *-commutative 78.0%

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

   4. Simplified 78.0%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+58}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -400000:\\ \;\;\;\;\frac{y \cdot z}{b + y \cdot \left(y + a\right)}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 9: 73.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -320000:\\ \;\;\;\;\frac{y \cdot z}{b + y \cdot \left(y + a\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ (/ z y) x) (/ a (/ y x)))))
   (if (<= y -2.8e+57)
     t_1
     (if (<= y -320000.0)
       (/ (* y z) (+ b (* y (+ y a))))
       (if (<= y 2.7e+42)
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -2.8e+57) {
		tmp = t_1;
	} else if (y <= -320000.0) {
		tmp = (y * z) / (b + (y * (y + a)));
	} else if (y <= 2.7e+42) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} 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) :: tmp
    t_1 = ((z / y) + x) - (a / (y / x))
    if (y <= (-2.8d+57)) then
        tmp = t_1
    else if (y <= (-320000.0d0)) then
        tmp = (y * z) / (b + (y * (y + a)))
    else if (y <= 2.7d+42) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -2.8e+57) {
		tmp = t_1;
	} else if (y <= -320000.0) {
		tmp = (y * z) / (b + (y * (y + a)));
	} else if (y <= 2.7e+42) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((z / y) + x) - (a / (y / x))
	tmp = 0
	if y <= -2.8e+57:
		tmp = t_1
	elif y <= -320000.0:
		tmp = (y * z) / (b + (y * (y + a)))
	elif y <= 2.7e+42:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(z / y) + x) - Float64(a / Float64(y / x)))
	tmp = 0.0
	if (y <= -2.8e+57)
		tmp = t_1;
	elseif (y <= -320000.0)
		tmp = Float64(Float64(y * z) / Float64(b + Float64(y * Float64(y + a))));
	elseif (y <= 2.7e+42)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((z / y) + x) - (a / (y / x));
	tmp = 0.0;
	if (y <= -2.8e+57)
		tmp = t_1;
	elseif (y <= -320000.0)
		tmp = (y * z) / (b + (y * (y + a)));
	elseif (y <= 2.7e+42)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	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[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+57], t$95$1, If[LessEqual[y, -320000.0], N[(N[(y * z), $MachinePrecision] / N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+42], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8e57 or 2.7000000000000001e42 < 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 i around 0 6.1%

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

   3. Taylor expanded in c around 0 6.1%

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

   4. Taylor expanded in y around inf 69.4%

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

      1. +-commutative 69.4%

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

      2. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   if -2.8e57 < y < -3.2e5

   1. Initial program 46.5%

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

   2. Taylor expanded in i around 0 41.0%

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

   3. Taylor expanded in c around 0 40.7%

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

   4. Taylor expanded in z around inf 34.1%

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

   if -3.2e5 < y < 2.7000000000000001e42

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 79.1%

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

      1. *-commutative 79.1%

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

   4. Simplified 79.1%

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

   5. Taylor expanded in y around 0 76.4%

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

      1. *-commutative 76.4%

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

   7. Simplified 76.4%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+57}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -320000:\\ \;\;\;\;\frac{y \cdot z}{b + y \cdot \left(y + a\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 10: 70.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -32500:\\ \;\;\;\;\frac{y \cdot z}{b + y \cdot \left(y + a\right)}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ (/ z y) x) (/ a (/ y x)))))
   (if (<= y -3.4e+57)
     t_1
     (if (<= y -32500.0)
       (/ (* y z) (+ b (* y (+ y a))))
       (if (<= y 3.6e-94)
         (/ (+ t (* y 230661.510616)) (+ i (* y c)))
         (if (<= y 2.3e+53) (/ t (+ i (* y (+ c (* y b))))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -3.4e+57) {
		tmp = t_1;
	} else if (y <= -32500.0) {
		tmp = (y * z) / (b + (y * (y + a)));
	} else if (y <= 3.6e-94) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 2.3e+53) {
		tmp = t / (i + (y * (c + (y * b))));
	} 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) :: tmp
    t_1 = ((z / y) + x) - (a / (y / x))
    if (y <= (-3.4d+57)) then
        tmp = t_1
    else if (y <= (-32500.0d0)) then
        tmp = (y * z) / (b + (y * (y + a)))
    else if (y <= 3.6d-94) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else if (y <= 2.3d+53) then
        tmp = t / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -3.4e+57) {
		tmp = t_1;
	} else if (y <= -32500.0) {
		tmp = (y * z) / (b + (y * (y + a)));
	} else if (y <= 3.6e-94) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 2.3e+53) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((z / y) + x) - (a / (y / x))
	tmp = 0
	if y <= -3.4e+57:
		tmp = t_1
	elif y <= -32500.0:
		tmp = (y * z) / (b + (y * (y + a)))
	elif y <= 3.6e-94:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	elif y <= 2.3e+53:
		tmp = t / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(z / y) + x) - Float64(a / Float64(y / x)))
	tmp = 0.0
	if (y <= -3.4e+57)
		tmp = t_1;
	elseif (y <= -32500.0)
		tmp = Float64(Float64(y * z) / Float64(b + Float64(y * Float64(y + a))));
	elseif (y <= 3.6e-94)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	elseif (y <= 2.3e+53)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((z / y) + x) - (a / (y / x));
	tmp = 0.0;
	if (y <= -3.4e+57)
		tmp = t_1;
	elseif (y <= -32500.0)
		tmp = (y * z) / (b + (y * (y + a)));
	elseif (y <= 3.6e-94)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	elseif (y <= 2.3e+53)
		tmp = t / (i + (y * (c + (y * b))));
	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[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+57], t$95$1, If[LessEqual[y, -32500.0], N[(N[(y * z), $MachinePrecision] / N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-94], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+53], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.39999999999999992e57 or 2.3000000000000002e53 < y

   1. Initial program 5.2%

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

   2. Taylor expanded in i around 0 5.2%

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

   3. Taylor expanded in c around 0 5.2%

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

   4. Taylor expanded in y around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-/l* 77.2%

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

   6. Simplified 77.2%

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

   if -3.39999999999999992e57 < y < -32500

   1. Initial program 49.3%

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

   2. Taylor expanded in i around 0 44.1%

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

   3. Taylor expanded in c around 0 43.7%

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

   4. Taylor expanded in z around inf 32.3%

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

   if -32500 < y < 3.6e-94

   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 y around 0 86.8%

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

      1. *-commutative 86.8%

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

   4. Simplified 86.8%

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

   5. Taylor expanded in y around 0 83.0%

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

      1. *-commutative 83.0%

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

   7. Simplified 83.0%

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

   if 3.6e-94 < y < 2.3000000000000002e53

   1. Initial program 82.6%

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

   2. Taylor expanded in y around 0 54.2%

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

      1. *-commutative 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in y around 0 51.3%

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

      1. *-commutative 51.3%

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

   7. Simplified 51.3%

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

   8. Taylor expanded in t around inf 43.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+57}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -32500:\\ \;\;\;\;\frac{y \cdot z}{b + y \cdot \left(y + a\right)}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 11: 66.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1100000:\\ \;\;\;\;\frac{y \cdot z}{b + y \cdot \left(y + a\right)}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ (/ z y) x) (/ a (/ y x)))))
   (if (<= y -6.2e+57)
     t_1
     (if (<= y -1100000.0)
       (/ (* y z) (+ b (* y (+ y a))))
       (if (<= y 3.4e+53) (/ t (+ i (* y (+ c (* y b))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -6.2e+57) {
		tmp = t_1;
	} else if (y <= -1100000.0) {
		tmp = (y * z) / (b + (y * (y + a)));
	} else if (y <= 3.4e+53) {
		tmp = t / (i + (y * (c + (y * b))));
	} 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) :: tmp
    t_1 = ((z / y) + x) - (a / (y / x))
    if (y <= (-6.2d+57)) then
        tmp = t_1
    else if (y <= (-1100000.0d0)) then
        tmp = (y * z) / (b + (y * (y + a)))
    else if (y <= 3.4d+53) then
        tmp = t / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((z / y) + x) - (a / (y / x));
	double tmp;
	if (y <= -6.2e+57) {
		tmp = t_1;
	} else if (y <= -1100000.0) {
		tmp = (y * z) / (b + (y * (y + a)));
	} else if (y <= 3.4e+53) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((z / y) + x) - (a / (y / x))
	tmp = 0
	if y <= -6.2e+57:
		tmp = t_1
	elif y <= -1100000.0:
		tmp = (y * z) / (b + (y * (y + a)))
	elif y <= 3.4e+53:
		tmp = t / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(z / y) + x) - Float64(a / Float64(y / x)))
	tmp = 0.0
	if (y <= -6.2e+57)
		tmp = t_1;
	elseif (y <= -1100000.0)
		tmp = Float64(Float64(y * z) / Float64(b + Float64(y * Float64(y + a))));
	elseif (y <= 3.4e+53)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((z / y) + x) - (a / (y / x));
	tmp = 0.0;
	if (y <= -6.2e+57)
		tmp = t_1;
	elseif (y <= -1100000.0)
		tmp = (y * z) / (b + (y * (y + a)));
	elseif (y <= 3.4e+53)
		tmp = t / (i + (y * (c + (y * b))));
	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[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+57], t$95$1, If[LessEqual[y, -1100000.0], N[(N[(y * z), $MachinePrecision] / N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+53], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000026e57 or 3.39999999999999998e53 < y

   1. Initial program 5.2%

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

   2. Taylor expanded in i around 0 5.2%

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

   3. Taylor expanded in c around 0 5.2%

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

   4. Taylor expanded in y around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-/l* 77.2%

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

   6. Simplified 77.2%

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

   if -6.20000000000000026e57 < y < -1.1e6

   1. Initial program 46.5%

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

   2. Taylor expanded in i around 0 41.0%

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

   3. Taylor expanded in c around 0 40.7%

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

   4. Taylor expanded in z around inf 34.1%

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

   if -1.1e6 < y < 3.39999999999999998e53

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0 78.0%

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

      1. *-commutative 78.0%

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

   4. Simplified 78.0%

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

   5. Taylor expanded in y around 0 75.3%

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

      1. *-commutative 75.3%

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

   7. Simplified 75.3%

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

   8. Taylor expanded in t around inf 69.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+57}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1100000:\\ \;\;\;\;\frac{y \cdot z}{b + y \cdot \left(y + a\right)}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 12: 55.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5000000000 \lor \neg \left(y \leq 4.2 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5000000000.0) (not (<= y 4.2e+22)))
   (- (+ (/ z y) x) (/ (* x a) y))
   (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5000000000.0) || !(y <= 4.2e+22)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-5000000000.0d0)) .or. (.not. (y <= 4.2d+22))) then
        tmp = ((z / y) + x) - ((x * a) / y)
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5000000000.0) || !(y <= 4.2e+22)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5000000000.0) or not (y <= 4.2e+22):
		tmp = ((z / y) + x) - ((x * a) / y)
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5000000000.0) || !(y <= 4.2e+22))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5000000000.0) || ~((y <= 4.2e+22)))
		tmp = ((z / y) + x) - ((x * a) / y);
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5000000000.0], N[Not[LessEqual[y, 4.2e+22]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e9 or 4.1999999999999996e22 < y

   1. Initial program 12.7%

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

   2. Taylor expanded in y around inf 59.2%

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

   if -5e9 < y < 4.1999999999999996e22

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 52.6%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5000000000 \lor \neg \left(y \leq 4.2 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]

Alternative 13: 57.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -550000000 \lor \neg \left(y \leq 8.5 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -550000000.0) (not (<= y 8.5e+22)))
   (- (+ (/ z y) x) (/ a (/ y x)))
   (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -550000000.0) || !(y <= 8.5e+22)) {
		tmp = ((z / y) + x) - (a / (y / x));
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-550000000.0d0)) .or. (.not. (y <= 8.5d+22))) then
        tmp = ((z / y) + x) - (a / (y / x))
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -550000000.0) || !(y <= 8.5e+22)) {
		tmp = ((z / y) + x) - (a / (y / x));
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -550000000.0) or not (y <= 8.5e+22):
		tmp = ((z / y) + x) - (a / (y / x))
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -550000000.0) || !(y <= 8.5e+22))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(a / Float64(y / x)));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -550000000.0) || ~((y <= 8.5e+22)))
		tmp = ((z / y) + x) - (a / (y / x));
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -550000000.0], N[Not[LessEqual[y, 8.5e+22]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5e8 or 8.49999999999999979e22 < y

   1. Initial program 12.7%

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

   2. Taylor expanded in i around 0 11.9%

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

   3. Taylor expanded in c around 0 11.0%

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

   4. Taylor expanded in y around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. associate-/l* 64.6%

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

   6. Simplified 64.6%

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

   if -5.5e8 < y < 8.49999999999999979e22

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 52.6%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -550000000 \lor \neg \left(y \leq 8.5 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]

Alternative 14: 66.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9000000000 \lor \neg \left(y \leq 2.3 \cdot 10^{+53}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -9000000000.0) (not (<= y 2.3e+53)))
   (- (+ (/ z y) x) (/ a (/ y x)))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9000000000.0) || !(y <= 2.3e+53)) {
		tmp = ((z / y) + x) - (a / (y / x));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-9000000000.0d0)) .or. (.not. (y <= 2.3d+53))) then
        tmp = ((z / y) + x) - (a / (y / x))
    else
        tmp = t / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9000000000.0) || !(y <= 2.3e+53)) {
		tmp = ((z / y) + x) - (a / (y / x));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -9000000000.0) or not (y <= 2.3e+53):
		tmp = ((z / y) + x) - (a / (y / x))
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -9000000000.0) || !(y <= 2.3e+53))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(a / Float64(y / x)));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -9000000000.0) || ~((y <= 2.3e+53)))
		tmp = ((z / y) + x) - (a / (y / x));
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -9000000000.0], N[Not[LessEqual[y, 2.3e+53]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e9 or 2.3000000000000002e53 < y

   1. Initial program 11.5%

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

   2. Taylor expanded in i around 0 10.7%

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

   3. Taylor expanded in c around 0 10.6%

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

   4. Taylor expanded in y around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. associate-/l* 67.7%

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

   6. Simplified 67.7%

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

   if -9e9 < y < 2.3000000000000002e53

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0 77.5%

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

      1. *-commutative 77.5%

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

   4. Simplified 77.5%

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

   5. Taylor expanded in y around 0 74.8%

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

      1. *-commutative 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in t around inf 68.8%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9000000000 \lor \neg \left(y \leq 2.3 \cdot 10^{+53}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 15: 49.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -0.18:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.12e+125)
   x
   (if (<= y -0.18)
     (/ x (/ a y))
     (if (<= y 4.8e+22) (/ t i) (- x (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.12e+125) {
		tmp = x;
	} else if (y <= -0.18) {
		tmp = x / (a / y);
	} else if (y <= 4.8e+22) {
		tmp = t / i;
	} else {
		tmp = x - (a / (y / 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 <= (-1.12d+125)) then
        tmp = x
    else if (y <= (-0.18d0)) then
        tmp = x / (a / y)
    else if (y <= 4.8d+22) then
        tmp = t / i
    else
        tmp = x - (a / (y / 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 <= -1.12e+125) {
		tmp = x;
	} else if (y <= -0.18) {
		tmp = x / (a / y);
	} else if (y <= 4.8e+22) {
		tmp = t / i;
	} else {
		tmp = x - (a / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.12e+125:
		tmp = x
	elif y <= -0.18:
		tmp = x / (a / y)
	elif y <= 4.8e+22:
		tmp = t / i
	else:
		tmp = x - (a / (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.12e+125)
		tmp = x;
	elseif (y <= -0.18)
		tmp = Float64(x / Float64(a / y));
	elseif (y <= 4.8e+22)
		tmp = Float64(t / i);
	else
		tmp = Float64(x - Float64(a / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.12e+125)
		tmp = x;
	elseif (y <= -0.18)
		tmp = x / (a / y);
	elseif (y <= 4.8e+22)
		tmp = t / i;
	else
		tmp = x - (a / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.12e+125], x, If[LessEqual[y, -0.18], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+22], N[(t / i), $MachinePrecision], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.12e125

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 68.3%

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

   if -1.12e125 < y < -0.17999999999999999

   1. Initial program 44.0%

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

   2. Taylor expanded in x around inf 24.2%

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

   3. Taylor expanded in a around inf 20.1%

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

      1. associate-/l* 27.3%

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

   5. Simplified 27.3%

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

   if -0.17999999999999999 < y < 4.8e22

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 55.0%

      \[\leadsto \color{blue}{\frac{t}{i}} \]

   if 4.8e22 < y

   1. Initial program 6.6%

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

   2. Taylor expanded in x around inf 0.6%

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

   3. Taylor expanded in y around inf 38.2%

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

      1. mul-1-neg 38.2%

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

      2. unsub-neg 38.2%

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

      3. associate-/l* 46.0%

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

   5. Simplified 46.0%

      \[\leadsto \color{blue}{x - \frac{a}{\frac{y}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -0.18:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 16: 49.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -0.0064:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.12e+125)
   x
   (if (<= y -0.0064) (/ x (/ a y)) (if (<= y 2.65e+20) (/ 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 <= -1.12e+125) {
		tmp = x;
	} else if (y <= -0.0064) {
		tmp = x / (a / y);
	} else if (y <= 2.65e+20) {
		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 <= (-1.12d+125)) then
        tmp = x
    else if (y <= (-0.0064d0)) then
        tmp = x / (a / y)
    else if (y <= 2.65d+20) 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 <= -1.12e+125) {
		tmp = x;
	} else if (y <= -0.0064) {
		tmp = x / (a / y);
	} else if (y <= 2.65e+20) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.12e+125:
		tmp = x
	elif y <= -0.0064:
		tmp = x / (a / y)
	elif y <= 2.65e+20:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.12e+125)
		tmp = x;
	elseif (y <= -0.0064)
		tmp = Float64(x / Float64(a / y));
	elseif (y <= 2.65e+20)
		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 <= -1.12e+125)
		tmp = x;
	elseif (y <= -0.0064)
		tmp = x / (a / y);
	elseif (y <= 2.65e+20)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.12e+125], x, If[LessEqual[y, -0.0064], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e+20], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e125 or 2.65e20 < 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 55.6%

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

   if -1.12e125 < y < -0.00640000000000000031

   1. Initial program 44.0%

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

   2. Taylor expanded in x around inf 24.2%

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

   3. Taylor expanded in a around inf 20.1%

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

      1. associate-/l* 27.3%

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

   5. Simplified 27.3%

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

   if -0.00640000000000000031 < y < 2.65e20

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 55.4%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -0.0064:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 50.1% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.2e+31) x (if (<= y 2.35e+20) (/ 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 <= -3.2e+31) {
		tmp = x;
	} else if (y <= 2.35e+20) {
		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 <= (-3.2d+31)) then
        tmp = x
    else if (y <= 2.35d+20) 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 <= -3.2e+31) {
		tmp = x;
	} else if (y <= 2.35e+20) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.2e+31:
		tmp = x
	elif y <= 2.35e+20:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.2e+31)
		tmp = x;
	elseif (y <= 2.35e+20)
		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 <= -3.2e+31)
		tmp = x;
	elseif (y <= 2.35e+20)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.2e+31], x, If[LessEqual[y, 2.35e+20], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000001e31 or 2.35e20 < y

   1. Initial program 8.3%

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

   2. Taylor expanded in y around inf 47.9%

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

   if -3.2000000000000001e31 < y < 2.35e20

   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 49.9%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 25.7% 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 56.0%

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

2. Taylor expanded in y around inf 23.8%

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

3. Final simplification 23.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023318 
(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)))