Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.4% → 83.8%

Time: 40.2s

Alternatives: 21

Speedup: 2.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.4% 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: 83.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ t_2 := \frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{t\_1}\\ t_3 := z \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{t}{t\_3} + \left(\frac{y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{t\_3} + \frac{{y}^{3}}{t\_1}\right)\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+207}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
        (t_2
         (/
          (+
           t
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)))
          t_1))
        (t_3 (* z t_1)))
   (if (<= t_2 (- INFINITY))
     (*
      z
      (+
       (/ t t_3)
       (+
        (/ (* y (+ 230661.510616 (* y 27464.7644705))) t_3)
        (/ (pow y 3.0) t_1))))
     (if (<= t_2 2e+207)
       (/
        (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
        (fma (fma (fma (+ y a) y b) y c) y i))
       (+ x (/ (+ z (/ 27464.7644705 y)) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / t_1;
	double t_3 = z * t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * ((t / t_3) + (((y * (230661.510616 + (y * 27464.7644705))) / t_3) + (pow(y, 3.0) / t_1)));
	} else if (t_2 <= 2e+207) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((y + a), y, b), y, c), y, i);
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	t_2 = Float64(Float64(t + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616))) / t_1)
	t_3 = Float64(z * t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(t / t_3) + Float64(Float64(Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705))) / t_3) + Float64((y ^ 3.0) / t_1))));
	elseif (t_2 <= 2e+207)
		tmp = Float64(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(y + a), y, b), y, c), y, i));
	else
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t + N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(N[(t / t$95$3), $MachinePrecision] + N[(N[(N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(N[Power[y, 3.0], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+207], N[(N[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 25.8%

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

   3. Taylor expanded in x around 0 25.8%

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

   4. Taylor expanded in z around inf 89.2%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2.0000000000000001e207

   1. Initial program 94.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Step-by-step derivation

      1. fma-define 94.0%

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

      2. fma-define 94.0%

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

      3. fma-define 94.0%

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

      4. fma-define 94.0%

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

      5. fma-define 94.0%

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

      6. fma-define 94.0%

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

      7. fma-define 94.0%

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

   3. Simplified 94.0%

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

   if 2.0000000000000001e207 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 7.2%

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

   3. Taylor expanded in y around -inf 44.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in c around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. associate-*r/ 64.0%

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

   8. Simplified 64.0%

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

   9. Taylor expanded in x around 0 72.6%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 72.6%

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

       2. mul-1-neg 72.6%

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

       3. +-commutative 72.6%

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

       4. associate-*r/ 72.6%

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

       5. metadata-eval 72.6%

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

   11. Simplified 72.6%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{t}{z \cdot \left(y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\right)} + \left(\frac{y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{z \cdot \left(y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\right)} + \frac{{y}^{3}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\right)\right)\\ \mathbf{elif}\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq 2 \cdot 10^{+207}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)\\ t_2 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ t_3 := \frac{t + t\_1}{t\_2}\\ t_4 := z \cdot t\_2\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{t}{t\_4} + \left(\frac{y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{t\_4} + \frac{{y}^{3}}{t\_2}\right)\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+207}:\\ \;\;\;\;\frac{t}{t\_2} + \frac{t\_1}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)))
        (t_2 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
        (t_3 (/ (+ t t_1) t_2))
        (t_4 (* z t_2)))
   (if (<= t_3 (- INFINITY))
     (*
      z
      (+
       (/ t t_4)
       (+
        (/ (* y (+ 230661.510616 (* y 27464.7644705))) t_4)
        (/ (pow y 3.0) t_2))))
     (if (<= t_3 2e+207)
       (+ (/ t t_2) (/ t_1 t_2))
       (+ x (/ (+ z (/ 27464.7644705 y)) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_3 = (t + t_1) / t_2;
	double t_4 = z * t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = z * ((t / t_4) + (((y * (230661.510616 + (y * 27464.7644705))) / t_4) + (pow(y, 3.0) / t_2)));
	} else if (t_3 <= 2e+207) {
		tmp = (t / t_2) + (t_1 / t_2);
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_3 = (t + t_1) / t_2;
	double t_4 = z * t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((t / t_4) + (((y * (230661.510616 + (y * 27464.7644705))) / t_4) + (Math.pow(y, 3.0) / t_2)));
	} else if (t_3 <= 2e+207) {
		tmp = (t / t_2) + (t_1 / t_2);
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)
	t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	t_3 = (t + t_1) / t_2
	t_4 = z * t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = z * ((t / t_4) + (((y * (230661.510616 + (y * 27464.7644705))) / t_4) + (math.pow(y, 3.0) / t_2)))
	elif t_3 <= 2e+207:
		tmp = (t / t_2) + (t_1 / t_2)
	else:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616))
	t_2 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	t_3 = Float64(Float64(t + t_1) / t_2)
	t_4 = Float64(z * t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(t / t_4) + Float64(Float64(Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705))) / t_4) + Float64((y ^ 3.0) / t_2))));
	elseif (t_3 <= 2e+207)
		tmp = Float64(Float64(t / t_2) + Float64(t_1 / t_2));
	else
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	t_3 = (t + t_1) / t_2;
	t_4 = z * t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = z * ((t / t_4) + (((y * (230661.510616 + (y * 27464.7644705))) / t_4) + ((y ^ 3.0) / t_2)));
	elseif (t_3 <= 2e+207)
		tmp = (t / t_2) + (t_1 / t_2);
	else
		tmp = x + ((z + (27464.7644705 / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(z * t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(z * N[(N[(t / t$95$4), $MachinePrecision] + N[(N[(N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision] + N[(N[Power[y, 3.0], $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+207], N[(N[(t / t$95$2), $MachinePrecision] + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 25.8%

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

   3. Taylor expanded in x around 0 25.8%

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

   4. Taylor expanded in z around inf 89.2%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2.0000000000000001e207

   1. Initial program 94.0%

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

   3. Taylor expanded in t around 0 94.0%

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

   if 2.0000000000000001e207 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 7.2%

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

   3. Taylor expanded in y around -inf 44.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in c around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. associate-*r/ 64.0%

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

   8. Simplified 64.0%

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

   9. Taylor expanded in x around 0 72.6%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 72.6%

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

       2. mul-1-neg 72.6%

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

       3. +-commutative 72.6%

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

       4. associate-*r/ 72.6%

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

       5. metadata-eval 72.6%

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

   11. Simplified 72.6%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{t}{z \cdot \left(y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\right)} + \left(\frac{y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{z \cdot \left(y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\right)} + \frac{{y}^{3}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\right)\right)\\ \mathbf{elif}\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq 2 \cdot 10^{+207}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ t_2 := y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)\\ \mathbf{if}\;\frac{t + t\_2}{t\_1} \leq 2 \cdot 10^{+207}:\\ \;\;\;\;\frac{t}{t\_1} + \frac{t\_2}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
        (t_2
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))))
   (if (<= (/ (+ t t_2) t_1) 2e+207)
     (+ (/ t t_1) (/ t_2 t_1))
     (+ x (/ (+ z (/ 27464.7644705 y)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double tmp;
	if (((t + t_2) / t_1) <= 2e+207) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)
    if (((t + t_2) / t_1) <= 2d+207) then
        tmp = (t / t_1) + (t_2 / t_1)
    else
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double tmp;
	if (((t + t_2) / t_1) <= 2e+207) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)
	tmp = 0
	if ((t + t_2) / t_1) <= 2e+207:
		tmp = (t / t_1) + (t_2 / t_1)
	else:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	t_2 = Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616))
	tmp = 0.0
	if (Float64(Float64(t + t_2) / t_1) <= 2e+207)
		tmp = Float64(Float64(t / t_1) + Float64(t_2 / t_1));
	else
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	tmp = 0.0;
	if (((t + t_2) / t_1) <= 2e+207)
		tmp = (t / t_1) + (t_2 / t_1);
	else
		tmp = x + ((z + (27464.7644705 / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], 2e+207], N[(N[(t / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2.0000000000000001e207

   1. Initial program 89.7%

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

   3. Taylor expanded in t around 0 89.7%

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

   if 2.0000000000000001e207 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 7.2%

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

   3. Taylor expanded in y around -inf 44.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in c around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. associate-*r/ 64.0%

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

   8. Simplified 64.0%

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

   9. Taylor expanded in x around 0 72.6%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 72.6%

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

       2. mul-1-neg 72.6%

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

       3. +-commutative 72.6%

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

       4. associate-*r/ 72.6%

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

       5. metadata-eval 72.6%

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

   11. Simplified 72.6%

       \[\leadsto x + \left(-\color{blue}{\frac{-\left(\frac{27464.7644705}{y} + z\right)}{y}}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq 2 \cdot 10^{+207}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           t
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)))
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))
   (if (<= t_1 2e+207) t_1 (+ x (/ (+ z (/ 27464.7644705 y)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	double tmp;
	if (t_1 <= 2e+207) {
		tmp = t_1;
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    if (t_1 <= 2d+207) then
        tmp = t_1
    else
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	double tmp;
	if (t_1 <= 2e+207) {
		tmp = t_1;
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	tmp = 0
	if t_1 <= 2e+207:
		tmp = t_1
	else:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i))
	tmp = 0.0
	if (t_1 <= 2e+207)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	tmp = 0.0;
	if (t_1 <= 2e+207)
		tmp = t_1;
	else
		tmp = x + ((z + (27464.7644705 / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+207], t$95$1, N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2.0000000000000001e207

   1. Initial program 89.7%

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

   if 2.0000000000000001e207 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 7.2%

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

   3. Taylor expanded in y around -inf 44.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in c around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. associate-*r/ 64.0%

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

   8. Simplified 64.0%

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

   9. Taylor expanded in x around 0 72.6%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 72.6%

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

       2. mul-1-neg 72.6%

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

       3. +-commutative 72.6%

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

       4. associate-*r/ 72.6%

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

       5. metadata-eval 72.6%

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

   11. Simplified 72.6%

       \[\leadsto x + \left(-\color{blue}{\frac{-\left(\frac{27464.7644705}{y} + z\right)}{y}}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq 2 \cdot 10^{+207}:\\ \;\;\;\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-77}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{t\_1}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(\frac{1}{t\_1} + \frac{x}{t}\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<= y -3.4e+54)
     (+ x (/ (+ z (/ 27464.7644705 y)) y))
     (if (<= y -7e-77)
       (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) t_1)
       (if (<= y 5.2e-27)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y (+ c (* y b)))))
         (if (<= y 3.4e-21)
           (* t (+ (/ 1.0 t_1) (/ x t)))
           (if (<= y 1.75e+26)
             (/
              (+
               t
               (*
                y
                (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)))
              (* y c))
             (+ x (- (/ z y) (* a (/ x y)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -3.4e+54) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -7e-77) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / t_1;
	} else if (y <= 5.2e-27) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else if (y <= 3.4e-21) {
		tmp = t * ((1.0 / t_1) + (x / t));
	} else if (y <= 1.75e+26) {
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / (y * c);
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    if (y <= (-3.4d+54)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= (-7d-77)) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / t_1
    else if (y <= 5.2d-27) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    else if (y <= 3.4d-21) then
        tmp = t * ((1.0d0 / t_1) + (x / t))
    else if (y <= 1.75d+26) then
        tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0))) / (y * c)
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -3.4e+54) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -7e-77) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / t_1;
	} else if (y <= 5.2e-27) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else if (y <= 3.4e-21) {
		tmp = t * ((1.0 / t_1) + (x / t));
	} else if (y <= 1.75e+26) {
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / (y * c);
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if y <= -3.4e+54:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= -7e-77:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / t_1
	elif y <= 5.2e-27:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	elif y <= 3.4e-21:
		tmp = t * ((1.0 / t_1) + (x / t))
	elif y <= 1.75e+26:
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / (y * c)
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (y <= -3.4e+54)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= -7e-77)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / t_1);
	elseif (y <= 5.2e-27)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 3.4e-21)
		tmp = Float64(t * Float64(Float64(1.0 / t_1) + Float64(x / t)));
	elseif (y <= 1.75e+26)
		tmp = Float64(Float64(t + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616))) / Float64(y * c));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if (y <= -3.4e+54)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= -7e-77)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / t_1;
	elseif (y <= 5.2e-27)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	elseif (y <= 3.4e-21)
		tmp = t * ((1.0 / t_1) + (x / t));
	elseif (y <= 1.75e+26)
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / (y * c);
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -3.4e+54], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-77], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 5.2e-27], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-21], N[(t * N[(N[(1.0 / t$95$1), $MachinePrecision] + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+26], N[(N[(t + N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.4000000000000001e54

   1. Initial program 3.8%

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

   3. Taylor expanded in y around -inf 53.2%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in c around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-*r/ 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in x around 0 77.3%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 77.3%

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

       2. mul-1-neg 77.3%

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

       3. +-commutative 77.3%

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

       4. associate-*r/ 77.3%

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

       5. metadata-eval 77.3%

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

   11. Simplified 77.3%

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

   if -3.4000000000000001e54 < y < -7.00000000000000026e-77

   1. Initial program 69.0%

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

   3. Taylor expanded in y around 0 53.9%

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

      1. *-commutative 53.9%

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

   5. Simplified 53.9%

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

   if -7.00000000000000026e-77 < y < 5.20000000000000034e-27

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 98.9%

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

   4. Taylor expanded in y around 0 98.0%

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

   if 5.20000000000000034e-27 < y < 3.4e-21

   1. Initial program 98.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Step-by-step derivation

      1. fma-define 98.4%

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

      2. fma-define 98.4%

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

      3. fma-define 98.4%

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

      4. fma-define 98.4%

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

      5. fma-define 98.4%

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

      6. fma-define 99.2%

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

      7. fma-define 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around inf 99.2%

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

   6. Taylor expanded in t around inf 99.2%

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

      1. times-frac 99.2%

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

   8. Simplified 99.2%

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

   9. Taylor expanded in y around inf 53.4%

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

   if 3.4e-21 < y < 1.75e26

   1. Initial program 85.6%

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

   3. Taylor expanded in c around inf 72.4%

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

   if 1.75e26 < y

   1. Initial program 7.1%

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

   3. Taylor expanded in y around inf 58.2%

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

      1. associate--l+ 58.2%

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

      2. associate-/l* 64.2%

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

   5. Simplified 64.2%

      \[\leadsto \color{blue}{x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-77}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(\frac{1}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \frac{x}{t}\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.68 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.68e+56)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 1.3e+40)
     (/
      (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
      (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
     (+ x (- (/ z y) (* a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.68e+56) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 1.3e+40) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.68d+56)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 1.3d+40) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.68e+56) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 1.3e+40) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.68e+56:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 1.3e+40:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.68e+56)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 1.3e+40)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.68e+56)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 1.3e+40)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.68e+56], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+40], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.68e56

   1. Initial program 3.8%

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

   3. Taylor expanded in y around -inf 53.2%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in c around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-*r/ 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in x around 0 77.3%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 77.3%

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

       2. mul-1-neg 77.3%

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

       3. +-commutative 77.3%

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

       4. associate-*r/ 77.3%

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

       5. metadata-eval 77.3%

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

   11. Simplified 77.3%

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

   if -1.68e56 < y < 1.3e40

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0 91.5%

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

   if 1.3e40 < y

   1. Initial program 4.2%

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

   3. Taylor expanded in y around inf 60.8%

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

      1. associate--l+ 60.8%

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

      2. associate-/l* 67.1%

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

   5. Simplified 67.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.68 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{i}\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+84} \lor \neg \left(y \leq 9.2 \cdot 10^{+161}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (+ t (* y 230661.510616)) i)) (t_2 (+ x (/ z y))))
   (if (<= y -3.4e+54)
     t_2
     (if (<= y -5.8e-125)
       t_1
       (if (<= y -1.6e-146)
         (* (/ t c) (/ 1.0 y))
         (if (<= y 9.8e+45)
           t_1
           (if (or (<= y 1.7e+84) (not (<= y 9.2e+161)))
             t_2
             (- x (* a (/ x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -3.4e+54) {
		tmp = t_2;
	} else if (y <= -5.8e-125) {
		tmp = t_1;
	} else if (y <= -1.6e-146) {
		tmp = (t / c) * (1.0 / y);
	} else if (y <= 9.8e+45) {
		tmp = t_1;
	} else if ((y <= 1.7e+84) || !(y <= 9.2e+161)) {
		tmp = t_2;
	} else {
		tmp = x - (a * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t + (y * 230661.510616d0)) / i
    t_2 = x + (z / y)
    if (y <= (-3.4d+54)) then
        tmp = t_2
    else if (y <= (-5.8d-125)) then
        tmp = t_1
    else if (y <= (-1.6d-146)) then
        tmp = (t / c) * (1.0d0 / y)
    else if (y <= 9.8d+45) then
        tmp = t_1
    else if ((y <= 1.7d+84) .or. (.not. (y <= 9.2d+161))) then
        tmp = t_2
    else
        tmp = x - (a * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -3.4e+54) {
		tmp = t_2;
	} else if (y <= -5.8e-125) {
		tmp = t_1;
	} else if (y <= -1.6e-146) {
		tmp = (t / c) * (1.0 / y);
	} else if (y <= 9.8e+45) {
		tmp = t_1;
	} else if ((y <= 1.7e+84) || !(y <= 9.2e+161)) {
		tmp = t_2;
	} else {
		tmp = x - (a * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * 230661.510616)) / i
	t_2 = x + (z / y)
	tmp = 0
	if y <= -3.4e+54:
		tmp = t_2
	elif y <= -5.8e-125:
		tmp = t_1
	elif y <= -1.6e-146:
		tmp = (t / c) * (1.0 / y)
	elif y <= 9.8e+45:
		tmp = t_1
	elif (y <= 1.7e+84) or not (y <= 9.2e+161):
		tmp = t_2
	else:
		tmp = x - (a * (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * 230661.510616)) / i)
	t_2 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -3.4e+54)
		tmp = t_2;
	elseif (y <= -5.8e-125)
		tmp = t_1;
	elseif (y <= -1.6e-146)
		tmp = Float64(Float64(t / c) * Float64(1.0 / y));
	elseif (y <= 9.8e+45)
		tmp = t_1;
	elseif ((y <= 1.7e+84) || !(y <= 9.2e+161))
		tmp = t_2;
	else
		tmp = Float64(x - Float64(a * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * 230661.510616)) / i;
	t_2 = x + (z / y);
	tmp = 0.0;
	if (y <= -3.4e+54)
		tmp = t_2;
	elseif (y <= -5.8e-125)
		tmp = t_1;
	elseif (y <= -1.6e-146)
		tmp = (t / c) * (1.0 / y);
	elseif (y <= 9.8e+45)
		tmp = t_1;
	elseif ((y <= 1.7e+84) || ~((y <= 9.2e+161)))
		tmp = t_2;
	else
		tmp = x - (a * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+54], t$95$2, If[LessEqual[y, -5.8e-125], t$95$1, If[LessEqual[y, -1.6e-146], N[(N[(t / c), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+45], t$95$1, If[Or[LessEqual[y, 1.7e+84], N[Not[LessEqual[y, 9.2e+161]], $MachinePrecision]], t$95$2, N[(x - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4000000000000001e54 or 9.8000000000000004e45 < y < 1.6999999999999999e84 or 9.1999999999999997e161 < y

   1. Initial program 3.6%

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

   3. Taylor expanded in y around -inf 52.3%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in c around inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. associate-*r/ 71.4%

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

   8. Simplified 71.4%

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

   9. Taylor expanded in z around inf 78.6%

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

       1. associate-*r/ 78.6%

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

       2. mul-1-neg 78.6%

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

   11. Simplified 78.6%

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

   if -3.4000000000000001e54 < y < -5.8000000000000004e-125 or -1.6e-146 < y < 9.8000000000000004e45

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 82.6%

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

      1. *-commutative 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in i around inf 55.2%

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

   if -5.8000000000000004e-125 < y < -1.6e-146

   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. Step-by-step derivation

      1. fma-define 99.7%

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

      2. fma-define 99.7%

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

      3. fma-define 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 99.4%

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

   6. Taylor expanded in c around inf 79.9%

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

      1. times-frac 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in y around 0 80.6%

      \[\leadsto \frac{t}{c} \cdot \color{blue}{\frac{1}{y}} \]

   if 1.6999999999999999e84 < y < 9.1999999999999997e161

   1. Initial program 1.1%

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

   3. Taylor expanded in y around -inf 25.1%

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

   5. Simplified 29.8%

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

   6. Taylor expanded in c around inf 34.3%

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

      1. mul-1-neg 34.3%

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

      2. associate-*r/ 39.5%

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

   8. Simplified 39.5%

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

   9. Taylor expanded in a around inf 40.0%

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

       1. associate-/l* 44.9%

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

   11. Simplified 44.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+84} \lor \neg \left(y \leq 9.2 \cdot 10^{+161}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(\frac{1}{i} + y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t \cdot i}\right)\\ \mathbf{elif}\;y \leq 240000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4e+54)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y -2.1e-55)
     (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
     (if (<= y -9.5e-95)
       (*
        t
        (+
         (/ 1.0 i)
         (* y (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) (* t i)))))
       (if (<= y 240000000000.0)
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
         (+ x (- (/ z y) (* a (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4e+54) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -2.1e-55) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= -9.5e-95) {
		tmp = t * ((1.0 / i) + (y * ((230661.510616 + (y * (27464.7644705 + (y * z)))) / (t * i))));
	} else if (y <= 240000000000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4d+54)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= (-2.1d-55)) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= (-9.5d-95)) then
        tmp = t * ((1.0d0 / i) + (y * ((230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / (t * i))))
    else if (y <= 240000000000.0d0) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4e+54) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -2.1e-55) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= -9.5e-95) {
		tmp = t * ((1.0 / i) + (y * ((230661.510616 + (y * (27464.7644705 + (y * z)))) / (t * i))));
	} else if (y <= 240000000000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4e+54:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= -2.1e-55:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= -9.5e-95:
		tmp = t * ((1.0 / i) + (y * ((230661.510616 + (y * (27464.7644705 + (y * z)))) / (t * i))))
	elif y <= 240000000000.0:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4e+54)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= -2.1e-55)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= -9.5e-95)
		tmp = Float64(t * Float64(Float64(1.0 / i) + Float64(y * Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / Float64(t * i)))));
	elseif (y <= 240000000000.0)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4e+54)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= -2.1e-55)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= -9.5e-95)
		tmp = t * ((1.0 / i) + (y * ((230661.510616 + (y * (27464.7644705 + (y * z)))) / (t * i))));
	elseif (y <= 240000000000.0)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4e+54], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-55], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-95], N[(t * N[(N[(1.0 / i), $MachinePrecision] + N[(y * N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 240000000000.0], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.0000000000000003e54

   1. Initial program 3.8%

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

   3. Taylor expanded in y around -inf 53.2%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in c around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-*r/ 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in x around 0 77.3%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 77.3%

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

       2. mul-1-neg 77.3%

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

       3. +-commutative 77.3%

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

       4. associate-*r/ 77.3%

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

       5. metadata-eval 77.3%

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

   11. Simplified 77.3%

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

   if -4.0000000000000003e54 < y < -2.1000000000000002e-55

   1. Initial program 63.3%

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

   3. Taylor expanded in t around inf 33.1%

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

   if -2.1000000000000002e-55 < y < -9.49999999999999998e-95

   1. Initial program 99.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Step-by-step derivation

      1. fma-define 99.1%

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

      2. fma-define 99.1%

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

      3. fma-define 99.1%

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

      4. fma-define 99.1%

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

      5. fma-define 99.1%

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

      6. fma-define 99.1%

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

      7. fma-define 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf 99.0%

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

   6. Taylor expanded in t around inf 98.9%

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

      1. times-frac 98.4%

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

   8. Simplified 98.4%

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

   9. Taylor expanded in i around inf 66.6%

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

   10. Taylor expanded in i around inf 66.6%

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

   11. Taylor expanded in x around 0 66.9%

       \[\leadsto t \cdot \left(\frac{1}{i} + \color{blue}{\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i \cdot t}}\right) \]
   12. Step-by-step derivation

       1. associate-/l* 67.4%

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

   13. Simplified 67.4%

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

   if -9.49999999999999998e-95 < y < 2.4e11

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 95.2%

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

      1. *-commutative 95.2%

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

   5. Simplified 95.2%

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

   6. Taylor expanded in y around 0 93.4%

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

   if 2.4e11 < y

   1. Initial program 11.1%

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

   3. Taylor expanded in y around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. associate-/l* 60.7%

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

   5. Simplified 60.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(\frac{1}{i} + y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t \cdot i}\right)\\ \mathbf{elif}\;y \leq 240000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{i}\\ \mathbf{elif}\;y \leq 140000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.7e+57)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y -3.15e-55)
     (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
     (if (<= y -9.5e-95)
       (/
        (+
         t
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)))
        i)
       (if (<= y 140000000000.0)
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
         (+ x (- (/ z y) (* a (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.7e+57) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -3.15e-55) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= -9.5e-95) {
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / i;
	} else if (y <= 140000000000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.7d+57)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= (-3.15d-55)) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= (-9.5d-95)) then
        tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0))) / i
    else if (y <= 140000000000.0d0) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.7e+57) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -3.15e-55) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= -9.5e-95) {
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / i;
	} else if (y <= 140000000000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.7e+57:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= -3.15e-55:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= -9.5e-95:
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / i
	elif y <= 140000000000.0:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.7e+57)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= -3.15e-55)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= -9.5e-95)
		tmp = Float64(Float64(t + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616))) / i);
	elseif (y <= 140000000000.0)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.7e+57)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= -3.15e-55)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= -9.5e-95)
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / i;
	elseif (y <= 140000000000.0)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.7e+57], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.15e-55], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-95], N[(N[(t + N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 140000000000.0], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.69999999999999996e57

   1. Initial program 3.8%

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

   3. Taylor expanded in y around -inf 53.2%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in c around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-*r/ 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in x around 0 77.3%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 77.3%

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

       2. mul-1-neg 77.3%

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

       3. +-commutative 77.3%

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

       4. associate-*r/ 77.3%

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

       5. metadata-eval 77.3%

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

   11. Simplified 77.3%

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

   if -1.69999999999999996e57 < y < -3.1499999999999999e-55

   1. Initial program 63.3%

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

   3. Taylor expanded in t around inf 33.1%

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

   if -3.1499999999999999e-55 < y < -9.49999999999999998e-95

   1. Initial program 99.0%

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

   3. Taylor expanded in i around inf 67.3%

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

   if -9.49999999999999998e-95 < y < 1.4e11

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 95.2%

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

      1. *-commutative 95.2%

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

   5. Simplified 95.2%

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

   6. Taylor expanded in y around 0 93.4%

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

   if 1.4e11 < y

   1. Initial program 11.1%

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

   3. Taylor expanded in y around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. associate-/l* 60.7%

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

   5. Simplified 60.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{i}\\ \mathbf{elif}\;y \leq 140000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{elif}\;y \leq 240000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.8e+54)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y -1.85e-55)
     (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
     (if (<= y -9.5e-95)
       (/ (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))) i)
       (if (<= y 240000000000.0)
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
         (+ x (- (/ z y) (* a (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.8e+54) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -1.85e-55) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= -9.5e-95) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	} else if (y <= 240000000000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.8d+54)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= (-1.85d-55)) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= (-9.5d-95)) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / i
    else if (y <= 240000000000.0d0) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.8e+54) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -1.85e-55) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= -9.5e-95) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	} else if (y <= 240000000000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.8e+54:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= -1.85e-55:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= -9.5e-95:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i
	elif y <= 240000000000.0:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.8e+54)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= -1.85e-55)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= -9.5e-95)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / i);
	elseif (y <= 240000000000.0)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.8e+54)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= -1.85e-55)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= -9.5e-95)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	elseif (y <= 240000000000.0)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.8e+54], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-55], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-95], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 240000000000.0], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.8000000000000002e54

   1. Initial program 3.8%

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

   3. Taylor expanded in y around -inf 53.2%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in c around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-*r/ 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in x around 0 77.3%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 77.3%

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

       2. mul-1-neg 77.3%

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

       3. +-commutative 77.3%

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

       4. associate-*r/ 77.3%

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

       5. metadata-eval 77.3%

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

   11. Simplified 77.3%

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

   if -3.8000000000000002e54 < y < -1.84999999999999993e-55

   1. Initial program 63.3%

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

   3. Taylor expanded in t around inf 33.1%

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

   if -1.84999999999999993e-55 < y < -9.49999999999999998e-95

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 99.0%

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

   4. Taylor expanded in i around inf 67.3%

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

   if -9.49999999999999998e-95 < y < 2.4e11

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 95.2%

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

      1. *-commutative 95.2%

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

   5. Simplified 95.2%

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

   6. Taylor expanded in y around 0 93.4%

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

   if 2.4e11 < y

   1. Initial program 11.1%

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

   3. Taylor expanded in y around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. associate-/l* 60.7%

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

   5. Simplified 60.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{elif}\;y \leq 240000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+65}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.1e+65)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 1.4e+36)
     (/
      (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
      (+ i (* y (+ c (* y b)))))
     (+ x (- (/ z y) (* a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.1e+65) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 1.4e+36) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.1d+65)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 1.4d+36) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.1e+65) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 1.4e+36) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.1e+65:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 1.4e+36:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.1e+65)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 1.4e+36)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.1e+65)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 1.4e+36)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.1e+65], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+36], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999991e65

   1. Initial program 3.8%

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

   3. Taylor expanded in y around -inf 52.4%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in c around inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. associate-*r/ 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in x around 0 76.9%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 76.9%

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

       2. mul-1-neg 76.9%

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

       3. +-commutative 76.9%

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

       4. associate-*r/ 76.9%

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

       5. metadata-eval 76.9%

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

   11. Simplified 76.9%

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

   if -2.09999999999999991e65 < y < 1.4e36

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 90.9%

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

   4. Taylor expanded in y around 0 85.3%

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

   if 1.4e36 < y

   1. Initial program 4.2%

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

   3. Taylor expanded in y around inf 60.8%

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

      1. associate--l+ 60.8%

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

      2. associate-/l* 67.1%

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

   5. Simplified 67.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+65}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{i}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (+ t (* y 230661.510616)) i)))
   (if (<= y -3.4e+54)
     (+ x (/ (+ z (/ 27464.7644705 y)) y))
     (if (<= y -5.8e-125)
       t_1
       (if (<= y -1.6e-146)
         (* (/ t c) (/ 1.0 y))
         (if (<= y 1.9e-74) t_1 (+ x (- (/ z y) (* a (/ x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double tmp;
	if (y <= -3.4e+54) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -5.8e-125) {
		tmp = t_1;
	} else if (y <= -1.6e-146) {
		tmp = (t / c) * (1.0 / y);
	} else if (y <= 1.9e-74) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t + (y * 230661.510616d0)) / i
    if (y <= (-3.4d+54)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= (-5.8d-125)) then
        tmp = t_1
    else if (y <= (-1.6d-146)) then
        tmp = (t / c) * (1.0d0 / y)
    else if (y <= 1.9d-74) then
        tmp = t_1
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double tmp;
	if (y <= -3.4e+54) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -5.8e-125) {
		tmp = t_1;
	} else if (y <= -1.6e-146) {
		tmp = (t / c) * (1.0 / y);
	} else if (y <= 1.9e-74) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * 230661.510616)) / i
	tmp = 0
	if y <= -3.4e+54:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= -5.8e-125:
		tmp = t_1
	elif y <= -1.6e-146:
		tmp = (t / c) * (1.0 / y)
	elif y <= 1.9e-74:
		tmp = t_1
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * 230661.510616)) / i)
	tmp = 0.0
	if (y <= -3.4e+54)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= -5.8e-125)
		tmp = t_1;
	elseif (y <= -1.6e-146)
		tmp = Float64(Float64(t / c) * Float64(1.0 / y));
	elseif (y <= 1.9e-74)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * 230661.510616)) / i;
	tmp = 0.0;
	if (y <= -3.4e+54)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= -5.8e-125)
		tmp = t_1;
	elseif (y <= -1.6e-146)
		tmp = (t / c) * (1.0 / y);
	elseif (y <= 1.9e-74)
		tmp = t_1;
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]}, If[LessEqual[y, -3.4e+54], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-125], t$95$1, If[LessEqual[y, -1.6e-146], N[(N[(t / c), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-74], t$95$1, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4000000000000001e54

   1. Initial program 3.8%

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

   3. Taylor expanded in y around -inf 53.2%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in c around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-*r/ 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in x around 0 77.3%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 77.3%

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

       2. mul-1-neg 77.3%

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

       3. +-commutative 77.3%

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

       4. associate-*r/ 77.3%

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

       5. metadata-eval 77.3%

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

   11. Simplified 77.3%

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

   if -3.4000000000000001e54 < y < -5.8000000000000004e-125 or -1.6e-146 < y < 1.8999999999999998e-74

   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. Add Preprocessing

   3. Taylor expanded in y around 0 88.9%

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

      1. *-commutative 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in i around inf 62.4%

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

   if -5.8000000000000004e-125 < y < -1.6e-146

   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. Step-by-step derivation

      1. fma-define 99.7%

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

      2. fma-define 99.7%

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

      3. fma-define 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 99.4%

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

   6. Taylor expanded in c around inf 79.9%

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

      1. times-frac 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in y around 0 80.6%

      \[\leadsto \frac{t}{c} \cdot \color{blue}{\frac{1}{y}} \]

   if 1.8999999999999998e-74 < y

   1. Initial program 24.1%

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

   3. Taylor expanded in y around inf 47.1%

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

      1. associate--l+ 47.1%

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

      2. associate-/l* 51.9%

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

   5. Simplified 51.9%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-74}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 240000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.05e+74)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 240000000000.0)
     (/ (+ t (* y 230661.510616)) (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
     (+ x (- (/ z y) (* a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.05e+74) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 240000000000.0) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.05d+74)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 240000000000.0d0) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.05e+74) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 240000000000.0) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.05e+74:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 240000000000.0:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.05e+74)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 240000000000.0)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.05e+74)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 240000000000.0)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.05e+74], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 240000000000.0], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e74

   1. Initial program 2.0%

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

   3. Taylor expanded in y around -inf 54.5%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in c around inf 74.4%

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

      1. mul-1-neg 74.4%

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

      2. associate-*r/ 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in x around 0 80.9%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 80.9%

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

       2. mul-1-neg 80.9%

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

       3. +-commutative 80.9%

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

       4. associate-*r/ 80.9%

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

       5. metadata-eval 80.9%

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

   11. Simplified 80.9%

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

   if -2.05e74 < y < 2.4e11

   1. Initial program 92.6%

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

   3. Taylor expanded in y around 0 83.5%

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

      1. *-commutative 83.5%

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

   5. Simplified 83.5%

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

   if 2.4e11 < y

   1. Initial program 11.1%

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

   3. Taylor expanded in y around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. associate-/l* 60.7%

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

   5. Simplified 60.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 240000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{i}\\ t_2 := x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (+ t (* y 230661.510616)) i))
        (t_2 (+ x (/ (+ z (/ 27464.7644705 y)) y))))
   (if (<= y -3.4e+54)
     t_2
     (if (<= y -5.8e-125)
       t_1
       (if (<= y -1.6e-146)
         (* (/ t c) (/ 1.0 y))
         (if (<= y 1.9e-74) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double t_2 = x + ((z + (27464.7644705 / y)) / y);
	double tmp;
	if (y <= -3.4e+54) {
		tmp = t_2;
	} else if (y <= -5.8e-125) {
		tmp = t_1;
	} else if (y <= -1.6e-146) {
		tmp = (t / c) * (1.0 / y);
	} else if (y <= 1.9e-74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t + (y * 230661.510616d0)) / i
    t_2 = x + ((z + (27464.7644705d0 / y)) / y)
    if (y <= (-3.4d+54)) then
        tmp = t_2
    else if (y <= (-5.8d-125)) then
        tmp = t_1
    else if (y <= (-1.6d-146)) then
        tmp = (t / c) * (1.0d0 / y)
    else if (y <= 1.9d-74) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double t_2 = x + ((z + (27464.7644705 / y)) / y);
	double tmp;
	if (y <= -3.4e+54) {
		tmp = t_2;
	} else if (y <= -5.8e-125) {
		tmp = t_1;
	} else if (y <= -1.6e-146) {
		tmp = (t / c) * (1.0 / y);
	} else if (y <= 1.9e-74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * 230661.510616)) / i
	t_2 = x + ((z + (27464.7644705 / y)) / y)
	tmp = 0
	if y <= -3.4e+54:
		tmp = t_2
	elif y <= -5.8e-125:
		tmp = t_1
	elif y <= -1.6e-146:
		tmp = (t / c) * (1.0 / y)
	elif y <= 1.9e-74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * 230661.510616)) / i)
	t_2 = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y))
	tmp = 0.0
	if (y <= -3.4e+54)
		tmp = t_2;
	elseif (y <= -5.8e-125)
		tmp = t_1;
	elseif (y <= -1.6e-146)
		tmp = Float64(Float64(t / c) * Float64(1.0 / y));
	elseif (y <= 1.9e-74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * 230661.510616)) / i;
	t_2 = x + ((z + (27464.7644705 / y)) / y);
	tmp = 0.0;
	if (y <= -3.4e+54)
		tmp = t_2;
	elseif (y <= -5.8e-125)
		tmp = t_1;
	elseif (y <= -1.6e-146)
		tmp = (t / c) * (1.0 / y);
	elseif (y <= 1.9e-74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+54], t$95$2, If[LessEqual[y, -5.8e-125], t$95$1, If[LessEqual[y, -1.6e-146], N[(N[(t / c), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-74], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4000000000000001e54 or 1.8999999999999998e-74 < y

   1. Initial program 15.9%

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

   3. Taylor expanded in y around -inf 40.6%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in c around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. associate-*r/ 56.2%

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

   8. Simplified 56.2%

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

   9. Taylor expanded in x around 0 62.1%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 62.1%

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

       2. mul-1-neg 62.1%

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

       3. +-commutative 62.1%

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

       4. associate-*r/ 62.1%

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

       5. metadata-eval 62.1%

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

   11. Simplified 62.1%

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

   if -3.4000000000000001e54 < y < -5.8000000000000004e-125 or -1.6e-146 < y < 1.8999999999999998e-74

   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. Add Preprocessing

   3. Taylor expanded in y around 0 88.9%

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

      1. *-commutative 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in i around inf 62.4%

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

   if -5.8000000000000004e-125 < y < -1.6e-146

   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. Step-by-step derivation

      1. fma-define 99.7%

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

      2. fma-define 99.7%

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

      3. fma-define 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 99.4%

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

   6. Taylor expanded in c around inf 79.9%

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

      1. times-frac 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in y around 0 80.6%

      \[\leadsto \frac{t}{c} \cdot \color{blue}{\frac{1}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-74}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{i}\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (+ t (* y 230661.510616)) i)) (t_2 (+ x (/ z y))))
   (if (<= y -3.4e+54)
     t_2
     (if (<= y -5.8e-125)
       t_1
       (if (<= y -1.6e-146)
         (* (/ t c) (/ 1.0 y))
         (if (<= y 1.9e-109) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -3.4e+54) {
		tmp = t_2;
	} else if (y <= -5.8e-125) {
		tmp = t_1;
	} else if (y <= -1.6e-146) {
		tmp = (t / c) * (1.0 / y);
	} else if (y <= 1.9e-109) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t + (y * 230661.510616d0)) / i
    t_2 = x + (z / y)
    if (y <= (-3.4d+54)) then
        tmp = t_2
    else if (y <= (-5.8d-125)) then
        tmp = t_1
    else if (y <= (-1.6d-146)) then
        tmp = (t / c) * (1.0d0 / y)
    else if (y <= 1.9d-109) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -3.4e+54) {
		tmp = t_2;
	} else if (y <= -5.8e-125) {
		tmp = t_1;
	} else if (y <= -1.6e-146) {
		tmp = (t / c) * (1.0 / y);
	} else if (y <= 1.9e-109) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * 230661.510616)) / i
	t_2 = x + (z / y)
	tmp = 0
	if y <= -3.4e+54:
		tmp = t_2
	elif y <= -5.8e-125:
		tmp = t_1
	elif y <= -1.6e-146:
		tmp = (t / c) * (1.0 / y)
	elif y <= 1.9e-109:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * 230661.510616)) / i)
	t_2 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -3.4e+54)
		tmp = t_2;
	elseif (y <= -5.8e-125)
		tmp = t_1;
	elseif (y <= -1.6e-146)
		tmp = Float64(Float64(t / c) * Float64(1.0 / y));
	elseif (y <= 1.9e-109)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * 230661.510616)) / i;
	t_2 = x + (z / y);
	tmp = 0.0;
	if (y <= -3.4e+54)
		tmp = t_2;
	elseif (y <= -5.8e-125)
		tmp = t_1;
	elseif (y <= -1.6e-146)
		tmp = (t / c) * (1.0 / y);
	elseif (y <= 1.9e-109)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+54], t$95$2, If[LessEqual[y, -5.8e-125], t$95$1, If[LessEqual[y, -1.6e-146], N[(N[(t / c), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-109], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4000000000000001e54 or 1.90000000000000001e-109 < y

   1. Initial program 20.6%

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

   3. Taylor expanded in y around -inf 38.4%

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

   5. Simplified 43.2%

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

   6. Taylor expanded in c around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-*r/ 53.9%

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

   8. Simplified 53.9%

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

   9. Taylor expanded in z around inf 59.5%

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

       1. associate-*r/ 59.5%

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

       2. mul-1-neg 59.5%

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

   11. Simplified 59.5%

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

   if -3.4000000000000001e54 < y < -5.8000000000000004e-125 or -1.6e-146 < y < 1.90000000000000001e-109

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0 88.1%

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

      1. *-commutative 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in i around inf 64.2%

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

   if -5.8000000000000004e-125 < y < -1.6e-146

   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. Step-by-step derivation

      1. fma-define 99.7%

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

      2. fma-define 99.7%

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

      3. fma-define 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 99.4%

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

   6. Taylor expanded in c around inf 79.9%

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

      1. times-frac 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in y around 0 80.6%

      \[\leadsto \frac{t}{c} \cdot \color{blue}{\frac{1}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-109}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 70.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-77}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.4e+54)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y -3e-77)
     (/ t (+ i (* y (+ c (* y b)))))
     (if (<= y 5e-26)
       (/ (+ t (* y 230661.510616)) (+ i (* y c)))
       (+ x (- (/ z y) (* a (/ x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.4e+54) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -3e-77) {
		tmp = t / (i + (y * (c + (y * b))));
	} else if (y <= 5e-26) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.4d+54)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= (-3d-77)) then
        tmp = t / (i + (y * (c + (y * b))))
    else if (y <= 5d-26) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.4e+54) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -3e-77) {
		tmp = t / (i + (y * (c + (y * b))));
	} else if (y <= 5e-26) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.4e+54:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= -3e-77:
		tmp = t / (i + (y * (c + (y * b))))
	elif y <= 5e-26:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.4e+54)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= -3e-77)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 5e-26)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.4e+54)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= -3e-77)
		tmp = t / (i + (y * (c + (y * b))));
	elseif (y <= 5e-26)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.4e+54], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-77], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-26], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4000000000000001e54

   1. Initial program 3.8%

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

   3. Taylor expanded in y around -inf 53.2%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in c around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-*r/ 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in x around 0 77.3%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 77.3%

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

       2. mul-1-neg 77.3%

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

       3. +-commutative 77.3%

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

       4. associate-*r/ 77.3%

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

       5. metadata-eval 77.3%

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

   11. Simplified 77.3%

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

   if -3.4000000000000001e54 < y < -3.00000000000000016e-77

   1. Initial program 69.0%

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

   3. Taylor expanded in x around 0 69.2%

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

   4. Taylor expanded in y around 0 44.1%

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

   5. Taylor expanded in t around inf 28.7%

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

   if -3.00000000000000016e-77 < y < 5.00000000000000019e-26

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 95.3%

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

      1. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in y around 0 88.2%

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

   if 5.00000000000000019e-26 < y

   1. Initial program 15.9%

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

   3. Taylor expanded in y around inf 52.1%

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

      1. associate--l+ 52.1%

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

      2. associate-/l* 57.4%

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

   5. Simplified 57.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-77}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 73.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 190000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.05e+74)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 190000000000.0)
     (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
     (+ x (- (/ z y) (* a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.05e+74) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 190000000000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.05d+74)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 190000000000.0d0) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.05e+74) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 190000000000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.05e+74:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 190000000000.0:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.05e+74)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 190000000000.0)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.05e+74)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 190000000000.0)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.05e+74], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 190000000000.0], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e74

   1. Initial program 2.0%

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

   3. Taylor expanded in y around -inf 54.5%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in c around inf 74.4%

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

      1. mul-1-neg 74.4%

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

      2. associate-*r/ 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in x around 0 80.9%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 80.9%

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

       2. mul-1-neg 80.9%

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

       3. +-commutative 80.9%

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

       4. associate-*r/ 80.9%

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

       5. metadata-eval 80.9%

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

   11. Simplified 80.9%

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

   if -2.05e74 < y < 1.9e11

   1. Initial program 92.6%

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

   3. Taylor expanded in y around 0 83.5%

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

      1. *-commutative 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in y around 0 80.0%

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

   if 1.9e11 < y

   1. Initial program 11.1%

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

   3. Taylor expanded in y around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. associate-/l* 60.7%

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

   5. Simplified 60.7%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 190000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 65.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.05e+74)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 8.5e-65)
     (/ t (+ i (* y (+ c (* y b)))))
     (+ x (- (/ z y) (* a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.05e+74) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 8.5e-65) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.05d+74)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 8.5d-65) then
        tmp = t / (i + (y * (c + (y * b))))
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.05e+74) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 8.5e-65) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.05e+74:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 8.5e-65:
		tmp = t / (i + (y * (c + (y * b))))
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.05e+74)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 8.5e-65)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.05e+74)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 8.5e-65)
		tmp = t / (i + (y * (c + (y * b))));
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.05e+74], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-65], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e74

   1. Initial program 2.0%

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

   3. Taylor expanded in y around -inf 54.5%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in c around inf 74.4%

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

      1. mul-1-neg 74.4%

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

      2. associate-*r/ 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in x around 0 80.9%

      \[\leadsto x + \left(-\color{blue}{-1 \cdot \frac{z + 27464.7644705 \cdot \frac{1}{y}}{y}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 80.9%

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

       2. mul-1-neg 80.9%

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

       3. +-commutative 80.9%

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

       4. associate-*r/ 80.9%

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

       5. metadata-eval 80.9%

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

   11. Simplified 80.9%

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

   if -2.05e74 < y < 8.5000000000000003e-65

   1. Initial program 92.0%

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

   3. Taylor expanded in x around 0 91.3%

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

   4. Taylor expanded in y around 0 87.4%

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

   5. Taylor expanded in t around inf 70.2%

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

   if 8.5000000000000003e-65 < y

   1. Initial program 23.2%

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

   3. Taylor expanded in y around inf 47.6%

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

      1. associate--l+ 47.6%

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

      2. associate-/l* 52.5%

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

   5. Simplified 52.5%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+74} \lor \neg \left(y \leq 5 \cdot 10^{-26}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.05e+74) (not (<= y 5e-26))) (+ x (/ z 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 <= -2.05e+74) || !(y <= 5e-26)) {
		tmp = x + (z / 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 <= (-2.05d+74)) .or. (.not. (y <= 5d-26))) then
        tmp = x + (z / 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 <= -2.05e+74) || !(y <= 5e-26)) {
		tmp = x + (z / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.05e+74) or not (y <= 5e-26):
		tmp = x + (z / y)
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.05e+74) || !(y <= 5e-26))
		tmp = Float64(x + Float64(z / 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 <= -2.05e+74) || ~((y <= 5e-26)))
		tmp = x + (z / y);
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.05e+74], N[Not[LessEqual[y, 5e-26]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e74 or 5.00000000000000019e-26 < y

   1. Initial program 10.3%

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

   3. Taylor expanded in y around -inf 43.2%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in c around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. associate-*r/ 60.4%

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

   8. Simplified 60.4%

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

   9. Taylor expanded in z around inf 66.7%

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

       1. associate-*r/ 66.7%

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

       2. mul-1-neg 66.7%

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

   11. Simplified 66.7%

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

   if -2.05e74 < y < 5.00000000000000019e-26

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 47.1%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+74} \lor \neg \left(y \leq 5 \cdot 10^{-26}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 48.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-92}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.6e+76) x (if (<= y 1.42e-92) (/ 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 <= -6.6e+76) {
		tmp = x;
	} else if (y <= 1.42e-92) {
		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 <= (-6.6d+76)) then
        tmp = x
    else if (y <= 1.42d-92) 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 <= -6.6e+76) {
		tmp = x;
	} else if (y <= 1.42e-92) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.6e+76:
		tmp = x
	elif y <= 1.42e-92:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.6e+76)
		tmp = x;
	elseif (y <= 1.42e-92)
		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 <= -6.6e+76)
		tmp = x;
	elseif (y <= 1.42e-92)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.6e+76], x, If[LessEqual[y, 1.42e-92], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6000000000000001e76 or 1.42e-92 < y

   1. Initial program 18.3%

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

   3. Taylor expanded in y around inf 50.1%

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

   if -6.6000000000000001e76 < y < 1.42e-92

   1. Initial program 91.0%

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

   3. Taylor expanded in y around 0 50.2%

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

Alternative 21: 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 52.9%

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

3. Taylor expanded in y around inf 28.6%

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

Reproduce

herbie shell --seed 2024107 
(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)))