Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.1% → 82.1%

Time: 21.2s

Alternatives: 23

Speedup: 1.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\\ t_2 := x + \frac{z - x \cdot a}{y}\\ t_3 := \mathsf{fma}\left(y, t\_1, i\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{t\_3}, \mathsf{fma}\left(x, \frac{y \cdot \left(y \cdot y\right)}{t\_1}, \frac{t}{t\_3}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y (fma y (+ y a) b) c))
        (t_2 (+ x (/ (- z (* x a)) y)))
        (t_3 (fma y t_1 i)))
   (if (<= y -4.8e+87)
     t_2
     (if (<= y 1.8e+88)
       (fma
        y
        (/ (fma y (fma y z 27464.7644705) 230661.510616) t_3)
        (fma x (/ (* y (* y y)) t_1) (/ t t_3)))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, fma(y, (y + a), b), c);
	double t_2 = x + ((z - (x * a)) / y);
	double t_3 = fma(y, t_1, i);
	double tmp;
	if (y <= -4.8e+87) {
		tmp = t_2;
	} else if (y <= 1.8e+88) {
		tmp = fma(y, (fma(y, fma(y, z, 27464.7644705), 230661.510616) / t_3), fma(x, ((y * (y * y)) / t_1), (t / t_3)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, fma(y, Float64(y + a), b), c)
	t_2 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	t_3 = fma(y, t_1, i)
	tmp = 0.0
	if (y <= -4.8e+87)
		tmp = t_2;
	elseif (y <= 1.8e+88)
		tmp = fma(y, Float64(fma(y, fma(y, z, 27464.7644705), 230661.510616) / t_3), fma(x, Float64(Float64(y * Float64(y * y)) / t_1), Float64(t / t_3)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * t$95$1 + i), $MachinePrecision]}, If[LessEqual[y, -4.8e+87], t$95$2, If[LessEqual[y, 1.8e+88], N[(y * N[(N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(x * N[(N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999963e87 or 1.8000000000000001e88 < y

   1. Initial program 0.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 0.0%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 65.6

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

   8. Simplified 65.6%

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

   if -4.79999999999999963e87 < y < 1.8000000000000001e88

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 88.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{{y}^{4}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{{y}^{\color{blue}{\left(2 \cdot 2\right)}}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      2. pow-pow N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{\color{blue}{{\left({y}^{2}\right)}^{2}}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      3. pow2 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{{\color{blue}{\left(y \cdot y\right)}}^{2}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{\color{blue}{\left(y \cdot y\right) \cdot \left(y \cdot y\right)}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\left(y \cdot y\right) \cdot \frac{y \cdot y}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\left(y \cdot y\right) \cdot \frac{y \cdot y}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\left(y \cdot y\right)} \cdot \frac{y \cdot y}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \left(y \cdot y\right) \cdot \color{blue}{\frac{y \cdot y}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \left(y \cdot y\right) \cdot \frac{\color{blue}{y \cdot y}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \left(y \cdot y\right) \cdot \frac{y \cdot y}{\color{blue}{\mathsf{fma}\left(y, y \cdot \left(y \cdot \left(y + a\right) + b\right) + c, i\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \left(y \cdot y\right) \cdot \frac{y \cdot y}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, y \cdot \left(y + a\right) + b, c\right)}, i\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      12. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \left(y \cdot y\right) \cdot \frac{y \cdot y}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, y + a, b\right)}, c\right), i\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      13. +-lowering-+.f64 89.0

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

   7. Applied egg-rr 89.0%

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

   8. Taylor expanded in i around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{\color{blue}{y \cdot \left(y \cdot y\right)}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{y \cdot \color{blue}{{y}^{2}}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{\color{blue}{y \cdot {y}^{2}}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{y \cdot \color{blue}{\left(y \cdot y\right)}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{y \cdot \color{blue}{\left(y \cdot y\right)}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{y \cdot \left(y \cdot y\right)}{\color{blue}{y \cdot \left(b + y \cdot \left(a + y\right)\right) + c}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{y \cdot \left(y \cdot y\right)}{\color{blue}{\mathsf{fma}\left(y, b + y \cdot \left(a + y\right), c\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{y \cdot \left(y \cdot y\right)}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(a + y\right) + b}, c\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{y \cdot \left(y \cdot y\right)}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, a + y, b\right)}, c\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{y \cdot \left(y \cdot y\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      12. +-lowering-+.f64 89.6

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

   10. Simplified 89.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+87}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{y \cdot \left(y \cdot y\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.3% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(y * N[(N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(x * N[(N[(y * y), $MachinePrecision] * N[(N[(y * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - N[(x * a), $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)) < +inf.0

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 87.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{{y}^{4}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{{y}^{\color{blue}{\left(2 \cdot 2\right)}}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      2. pow-pow N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{\color{blue}{{\left({y}^{2}\right)}^{2}}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      3. pow2 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{{\color{blue}{\left(y \cdot y\right)}}^{2}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{\color{blue}{\left(y \cdot y\right) \cdot \left(y \cdot y\right)}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\left(y \cdot y\right) \cdot \frac{y \cdot y}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\left(y \cdot y\right) \cdot \frac{y \cdot y}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\left(y \cdot y\right)} \cdot \frac{y \cdot y}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \left(y \cdot y\right) \cdot \color{blue}{\frac{y \cdot y}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \left(y \cdot y\right) \cdot \frac{\color{blue}{y \cdot y}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \left(y \cdot y\right) \cdot \frac{y \cdot y}{\color{blue}{\mathsf{fma}\left(y, y \cdot \left(y \cdot \left(y + a\right) + b\right) + c, i\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \left(y \cdot y\right) \cdot \frac{y \cdot y}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, y \cdot \left(y + a\right) + b, c\right)}, i\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      12. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \left(y \cdot y\right) \cdot \frac{y \cdot y}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, y + a, b\right)}, c\right), i\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      13. +-lowering-+.f64 88.2

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

   7. Applied egg-rr 88.2%

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

   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))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 0.0%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 66.5

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

   8. Simplified 66.5%

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

4. Final simplification 79.6%

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

Alternative 3: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-76}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{elif}\;t\_1 \leq 10^{+153}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, 230661.510616, t\right)}{i + a \cdot \left(y \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \end{array} \]

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)
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))
   (if (<= t_1 -2e-76)
     (/ t (fma y (fma y (fma y (+ y a) b) c) i))
     (if (<= t_1 1e+153)
       (/ (fma y 230661.510616 t) (+ i (* a (* y (* y y)))))
       (+ x (/ (- z (* x a)) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	double tmp;
	if (t_1 <= -2e-76) {
		tmp = t / fma(y, fma(y, fma(y, (y + a), b), c), i);
	} else if (t_1 <= 1e+153) {
		tmp = fma(y, 230661.510616, t) / (i + (a * (y * (y * y))));
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i))
	tmp = 0.0
	if (t_1 <= -2e-76)
		tmp = Float64(t / fma(y, fma(y, fma(y, Float64(y + a), b), c), i));
	elseif (t_1 <= 1e+153)
		tmp = Float64(fma(y, 230661.510616, t) / Float64(i + Float64(a * Float64(y * Float64(y * y)))));
	else
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $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-76], N[(t / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+153], N[(N[(y * 230661.510616 + t), $MachinePrecision] / N[(i + N[(a * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - N[(x * a), $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)) < -1.99999999999999985e-76

   1. Initial program 97.6%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 74.0

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

   5. Simplified 74.0%

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

   if -1.99999999999999985e-76 < (/.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)) < 1e153

   1. Initial program 81.8%

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

   3. Taylor expanded in a around inf

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{a \cdot {y}^{3}} + i} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{{y}^{3} \cdot a} + i} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{{y}^{3} \cdot a} + i} \]

      3. cube-mult N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\left(y \cdot \left(y \cdot y\right)\right)} \cdot a + i} \]

      4. unpow2 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(y \cdot \color{blue}{{y}^{2}}\right) \cdot a + i} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\left(y \cdot {y}^{2}\right)} \cdot a + i} \]

      6. unpow2 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(y \cdot \color{blue}{\left(y \cdot y\right)}\right) \cdot a + i} \]

      7. *-lowering-*.f64 59.2

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

   5. Simplified 59.2%

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

      1. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{y \cdot \left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right)} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(y \cdot \left(\color{blue}{y \cdot \left(x \cdot y + z\right)} + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}\right) \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(y \cdot \left(y \cdot \left(\color{blue}{y \cdot x} + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}\right) \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      4. distribute-rgt-in N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\left(y \cdot \left(y \cdot x + z\right)\right) \cdot y + \frac{54929528941}{2000000} \cdot y\right)} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      5. associate-+l+ N/A

         \[\leadsto \frac{\color{blue}{\left(\left(y \cdot \left(y \cdot x + z\right)\right) \cdot y + \left(\frac{54929528941}{2000000} \cdot y + \frac{28832688827}{125000}\right)\right)} \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(\left(y \cdot \left(y \cdot x + z\right)\right) \cdot y + \left(\color{blue}{y \cdot \frac{54929528941}{2000000}} + \frac{28832688827}{125000}\right)\right) \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\left(y \cdot x + z\right) \cdot y\right)} \cdot y + \left(y \cdot \frac{54929528941}{2000000} + \frac{28832688827}{125000}\right)\right) \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      8. associate-*l* N/A

         \[\leadsto \frac{\left(\color{blue}{\left(y \cdot x + z\right) \cdot \left(y \cdot y\right)} + \left(y \cdot \frac{54929528941}{2000000} + \frac{28832688827}{125000}\right)\right) \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x + z, y \cdot y, y \cdot \frac{54929528941}{2000000} + \frac{28832688827}{125000}\right)} \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y, x, z\right)}, y \cdot y, y \cdot \frac{54929528941}{2000000} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), \color{blue}{y \cdot y}, y \cdot \frac{54929528941}{2000000} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      12. accelerator-lowering-fma.f64 59.2

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

   7. Applied egg-rr 59.2%

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

   8. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + \frac{28832688827}{125000} \cdot y}}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \frac{28832688827}{125000}} + t}{\left(y \cdot \left(y \cdot y\right)\right) \cdot a + i} \]

      3. accelerator-lowering-fma.f64 54.1

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

   10. Simplified 54.1%

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

   if 1e153 < (/.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 8.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 14.2%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 62.3

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

   8. Simplified 62.3%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq -2 \cdot 10^{-76}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{elif}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq 10^{+153}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, 230661.510616, t\right)}{i + a \cdot \left(y \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(y * N[(N[(y * N[(y * N[(y * x + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - N[(x * a), $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)) < +inf.0

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 85.8%

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

   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))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 0.0%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 66.5

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

   8. Simplified 66.5%

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

4. Final simplification 78.1%

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

Alternative 5: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+53}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + \mathsf{fma}\left(y \cdot \mathsf{fma}\left(x, y, z\right), y, y \cdot 27464.7644705\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -9.6e+41)
     t_1
     (if (<= y 6e+53)
       (/
        (+
         t
         (* y (+ 230661.510616 (fma (* y (fma x y z)) y (* y 27464.7644705)))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -9.6e+41) {
		tmp = t_1;
	} else if (y <= 6e+53) {
		tmp = (t + (y * (230661.510616 + fma((y * fma(x, y, z)), y, (y * 27464.7644705))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -9.6e+41)
		tmp = t_1;
	elseif (y <= 6e+53)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + fma(Float64(y * fma(x, y, z)), y, Float64(y * 27464.7644705))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+41], t$95$1, If[LessEqual[y, 6e+53], N[(N[(t + N[(y * N[(230661.510616 + N[(N[(y * N[(x * y + z), $MachinePrecision]), $MachinePrecision] * y + N[(y * 27464.7644705), $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], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.6000000000000007e41 or 5.99999999999999996e53 < y

   1. Initial program 2.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 5.1%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 62.6

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

   8. Simplified 62.6%

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

   if -9.6000000000000007e41 < y < 5.99999999999999996e53

   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. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{y \cdot \left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right)} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. distribute-rgt-in N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y\right) \cdot y + \frac{54929528941}{2000000} \cdot y\right)} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot y + z\right) \cdot y, y, \frac{54929528941}{2000000} \cdot y\right)} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\mathsf{fma}\left(\color{blue}{y \cdot \left(x \cdot y + z\right)}, y, \frac{54929528941}{2000000} \cdot y\right) + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \frac{\left(\mathsf{fma}\left(\color{blue}{y \cdot \left(x \cdot y + z\right)}, y, \frac{54929528941}{2000000} \cdot y\right) + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\left(\mathsf{fma}\left(y \cdot \color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, \frac{54929528941}{2000000} \cdot y\right) + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. *-lowering-*.f64 94.0

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

   4. Applied egg-rr 94.0%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+53}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + \mathsf{fma}\left(y \cdot \mathsf{fma}\left(x, y, z\right), y, y \cdot 27464.7644705\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -8.5e+41)
     t_1
     (if (<= y 2.3e+53)
       (/
        (+
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
         t)
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -8.5e+41) {
		tmp = t_1;
	} else if (y <= 2.3e+53) {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-8.5d+41)) then
        tmp = t_1
    else if (y <= 2.3d+53) then
        tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -8.5e+41) {
		tmp = t_1;
	} else if (y <= 2.3e+53) {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -8.5e+41:
		tmp = t_1
	elif y <= 2.3e+53:
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -8.5e+41)
		tmp = t_1;
	elseif (y <= 2.3e+53)
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -8.5e+41)
		tmp = t_1;
	elseif (y <= 2.3e+53)
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+41], t$95$1, If[LessEqual[y, 2.3e+53], N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.49999999999999938e41 or 2.3000000000000002e53 < y

   1. Initial program 2.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 5.1%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 62.6

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

   8. Simplified 62.6%

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

   if -8.49999999999999938e41 < y < 2.3000000000000002e53

   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. Recombined 2 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+52}:\\ \;\;\;\;\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -9.6e+41)
     t_1
     (if (<= y 8e+52)
       (/
        1.0
        (/
         (fma y (fma y (fma y (+ y a) b) c) i)
         (fma y (fma y (fma y (fma x y z) 27464.7644705) 230661.510616) t)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -9.6e+41) {
		tmp = t_1;
	} else if (y <= 8e+52) {
		tmp = 1.0 / (fma(y, fma(y, fma(y, (y + a), b), c), i) / fma(y, fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616), t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -9.6e+41)
		tmp = t_1;
	elseif (y <= 8e+52)
		tmp = Float64(1.0 / Float64(fma(y, fma(y, fma(y, Float64(y + a), b), c), i) / fma(y, fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616), t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+41], t$95$1, If[LessEqual[y, 8e+52], N[(1.0 / N[(N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision] / N[(y * N[(y * N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.6000000000000007e41 or 7.9999999999999999e52 < y

   1. Initial program 2.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 5.1%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 62.6

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

   8. Simplified 62.6%

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

   if -9.6000000000000007e41 < y < 7.9999999999999999e52

   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. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      4. *-commutative N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{y \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)} + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{\mathsf{fma}\left(y, \left(\left(y + a\right) \cdot y + b\right) \cdot y + c, i\right)}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}} \]

      6. *-commutative N/A

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + c, i\right)}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}} \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \left(y + a\right) \cdot y + b, c\right)}, i\right)}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}} \]

      8. *-commutative N/A

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(y + a\right)} + b, c\right), i\right)}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}} \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, y + a, b\right)}, c\right), i\right)}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}} \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}} \]

   4. Applied egg-rr 93.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+52}:\\ \;\;\;\;\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -9.6e+41)
     t_1
     (if (<= y 1.35e+48)
       (*
        (fma y (fma y (fma y (fma x y z) 27464.7644705) 230661.510616) t)
        (/ 1.0 (fma y (fma y (fma y (+ y a) b) c) i)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -9.6e+41) {
		tmp = t_1;
	} else if (y <= 1.35e+48) {
		tmp = fma(y, fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616), t) * (1.0 / fma(y, fma(y, fma(y, (y + a), b), c), i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -9.6e+41)
		tmp = t_1;
	elseif (y <= 1.35e+48)
		tmp = Float64(fma(y, fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616), t) * Float64(1.0 / fma(y, fma(y, fma(y, Float64(y + a), b), c), i)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+41], t$95$1, If[LessEqual[y, 1.35e+48], N[(N[(y * N[(y * N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision] * N[(1.0 / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.6000000000000007e41 or 1.35000000000000002e48 < y

   1. Initial program 2.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 5.1%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 62.6

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

   8. Simplified 62.6%

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

   if -9.6000000000000007e41 < y < 1.35000000000000002e48

   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. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}, t\right)} \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{y \cdot \left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right)} + \frac{28832688827}{125000}, t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}, \frac{28832688827}{125000}\right)}, t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(x \cdot y + z\right)} + \frac{54929528941}{2000000}, \frac{28832688827}{125000}\right), t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, \frac{54929528941}{2000000}\right)}, \frac{28832688827}{125000}\right), t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right) \cdot \color{blue}{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \]

   4. Applied egg-rr 93.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.55e+47)
     t_1
     (if (<= y 8.8e+26)
       (/
        (fma y (fma y (fma y (fma y x z) 27464.7644705) 230661.510616) t)
        (fma y (fma y (fma y y b) c) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.55e+47) {
		tmp = t_1;
	} else if (y <= 8.8e+26) {
		tmp = fma(y, fma(y, fma(y, fma(y, x, z), 27464.7644705), 230661.510616), t) / fma(y, fma(y, fma(y, y, b), c), i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.55e+47)
		tmp = t_1;
	elseif (y <= 8.8e+26)
		tmp = Float64(fma(y, fma(y, fma(y, fma(y, x, z), 27464.7644705), 230661.510616), t) / fma(y, fma(y, fma(y, y, b), c), i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+47], t$95$1, If[LessEqual[y, 8.8e+26], N[(N[(y * N[(y * N[(y * N[(y * x + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision] / N[(y * N[(y * N[(y * y + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e47 or 8.80000000000000028e26 < y

   1. Initial program 3.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 7.4%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 62.1

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

   8. Simplified 62.1%

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

   if -1.55e47 < y < 8.80000000000000028e26

   1. Initial program 93.9%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right) + t}}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right), t\right)}}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right) + \frac{28832688827}{125000}}, t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right), \frac{28832688827}{125000}\right)}, t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(z + x \cdot y\right) + \frac{54929528941}{2000000}}, \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, z + x \cdot y, \frac{54929528941}{2000000}\right)}, \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      11. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right) + i}} \]

      12. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(b + {y}^{2}\right), i\right)}} \]

      13. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(b + {y}^{2}\right) + c}, i\right)} \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, b + {y}^{2}, c\right)}, i\right)} \]

      15. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{{y}^{2} + b}, c\right), i\right)} \]

      16. unpow2 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot y} + b, c\right), i\right)} \]

      17. accelerator-lowering-fma.f64 89.6

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

   5. Simplified 89.6%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+23}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.55e+17)
     t_1
     (if (<= y 2.75e+23)
       (/
        (+
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
         t)
        (+ i (* y c)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.55e+17) {
		tmp = t_1;
	} else if (y <= 2.75e+23) {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-1.55d+17)) then
        tmp = t_1
    else if (y <= 2.75d+23) then
        tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t) / (i + (y * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.55e+17) {
		tmp = t_1;
	} else if (y <= 2.75e+23) {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -1.55e+17:
		tmp = t_1
	elif y <= 2.75e+23:
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.55e+17)
		tmp = t_1;
	elseif (y <= 2.75e+23)
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(i + Float64(y * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -1.55e+17)
		tmp = t_1;
	elseif (y <= 2.75e+23)
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+17], t$95$1, If[LessEqual[y, 2.75e+23], N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e17 or 2.75000000000000002e23 < 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 x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 10.7%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 58.3

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

   8. Simplified 58.3%

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

   if -1.55e17 < y < 2.75000000000000002e23

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{c \cdot y} + i} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{y \cdot c} + i} \]

      2. *-lowering-*.f64 82.2

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

   5. Simplified 82.2%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+23}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-24}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;\frac{\left(27464.7644705 + \frac{230661.510616}{y}\right) + \mathsf{fma}\left(x, y \cdot y, y \cdot z\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.32e+29)
     t_1
     (if (<= y 3e-24)
       (/ t (fma y (fma y (fma y (+ y a) b) c) i))
       (if (<= y 1.85e+53)
         (/
          (+ (+ 27464.7644705 (/ 230661.510616 y)) (fma x (* y y) (* y z)))
          b)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.32e+29) {
		tmp = t_1;
	} else if (y <= 3e-24) {
		tmp = t / fma(y, fma(y, fma(y, (y + a), b), c), i);
	} else if (y <= 1.85e+53) {
		tmp = ((27464.7644705 + (230661.510616 / y)) + fma(x, (y * y), (y * z))) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.32e+29)
		tmp = t_1;
	elseif (y <= 3e-24)
		tmp = Float64(t / fma(y, fma(y, fma(y, Float64(y + a), b), c), i));
	elseif (y <= 1.85e+53)
		tmp = Float64(Float64(Float64(27464.7644705 + Float64(230661.510616 / y)) + fma(x, Float64(y * y), Float64(y * z))) / b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.32e+29], t$95$1, If[LessEqual[y, 3e-24], N[(t / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+53], N[(N[(N[(27464.7644705 + N[(230661.510616 / y), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * y), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.32e29 or 1.85e53 < y

   1. Initial program 4.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 6.6%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 61.9

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

   8. Simplified 61.9%

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

   if -1.32e29 < y < 2.99999999999999995e-24

   1. Initial program 98.9%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 67.3

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

   5. Simplified 67.3%

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

   if 2.99999999999999995e-24 < y < 1.85e53

   1. Initial program 65.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 82.5%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}}{b} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{\mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}}{b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{y}}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z + \frac{t}{{y}^{2}}\right)}\right)}{b} \]

      6. unpow2 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \color{blue}{\mathsf{fma}\left(y, z, \frac{t}{{y}^{2}}\right)}\right)\right)}{b} \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \color{blue}{\frac{t}{{y}^{2}}}\right)\right)\right)}{b} \]

      10. unpow2 N/A

          \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \frac{t}{\color{blue}{y \cdot y}}\right)\right)\right)}{b} \]

      11. *-lowering-*.f64 49.0

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

   8. Simplified 49.0%

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

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + y \cdot z\right)\right)}{b}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + y \cdot z\right)\right)}{b}} \]

       2. associate-+r+ N/A

          \[\leadsto \frac{\color{blue}{\left(\frac{54929528941}{2000000} + \frac{28832688827}{125000} \cdot \frac{1}{y}\right) + \left(x \cdot {y}^{2} + y \cdot z\right)}}{b} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \frac{\color{blue}{\left(\frac{54929528941}{2000000} + \frac{28832688827}{125000} \cdot \frac{1}{y}\right) + \left(x \cdot {y}^{2} + y \cdot z\right)}}{b} \]

       4. +-lowering-+.f64 N/A

          \[\leadsto \frac{\color{blue}{\left(\frac{54929528941}{2000000} + \frac{28832688827}{125000} \cdot \frac{1}{y}\right)} + \left(x \cdot {y}^{2} + y \cdot z\right)}{b} \]

       5. associate-*r/ N/A

          \[\leadsto \frac{\left(\frac{54929528941}{2000000} + \color{blue}{\frac{\frac{28832688827}{125000} \cdot 1}{y}}\right) + \left(x \cdot {y}^{2} + y \cdot z\right)}{b} \]

       6. metadata-eval N/A

          \[\leadsto \frac{\left(\frac{54929528941}{2000000} + \frac{\color{blue}{\frac{28832688827}{125000}}}{y}\right) + \left(x \cdot {y}^{2} + y \cdot z\right)}{b} \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \frac{\left(\frac{54929528941}{2000000} + \color{blue}{\frac{\frac{28832688827}{125000}}{y}}\right) + \left(x \cdot {y}^{2} + y \cdot z\right)}{b} \]

       8. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{\left(\frac{54929528941}{2000000} + \frac{\frac{28832688827}{125000}}{y}\right) + \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z\right)}}{b} \]

       9. unpow2 N/A

          \[\leadsto \frac{\left(\frac{54929528941}{2000000} + \frac{\frac{28832688827}{125000}}{y}\right) + \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z\right)}{b} \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \frac{\left(\frac{54929528941}{2000000} + \frac{\frac{28832688827}{125000}}{y}\right) + \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z\right)}{b} \]

       11. *-lowering-*.f64 42.0

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

   11. Simplified 42.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-24}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;\frac{\left(27464.7644705 + \frac{230661.510616}{y}\right) + \mathsf{fma}\left(x, y \cdot y, y \cdot z\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-24}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+48}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(\frac{x}{b} + \frac{z}{y \cdot b}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -2.55e+28)
     t_1
     (if (<= y 3e-24)
       (/ t (fma y (fma y (fma y (+ y a) b) c) i))
       (if (<= y 3.3e+48) (* (* y y) (+ (/ x b) (/ z (* y b)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -2.55e+28) {
		tmp = t_1;
	} else if (y <= 3e-24) {
		tmp = t / fma(y, fma(y, fma(y, (y + a), b), c), i);
	} else if (y <= 3.3e+48) {
		tmp = (y * y) * ((x / b) + (z / (y * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -2.55e+28)
		tmp = t_1;
	elseif (y <= 3e-24)
		tmp = Float64(t / fma(y, fma(y, fma(y, Float64(y + a), b), c), i));
	elseif (y <= 3.3e+48)
		tmp = Float64(Float64(y * y) * Float64(Float64(x / b) + Float64(z / Float64(y * b))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+28], t$95$1, If[LessEqual[y, 3e-24], N[(t / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+48], N[(N[(y * y), $MachinePrecision] * N[(N[(x / b), $MachinePrecision] + N[(z / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5500000000000002e28 or 3.30000000000000023e48 < y

   1. Initial program 4.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 6.6%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 61.9

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

   8. Simplified 61.9%

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

   if -2.5500000000000002e28 < y < 2.99999999999999995e-24

   1. Initial program 98.9%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 67.3

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

   5. Simplified 67.3%

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

   if 2.99999999999999995e-24 < y < 3.30000000000000023e48

   1. Initial program 65.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 82.5%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}}{b} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{\mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}}{b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{y}}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z + \frac{t}{{y}^{2}}\right)}\right)}{b} \]

      6. unpow2 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \color{blue}{\mathsf{fma}\left(y, z, \frac{t}{{y}^{2}}\right)}\right)\right)}{b} \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \color{blue}{\frac{t}{{y}^{2}}}\right)\right)\right)}{b} \]

      10. unpow2 N/A

          \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \frac{t}{\color{blue}{y \cdot y}}\right)\right)\right)}{b} \]

      11. *-lowering-*.f64 49.0

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

   8. Simplified 49.0%

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

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{{y}^{2} \cdot \left(\frac{x}{b} + \frac{z}{b \cdot y}\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

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

       2. unpow2 N/A

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

       3. *-lowering-*.f64 N/A

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

       4. +-lowering-+.f64 N/A

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

       5. /-lowering-/.f64 N/A

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

       6. /-lowering-/.f64 N/A

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

       7. *-lowering-*.f64 41.7

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

   11. Simplified 41.7%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-24}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+48}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(\frac{x}{b} + \frac{z}{y \cdot b}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.52 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+46}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, 230661.510616, t\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.52e+29)
     t_1
     (if (<= y 2.1e+46)
       (/ (fma y 230661.510616 t) (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.52e+29) {
		tmp = t_1;
	} else if (y <= 2.1e+46) {
		tmp = fma(y, 230661.510616, t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.52e+29)
		tmp = t_1;
	elseif (y <= 2.1e+46)
		tmp = Float64(fma(y, 230661.510616, t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.52e+29], t$95$1, If[LessEqual[y, 2.1e+46], N[(N[(y * 230661.510616 + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.52e29 or 2.1e46 < y

   1. Initial program 4.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 6.6%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 61.9

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

   8. Simplified 61.9%

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

   if -1.52e29 < y < 2.1e46

   1. Initial program 94.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + \frac{28832688827}{125000} \cdot y}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \frac{28832688827}{125000}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. accelerator-lowering-fma.f64 76.9

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

   5. Simplified 76.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+46}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, 230661.510616, t\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{t}{y}}{y \cdot b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{i}\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+54}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -9e+44)
     t_1
     (if (<= y -2.7e-11)
       (/ (/ t y) (* y b))
       (if (<= y 1.35e-31)
         (fma y (/ 230661.510616 i) (/ t i))
         (if (<= y 7.6e+54) (/ (+ 27464.7644705 (* y z)) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -9e+44) {
		tmp = t_1;
	} else if (y <= -2.7e-11) {
		tmp = (t / y) / (y * b);
	} else if (y <= 1.35e-31) {
		tmp = fma(y, (230661.510616 / i), (t / i));
	} else if (y <= 7.6e+54) {
		tmp = (27464.7644705 + (y * z)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -9e+44)
		tmp = t_1;
	elseif (y <= -2.7e-11)
		tmp = Float64(Float64(t / y) / Float64(y * b));
	elseif (y <= 1.35e-31)
		tmp = fma(y, Float64(230661.510616 / i), Float64(t / i));
	elseif (y <= 7.6e+54)
		tmp = Float64(Float64(27464.7644705 + Float64(y * z)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+44], t$95$1, If[LessEqual[y, -2.7e-11], N[(N[(t / y), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-31], N[(y * N[(230661.510616 / i), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e+54], N[(N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9e44 or 7.6000000000000005e54 < y

   1. Initial program 2.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 5.1%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 64.0

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

   8. Simplified 64.0%

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

   if -9e44 < y < -2.70000000000000005e-11

   1. Initial program 78.2%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 78.2%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}}{b} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{\mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}}{b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{y}}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z + \frac{t}{{y}^{2}}\right)}\right)}{b} \]

      6. unpow2 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \color{blue}{\mathsf{fma}\left(y, z, \frac{t}{{y}^{2}}\right)}\right)\right)}{b} \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \color{blue}{\frac{t}{{y}^{2}}}\right)\right)\right)}{b} \]

      10. unpow2 N/A

          \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \frac{t}{\color{blue}{y \cdot y}}\right)\right)\right)}{b} \]

      11. *-lowering-*.f64 45.7

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

   8. Simplified 45.7%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{\frac{t}{{y}^{2}}}}{b} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \frac{\color{blue}{\frac{t}{{y}^{2}}}}{b} \]

       2. unpow2 N/A

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

       3. *-lowering-*.f64 33.5

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

   11. Simplified 33.5%

       \[\leadsto \frac{\color{blue}{\frac{t}{y \cdot y}}}{b} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{y}}}{b} \]

       2. associate-/l/ N/A

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

       3. /-lowering-/.f64 N/A

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

       4. /-lowering-/.f64 N/A

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 33.7

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

   13. Applied egg-rr 33.7%

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

   if -2.70000000000000005e-11 < y < 1.35000000000000007e-31

   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 t around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 82.5

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

   8. Simplified 82.5%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i}, \color{blue}{\frac{t}{i}}\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 72.2

          \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i}, \color{blue}{\frac{t}{i}}\right) \]

   11. Simplified 72.2%

       \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i}, \color{blue}{\frac{t}{i}}\right) \]

   if 1.35000000000000007e-31 < y < 7.6000000000000005e54

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 80.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}}{b} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{\mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}}{b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{y}}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z + \frac{t}{{y}^{2}}\right)}\right)}{b} \]

      6. unpow2 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \color{blue}{\mathsf{fma}\left(y, z, \frac{t}{{y}^{2}}\right)}\right)\right)}{b} \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \color{blue}{\frac{t}{{y}^{2}}}\right)\right)\right)}{b} \]

      10. unpow2 N/A

          \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \frac{t}{\color{blue}{y \cdot y}}\right)\right)\right)}{b} \]

      11. *-lowering-*.f64 41.9

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

   8. Simplified 41.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{y \cdot z}}{b} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 27.2

          \[\leadsto \frac{27464.7644705 + \color{blue}{y \cdot z}}{b} \]

   11. Simplified 27.2%

       \[\leadsto \frac{27464.7644705 + \color{blue}{y \cdot z}}{b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{t}{y}}{y \cdot b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{i}\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+54}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{t}{y}}{y \cdot b}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-32}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -8e+44)
     t_1
     (if (<= y -3.3e-10)
       (/ (/ t y) (* y b))
       (if (<= y 2.7e-32)
         (/ (fma 230661.510616 y t) i)
         (if (<= y 8.8e+55) (/ (+ 27464.7644705 (* y z)) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -8e+44) {
		tmp = t_1;
	} else if (y <= -3.3e-10) {
		tmp = (t / y) / (y * b);
	} else if (y <= 2.7e-32) {
		tmp = fma(230661.510616, y, t) / i;
	} else if (y <= 8.8e+55) {
		tmp = (27464.7644705 + (y * z)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -8e+44)
		tmp = t_1;
	elseif (y <= -3.3e-10)
		tmp = Float64(Float64(t / y) / Float64(y * b));
	elseif (y <= 2.7e-32)
		tmp = Float64(fma(230661.510616, y, t) / i);
	elseif (y <= 8.8e+55)
		tmp = Float64(Float64(27464.7644705 + Float64(y * z)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+44], t$95$1, If[LessEqual[y, -3.3e-10], N[(N[(t / y), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-32], N[(N[(230661.510616 * y + t), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 8.8e+55], N[(N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.0000000000000007e44 or 8.80000000000000042e55 < y

   1. Initial program 2.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 5.1%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 64.0

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

   8. Simplified 64.0%

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

   if -8.0000000000000007e44 < y < -3.3e-10

   1. Initial program 78.2%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 78.2%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}}{b} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{\mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}}{b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{y}}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z + \frac{t}{{y}^{2}}\right)}\right)}{b} \]

      6. unpow2 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \color{blue}{\mathsf{fma}\left(y, z, \frac{t}{{y}^{2}}\right)}\right)\right)}{b} \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \color{blue}{\frac{t}{{y}^{2}}}\right)\right)\right)}{b} \]

      10. unpow2 N/A

          \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \frac{t}{\color{blue}{y \cdot y}}\right)\right)\right)}{b} \]

      11. *-lowering-*.f64 45.7

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

   8. Simplified 45.7%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{\frac{t}{{y}^{2}}}}{b} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \frac{\color{blue}{\frac{t}{{y}^{2}}}}{b} \]

       2. unpow2 N/A

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

       3. *-lowering-*.f64 33.5

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

   11. Simplified 33.5%

       \[\leadsto \frac{\color{blue}{\frac{t}{y \cdot y}}}{b} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{y}}}{b} \]

       2. associate-/l/ N/A

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

       3. /-lowering-/.f64 N/A

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

       4. /-lowering-/.f64 N/A

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 33.7

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

   13. Applied egg-rr 33.7%

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

   if -3.3e-10 < y < 2.69999999999999981e-32

   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 t around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 82.5

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

   8. Simplified 82.5%

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

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]

       2. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{i} \]

       3. accelerator-lowering-fma.f64 72.2

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{i} \]

   11. Simplified 72.2%

       \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}} \]

   if 2.69999999999999981e-32 < y < 8.80000000000000042e55

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 80.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}}{b} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{\mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}}{b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{y}}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z + \frac{t}{{y}^{2}}\right)}\right)}{b} \]

      6. unpow2 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \color{blue}{\mathsf{fma}\left(y, z, \frac{t}{{y}^{2}}\right)}\right)\right)}{b} \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \color{blue}{\frac{t}{{y}^{2}}}\right)\right)\right)}{b} \]

      10. unpow2 N/A

          \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \frac{t}{\color{blue}{y \cdot y}}\right)\right)\right)}{b} \]

      11. *-lowering-*.f64 41.9

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

   8. Simplified 41.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{y \cdot z}}{b} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 27.2

          \[\leadsto \frac{27464.7644705 + \color{blue}{y \cdot z}}{b} \]

   11. Simplified 27.2%

       \[\leadsto \frac{27464.7644705 + \color{blue}{y \cdot z}}{b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{t}{y}}{y \cdot b}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-32}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{t}{b}}{y \cdot y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -9e+44)
     t_1
     (if (<= y -4.3e-10)
       (/ (/ t b) (* y y))
       (if (<= y 1.6e-31)
         (/ (fma 230661.510616 y t) i)
         (if (<= y 7.4e+53) (/ (+ 27464.7644705 (* y z)) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -9e+44) {
		tmp = t_1;
	} else if (y <= -4.3e-10) {
		tmp = (t / b) / (y * y);
	} else if (y <= 1.6e-31) {
		tmp = fma(230661.510616, y, t) / i;
	} else if (y <= 7.4e+53) {
		tmp = (27464.7644705 + (y * z)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -9e+44)
		tmp = t_1;
	elseif (y <= -4.3e-10)
		tmp = Float64(Float64(t / b) / Float64(y * y));
	elseif (y <= 1.6e-31)
		tmp = Float64(fma(230661.510616, y, t) / i);
	elseif (y <= 7.4e+53)
		tmp = Float64(Float64(27464.7644705 + Float64(y * z)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+44], t$95$1, If[LessEqual[y, -4.3e-10], N[(N[(t / b), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-31], N[(N[(230661.510616 * y + t), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 7.4e+53], N[(N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9e44 or 7.4e53 < y

   1. Initial program 2.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 5.1%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 64.0

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

   8. Simplified 64.0%

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

   if -9e44 < y < -4.30000000000000014e-10

   1. Initial program 78.2%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 78.2%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}}{b} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{\mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}}{b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{y}}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z + \frac{t}{{y}^{2}}\right)}\right)}{b} \]

      6. unpow2 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \color{blue}{\mathsf{fma}\left(y, z, \frac{t}{{y}^{2}}\right)}\right)\right)}{b} \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \color{blue}{\frac{t}{{y}^{2}}}\right)\right)\right)}{b} \]

      10. unpow2 N/A

          \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \frac{t}{\color{blue}{y \cdot y}}\right)\right)\right)}{b} \]

      11. *-lowering-*.f64 45.7

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

   8. Simplified 45.7%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{\frac{t}{{y}^{2}}}}{b} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \frac{\color{blue}{\frac{t}{{y}^{2}}}}{b} \]

       2. unpow2 N/A

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

       3. *-lowering-*.f64 33.5

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

   11. Simplified 33.5%

       \[\leadsto \frac{\color{blue}{\frac{t}{y \cdot y}}}{b} \]
   12. Step-by-step derivation

       1. associate-/l/ N/A

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

       2. associate-/r* N/A

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

       3. /-lowering-/.f64 N/A

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

       4. /-lowering-/.f64 N/A

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

       5. *-lowering-*.f64 33.6

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

   13. Applied egg-rr 33.6%

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

   if -4.30000000000000014e-10 < y < 1.60000000000000009e-31

   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 t around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 82.5

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

   8. Simplified 82.5%

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

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]

       2. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{i} \]

       3. accelerator-lowering-fma.f64 72.2

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{i} \]

   11. Simplified 72.2%

       \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}} \]

   if 1.60000000000000009e-31 < y < 7.4e53

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 80.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}}{b} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{\mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}}{b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{y}}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z + \frac{t}{{y}^{2}}\right)}\right)}{b} \]

      6. unpow2 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \color{blue}{\mathsf{fma}\left(y, z, \frac{t}{{y}^{2}}\right)}\right)\right)}{b} \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \color{blue}{\frac{t}{{y}^{2}}}\right)\right)\right)}{b} \]

      10. unpow2 N/A

          \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \frac{t}{\color{blue}{y \cdot y}}\right)\right)\right)}{b} \]

      11. *-lowering-*.f64 41.9

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

   8. Simplified 41.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{y \cdot z}}{b} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 27.2

          \[\leadsto \frac{27464.7644705 + \color{blue}{y \cdot z}}{b} \]

   11. Simplified 27.2%

       \[\leadsto \frac{27464.7644705 + \color{blue}{y \cdot z}}{b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{t}{b}}{y \cdot y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+46}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -3e+30)
     t_1
     (if (<= y 4.3e+46) (/ t (fma y (fma y (fma y (+ y a) b) c) i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -3e+30) {
		tmp = t_1;
	} else if (y <= 4.3e+46) {
		tmp = t / fma(y, fma(y, fma(y, (y + a), b), c), i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -3e+30)
		tmp = t_1;
	elseif (y <= 4.3e+46)
		tmp = Float64(t / fma(y, fma(y, fma(y, Float64(y + a), b), c), i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e+30], t$95$1, If[LessEqual[y, 4.3e+46], N[(t / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999978e30 or 4.30000000000000005e46 < y

   1. Initial program 4.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 6.6%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 61.9

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

   8. Simplified 61.9%

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

   if -2.99999999999999978e30 < y < 4.30000000000000005e46

   1. Initial program 94.6%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 60.4

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

   5. Simplified 60.4%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+46}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 59.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -0.32:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+62}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -0.32)
     t_1
     (if (<= y 1.6e-31)
       (/ (fma 230661.510616 y t) i)
       (if (<= y 1.35e+62) (/ (+ 27464.7644705 (* y z)) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -0.32) {
		tmp = t_1;
	} else if (y <= 1.6e-31) {
		tmp = fma(230661.510616, y, t) / i;
	} else if (y <= 1.35e+62) {
		tmp = (27464.7644705 + (y * z)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -0.32)
		tmp = t_1;
	elseif (y <= 1.6e-31)
		tmp = Float64(fma(230661.510616, y, t) / i);
	elseif (y <= 1.35e+62)
		tmp = Float64(Float64(27464.7644705 + Float64(y * z)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.32], t$95$1, If[LessEqual[y, 1.6e-31], N[(N[(230661.510616 * y + t), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 1.35e+62], N[(N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.320000000000000007 or 1.35e62 < y

   1. Initial program 9.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 11.5%

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

   6. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 58.9

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

   8. Simplified 58.9%

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

   if -0.320000000000000007 < y < 1.60000000000000009e-31

   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 t around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 79.0

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

   8. Simplified 79.0%

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

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]

       2. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{i} \]

       3. accelerator-lowering-fma.f64 69.0

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{i} \]

   11. Simplified 69.0%

       \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}} \]

   if 1.60000000000000009e-31 < y < 1.35e62

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 80.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}}{b} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{\mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}}{b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{y}}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z + \frac{t}{{y}^{2}}\right)}\right)}{b} \]

      6. unpow2 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \color{blue}{\mathsf{fma}\left(y, z, \frac{t}{{y}^{2}}\right)}\right)\right)}{b} \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \color{blue}{\frac{t}{{y}^{2}}}\right)\right)\right)}{b} \]

      10. unpow2 N/A

          \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \frac{t}{\color{blue}{y \cdot y}}\right)\right)\right)}{b} \]

      11. *-lowering-*.f64 41.9

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

   8. Simplified 41.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{y \cdot z}}{b} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 27.2

          \[\leadsto \frac{27464.7644705 + \color{blue}{y \cdot z}}{b} \]

   11. Simplified 27.2%

       \[\leadsto \frac{27464.7644705 + \color{blue}{y \cdot z}}{b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.32:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+62}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 54.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.059:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+62}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -0.059)
   x
   (if (<= y 1.6e-31)
     (/ (fma 230661.510616 y t) i)
     (if (<= y 1.35e+62) (/ (+ 27464.7644705 (* y z)) b) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -0.059) {
		tmp = x;
	} else if (y <= 1.6e-31) {
		tmp = fma(230661.510616, y, t) / i;
	} else if (y <= 1.35e+62) {
		tmp = (27464.7644705 + (y * z)) / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -0.059)
		tmp = x;
	elseif (y <= 1.6e-31)
		tmp = Float64(fma(230661.510616, y, t) / i);
	elseif (y <= 1.35e+62)
		tmp = Float64(Float64(27464.7644705 + Float64(y * z)) / b);
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -0.059], x, If[LessEqual[y, 1.6e-31], N[(N[(230661.510616 * y + t), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 1.35e+62], N[(N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.058999999999999997 or 1.35e62 < y

   1. Initial program 10.7%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 42.7%

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

   if -0.058999999999999997 < y < 1.60000000000000009e-31

   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 t around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 80.2

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

   8. Simplified 80.2%

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

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]

       2. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{i} \]

       3. accelerator-lowering-fma.f64 70.2

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{i} \]

   11. Simplified 70.2%

       \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}} \]

   if 1.60000000000000009e-31 < y < 1.35e62

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 80.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}{b}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{54929528941}{2000000} + \left(\frac{28832688827}{125000} \cdot \frac{1}{y} + \left(x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)\right)}}{b} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{\mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}}{b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{y}}, x \cdot {y}^{2} + \left(y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \color{blue}{\mathsf{fma}\left(x, {y}^{2}, y \cdot z + \frac{t}{{y}^{2}}\right)}\right)}{b} \]

      6. unpow2 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, \color{blue}{y \cdot y}, y \cdot z + \frac{t}{{y}^{2}}\right)\right)}{b} \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \color{blue}{\mathsf{fma}\left(y, z, \frac{t}{{y}^{2}}\right)}\right)\right)}{b} \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \color{blue}{\frac{t}{{y}^{2}}}\right)\right)\right)}{b} \]

      10. unpow2 N/A

          \[\leadsto \frac{\frac{54929528941}{2000000} + \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{1}{y}, \mathsf{fma}\left(x, y \cdot y, \mathsf{fma}\left(y, z, \frac{t}{\color{blue}{y \cdot y}}\right)\right)\right)}{b} \]

      11. *-lowering-*.f64 41.9

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

   8. Simplified 41.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \frac{\frac{54929528941}{2000000} + \color{blue}{y \cdot z}}{b} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 27.2

          \[\leadsto \frac{27464.7644705 + \color{blue}{y \cdot z}}{b} \]

   11. Simplified 27.2%

       \[\leadsto \frac{27464.7644705 + \color{blue}{y \cdot z}}{b} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 54.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-28}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+55}:\\ \;\;\;\;\frac{y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -0.054)
   x
   (if (<= y 8e-28)
     (/ (fma 230661.510616 y t) i)
     (if (<= y 1.1e+55) (/ (* y z) b) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -0.054) {
		tmp = x;
	} else if (y <= 8e-28) {
		tmp = fma(230661.510616, y, t) / i;
	} else if (y <= 1.1e+55) {
		tmp = (y * z) / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -0.054)
		tmp = x;
	elseif (y <= 8e-28)
		tmp = Float64(fma(230661.510616, y, t) / i);
	elseif (y <= 1.1e+55)
		tmp = Float64(Float64(y * z) / b);
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -0.054], x, If[LessEqual[y, 8e-28], N[(N[(230661.510616 * y + t), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 1.1e+55], N[(N[(y * z), $MachinePrecision] / b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0539999999999999994 or 1.10000000000000005e55 < y

   1. Initial program 10.7%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 42.7%

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

   if -0.0539999999999999994 < y < 7.99999999999999977e-28

   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 t around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 80.4

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

   8. Simplified 80.4%

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

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]

       2. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{i} \]

       3. accelerator-lowering-fma.f64 69.6

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{i} \]

   11. Simplified 69.6%

       \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}} \]

   if 7.99999999999999977e-28 < y < 1.10000000000000005e55

   1. Initial program 64.1%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. cube-mult N/A

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

      5. unpow2 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{{y}^{2}}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(y \cdot {y}^{2}\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      7. unpow2 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. +-lowering-+.f64 18.2

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

   5. Simplified 18.2%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{b}} \]

      2. *-lowering-*.f64 28.2

         \[\leadsto \frac{\color{blue}{y \cdot z}}{b} \]

   8. Simplified 28.2%

      \[\leadsto \color{blue}{\frac{y \cdot z}{b}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 50.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{y \cdot z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.5e-9)
   x
   (if (<= y 8e-28) (/ t i) (if (<= y 8.2e+55) (/ (* y z) b) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.5e-9) {
		tmp = x;
	} else if (y <= 8e-28) {
		tmp = t / i;
	} else if (y <= 8.2e+55) {
		tmp = (y * z) / b;
	} 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 <= (-6.5d-9)) then
        tmp = x
    else if (y <= 8d-28) then
        tmp = t / i
    else if (y <= 8.2d+55) then
        tmp = (y * z) / b
    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 <= -6.5e-9) {
		tmp = x;
	} else if (y <= 8e-28) {
		tmp = t / i;
	} else if (y <= 8.2e+55) {
		tmp = (y * z) / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.5e-9:
		tmp = x
	elif y <= 8e-28:
		tmp = t / i
	elif y <= 8.2e+55:
		tmp = (y * z) / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.5e-9)
		tmp = x;
	elseif (y <= 8e-28)
		tmp = Float64(t / i);
	elseif (y <= 8.2e+55)
		tmp = Float64(Float64(y * z) / b);
	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 <= -6.5e-9)
		tmp = x;
	elseif (y <= 8e-28)
		tmp = t / i;
	elseif (y <= 8.2e+55)
		tmp = (y * z) / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.5e-9], x, If[LessEqual[y, 8e-28], N[(t / i), $MachinePrecision], If[LessEqual[y, 8.2e+55], N[(N[(y * z), $MachinePrecision] / b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000003e-9 or 8.19999999999999962e55 < y

   1. Initial program 12.6%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 41.9%

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

   if -6.5000000000000003e-9 < y < 7.99999999999999977e-28

   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

      \[\leadsto \color{blue}{\frac{t}{i}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 56.7

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

   5. Simplified 56.7%

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

   if 7.99999999999999977e-28 < y < 8.19999999999999962e55

   1. Initial program 64.1%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. cube-mult N/A

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

      5. unpow2 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{{y}^{2}}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(y \cdot {y}^{2}\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      7. unpow2 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. +-lowering-+.f64 18.2

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

   5. Simplified 18.2%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{b}} \]

      2. *-lowering-*.f64 28.2

         \[\leadsto \frac{\color{blue}{y \cdot z}}{b} \]

   8. Simplified 28.2%

      \[\leadsto \color{blue}{\frac{y \cdot z}{b}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 50.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 85000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.6e-10) x (if (<= y 85000000.0) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.6e-10) {
		tmp = x;
	} else if (y <= 85000000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-5.6d-10)) then
        tmp = x
    else if (y <= 85000000.0d0) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.6e-10) {
		tmp = x;
	} else if (y <= 85000000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.6e-10:
		tmp = x
	elif y <= 85000000.0:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.6e-10)
		tmp = x;
	elseif (y <= 85000000.0)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -5.6e-10)
		tmp = x;
	elseif (y <= 85000000.0)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.6e-10], x, If[LessEqual[y, 85000000.0], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.60000000000000031e-10 or 8.5e7 < y

   1. Initial program 14.1%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 39.6%

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

   if -5.60000000000000031e-10 < y < 8.5e7

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t}{i}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 51.9

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

   5. Simplified 51.9%

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

Alternative 23: 25.5% accurate, 71.0× 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 50.5%

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

3. Taylor expanded in y around inf

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

5. Simplified 24.1%

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

Reproduce

herbie shell --seed 2024196 
(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)))