Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.1% → 81.9%

Time: 8.9s

Alternatives: 19

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)\\ t_2 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right)}{t\_1}, \frac{t}{t\_1}\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+144}:\\ \;\;\;\;\frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, \mathsf{fma}\left(230661.510616, \frac{1}{y \cdot y}, \mathsf{fma}\left(x, y, \frac{t}{\left(y \cdot y\right) \cdot y}\right)\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma (fma (fma (+ a y) y b) y c) y i))
        (t_2 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -2.9e+69)
     t_2
     (if (<= y 2.2e+75)
       (fma
        y
        (/ (fma (fma (fma y x z) y 27464.7644705) y 230661.510616) t_1)
        (/ t t_1))
       (if (<= y 1.45e+144)
         (/
          (+
           z
           (fma
            27464.7644705
            (/ 1.0 y)
            (fma 230661.510616 (/ 1.0 (* y y)) (fma x y (/ t (* (* y y) y))))))
          a)
         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(fma(fma((a + y), y, b), y, c), y, i);
	double t_2 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -2.9e+69) {
		tmp = t_2;
	} else if (y <= 2.2e+75) {
		tmp = fma(y, (fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616) / t_1), (t / t_1));
	} else if (y <= 1.45e+144) {
		tmp = (z + fma(27464.7644705, (1.0 / y), fma(230661.510616, (1.0 / (y * y)), fma(x, y, (t / ((y * y) * y)))))) / a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(fma(fma(Float64(a + y), y, b), y, c), y, i)
	t_2 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -2.9e+69)
		tmp = t_2;
	elseif (y <= 2.2e+75)
		tmp = fma(y, Float64(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616) / t_1), Float64(t / t_1));
	elseif (y <= 1.45e+144)
		tmp = Float64(Float64(z + fma(27464.7644705, Float64(1.0 / y), fma(230661.510616, Float64(1.0 / Float64(y * y)), fma(x, y, Float64(t / Float64(Float64(y * y) * y)))))) / a);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]}, Block[{t$95$2 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -2.9e+69], t$95$2, If[LessEqual[y, 2.2e+75], N[(y * N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+144], N[(N[(z + N[(27464.7644705 * N[(1.0 / y), $MachinePrecision] + N[(230661.510616 * N[(1.0 / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(x * y + N[(t / N[(N[(y * y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8999999999999998e69 or 1.44999999999999999e144 < y

   1. Initial program 0.6%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 74.1

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

   4. Applied rewrites 74.1%

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

   if -2.8999999999999998e69 < y < 2.20000000000000012e75

   1. Initial program 90.3%

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

   3. Applied rewrites 91.2%

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

   if 2.20000000000000012e75 < y < 1.44999999999999999e144

   1. Initial program 2.7%

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

   3. Applied rewrites 3.6%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 26.5%

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

Alternative 2: 81.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+75}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+144}:\\ \;\;\;\;\frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, \mathsf{fma}\left(230661.510616, \frac{1}{y \cdot y}, \mathsf{fma}\left(x, y, \frac{t}{\left(y \cdot y\right) \cdot y}\right)\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -2.3e+52)
     t_1
     (if (<= y 2.1e+75)
       (/
        (+
         (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
         t)
        (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
       (if (<= y 1.45e+144)
         (/
          (+
           z
           (fma
            27464.7644705
            (/ 1.0 y)
            (fma 230661.510616 (/ 1.0 (* y y)) (fma x y (/ t (* (* y y) y))))))
          a)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -2.3e+52) {
		tmp = t_1;
	} else if (y <= 2.1e+75) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else if (y <= 1.45e+144) {
		tmp = (z + fma(27464.7644705, (1.0 / y), fma(230661.510616, (1.0 / (y * y)), fma(x, y, (t / ((y * y) * y)))))) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -2.3e+52)
		tmp = t_1;
	elseif (y <= 2.1e+75)
		tmp = 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));
	elseif (y <= 1.45e+144)
		tmp = Float64(Float64(z + fma(27464.7644705, Float64(1.0 / y), fma(230661.510616, Float64(1.0 / Float64(y * y)), fma(x, y, Float64(t / Float64(Float64(y * y) * y)))))) / a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -2.3e+52], t$95$1, If[LessEqual[y, 2.1e+75], 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], If[LessEqual[y, 1.45e+144], N[(N[(z + N[(27464.7644705 * N[(1.0 / y), $MachinePrecision] + N[(230661.510616 * N[(1.0 / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(x * y + N[(t / N[(N[(y * y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3e52 or 1.44999999999999999e144 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.1

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

   4. Applied rewrites 72.1%

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

   if -2.3e52 < y < 2.09999999999999999e75

   1. Initial program 91.9%

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

   if 2.09999999999999999e75 < y < 1.44999999999999999e144

   1. Initial program 2.7%

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

   3. Applied rewrites 3.6%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 26.5%

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

Alternative 3: 79.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+45}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+144}:\\ \;\;\;\;\frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, \mathsf{fma}\left(230661.510616, \frac{1}{y \cdot y}, \mathsf{fma}\left(x, y, \frac{t}{\left(y \cdot y\right) \cdot y}\right)\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -2.2e+52)
     t_1
     (if (<= y 1.95e+45)
       (/
        (fma (fma (fma z y 27464.7644705) y 230661.510616) y t)
        (fma (fma (fma (+ a y) y b) y c) y i))
       (if (<= y 1.45e+144)
         (/
          (+
           z
           (fma
            27464.7644705
            (/ 1.0 y)
            (fma 230661.510616 (/ 1.0 (* y y)) (fma x y (/ t (* (* y y) y))))))
          a)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -2.2e+52) {
		tmp = t_1;
	} else if (y <= 1.95e+45) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else if (y <= 1.45e+144) {
		tmp = (z + fma(27464.7644705, (1.0 / y), fma(230661.510616, (1.0 / (y * y)), fma(x, y, (t / ((y * y) * y)))))) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -2.2e+52)
		tmp = t_1;
	elseif (y <= 1.95e+45)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	elseif (y <= 1.45e+144)
		tmp = Float64(Float64(z + fma(27464.7644705, Float64(1.0 / y), fma(230661.510616, Float64(1.0 / Float64(y * y)), fma(x, y, Float64(t / Float64(Float64(y * y) * y)))))) / a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -2.2e+52], t$95$1, If[LessEqual[y, 1.95e+45], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+144], N[(N[(z + N[(27464.7644705 * N[(1.0 / y), $MachinePrecision] + N[(230661.510616 * N[(1.0 / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(x * y + N[(t / N[(N[(y * y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2e52 or 1.44999999999999999e144 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.1

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

   4. Applied rewrites 72.1%

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

   if -2.2e52 < y < 1.95e45

   1. Initial program 94.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 89.1%

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

   if 1.95e45 < y < 1.44999999999999999e144

   1. Initial program 10.9%

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

   3. Applied rewrites 13.8%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 28.1%

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

Alternative 4: 78.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+46}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -2.2e+52)
     t_1
     (if (<= y 8.8e+46)
       (/
        (fma (fma (fma z y 27464.7644705) y 230661.510616) y t)
        (fma (fma (fma a y b) y c) y 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 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -2.2e+52) {
		tmp = t_1;
	} else if (y <= 8.8e+46) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(a, y, b), y, c), y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -2.2e+52)
		tmp = t_1;
	elseif (y <= 8.8e+46)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(a, y, b), y, c), y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -2.2e+52], t$95$1, If[LessEqual[y, 8.8e+46], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(a * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e52 or 8.8000000000000001e46 < y

   1. Initial program 3.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 67.2

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

   4. Applied rewrites 67.2%

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

   if -2.2e52 < y < 8.8000000000000001e46

   1. Initial program 94.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 88.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a, y, b\right), y, c\right), y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.6%

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

Alternative 5: 78.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[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], Infinity], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $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 90.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 84.3%

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

   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. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 70.0

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

   4. Applied rewrites 70.0%

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

Alternative 6: 72.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+25}:\\ \;\;\;\;\left(-z\right) \cdot \left(-1 \cdot \frac{y \cdot y}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+46}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -5.6e+71)
     t_1
     (if (<= y -8.5e+25)
       (* (- z) (* -1.0 (/ (* y y) (+ c (* y (+ b (* y (+ a y))))))))
       (if (<= y 7.8e+46)
         (/
          (fma (fma (fma z y 27464.7644705) y 230661.510616) y t)
          (fma c y 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 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -5.6e+71) {
		tmp = t_1;
	} else if (y <= -8.5e+25) {
		tmp = -z * (-1.0 * ((y * y) / (c + (y * (b + (y * (a + y)))))));
	} else if (y <= 7.8e+46) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -5.6e+71)
		tmp = t_1;
	elseif (y <= -8.5e+25)
		tmp = Float64(Float64(-z) * Float64(-1.0 * Float64(Float64(y * y) / Float64(c + Float64(y * Float64(b + Float64(y * Float64(a + y))))))));
	elseif (y <= 7.8e+46)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -5.6e+71], t$95$1, If[LessEqual[y, -8.5e+25], N[((-z) * N[(-1.0 * N[(N[(y * y), $MachinePrecision] / N[(c + N[(y * N[(b + N[(y * N[(a + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+46], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000004e71 or 7.7999999999999999e46 < y

   1. Initial program 2.5%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 68.7

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

   4. Applied rewrites 68.7%

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

   if -5.60000000000000004e71 < y < -8.5000000000000007e25

   1. Initial program 34.4%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}}{z} + -1 \cdot \frac{{y}^{3}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   4. Applied rewrites 43.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto \left(-z\right) \cdot \left(-1 \cdot \color{blue}{\frac{{y}^{3}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(-z\right) \cdot \left(-1 \cdot \frac{{y}^{3}}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}}\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \left(-z\right) \cdot \left(-1 \cdot \frac{{y}^{3}}{i + \color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}}\right) \]

      3. pow3 N/A

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

      4. lift-*.f64 N/A

         \[\leadsto \left(-z\right) \cdot \left(-1 \cdot \frac{\left(y \cdot y\right) \cdot y}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) \]

      5. lift-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lift-+.f64 26.8

          \[\leadsto \left(-z\right) \cdot \left(-1 \cdot \frac{\left(y \cdot y\right) \cdot y}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) \]

   7. Applied rewrites 26.8%

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

   8. Taylor expanded in i around 0

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

      1. lower-/.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-+.f64 30.1

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

   10. Applied rewrites 30.1%

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

   if -8.5000000000000007e25 < y < 7.7999999999999999e46

   1. Initial program 96.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 91.2%

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

   5. Taylor expanded in y around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(c, y, i\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\\ t_2 := \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-190}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(27464.7644705, y, 230661.510616\right), y, t\right)}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot y, y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
        (t_2
         (/
          (+
           (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
           t)
          t_1)))
   (if (<= t_2 -1e-190)
     (/ (fma (fma 27464.7644705 y 230661.510616) y t) t_1)
     (if (<= t_2 5e+297)
       (/
        (fma (fma (fma z y 27464.7644705) y 230661.510616) y t)
        (fma (fma (* y y) y c) y i))
       (+ (- (/ (- (- z) (* (- a) x)) y)) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((((((y + a) * y) + b) * y) + c) * y) + i;
	double t_2 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1;
	double tmp;
	if (t_2 <= -1e-190) {
		tmp = fma(fma(27464.7644705, y, 230661.510616), y, t) / t_1;
	} else if (t_2 <= 5e+297) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma((y * y), y, c), y, i);
	} else {
		tmp = -((-z - (-a * x)) / y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i)
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1)
	tmp = 0.0
	if (t_2 <= -1e-190)
		tmp = Float64(fma(fma(27464.7644705, y, 230661.510616), y, t) / t_1);
	elseif (t_2 <= 5e+297)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(Float64(y * y), y, c), y, i));
	else
		tmp = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$2 = 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] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-190], N[(N[(N[(27464.7644705 * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 5e+297], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(y * y), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $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)) < -1e-190

   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. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 78.4

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

   4. Applied rewrites 78.4%

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

   if -1e-190 < (/.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)) < 4.9999999999999998e297

   1. Initial program 90.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 84.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left({y}^{2}, y, c\right), y, i\right)} \]
   6. Step-by-step derivation

      1. pow2 N/A

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

      2. lift-*.f64 74.7

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

   7. Applied rewrites 74.7%

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

   if 4.9999999999999998e297 < (/.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 4.5%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 67.4

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

   4. Applied rewrites 67.4%

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

Alternative 8: 72.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+46}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1.3e+52)
     t_1
     (if (<= y 7.8e+46)
       (/ (fma (fma (fma z y 27464.7644705) y 230661.510616) y t) (fma c y 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 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1.3e+52) {
		tmp = t_1;
	} else if (y <= 7.8e+46) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1.3e+52)
		tmp = t_1;
	elseif (y <= 7.8e+46)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1.3e+52], t$95$1, If[LessEqual[y, 7.8e+46], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e52 or 7.7999999999999999e46 < y

   1. Initial program 3.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 67.2

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

   4. Applied rewrites 67.2%

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

   if -1.3e52 < y < 7.7999999999999999e46

   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. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 88.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 76.3%

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

Alternative 9: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot y, y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      5e+297)
   (/
    (fma (fma (fma z y 27464.7644705) y 230661.510616) y t)
    (fma (fma (* y y) y c) y i))
   (+ (- (/ (- (- z) (* (- a) x)) y)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 5e+297) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma((y * y), y, c), y, i);
	} else {
		tmp = -((-z - (-a * x)) / y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (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)) <= 5e+297)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(Float64(y * y), y, c), y, i));
	else
		tmp = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[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], 5e+297], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(y * y), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $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)) < 4.9999999999999998e297

   1. Initial program 92.0%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 85.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left({y}^{2}, y, c\right), y, i\right)} \]
   6. Step-by-step derivation

      1. pow2 N/A

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

      2. lift-*.f64 74.5

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

   7. Applied rewrites 74.5%

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

   if 4.9999999999999998e297 < (/.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 4.5%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 67.4

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

   4. Applied rewrites 67.4%

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

Alternative 10: 68.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1.95e+29)
     t_1
     (if (<= y 3.7e+31) (/ t (fma (fma (fma (+ a y) y b) y c) y 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 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1.95e+29) {
		tmp = t_1;
	} else if (y <= 3.7e+31) {
		tmp = t / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1.95e+29)
		tmp = t_1;
	elseif (y <= 3.7e+31)
		tmp = Float64(t / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1.95e+29], t$95$1, If[LessEqual[y, 3.7e+31], N[(t / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.94999999999999984e29 or 3.6999999999999998e31 < y

   1. Initial program 5.6%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 63.9

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

   4. Applied rewrites 63.9%

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

   if -1.94999999999999984e29 < y < 3.6999999999999998e31

   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. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 72.4

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

   4. Applied rewrites 72.4%

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

Alternative 11: 61.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;\left(\left(y \cdot y\right) \cdot y\right) \cdot \frac{z}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot \left(y \cdot y\right), y, 230661.510616\right), y, t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -3.8e+49)
     t_1
     (if (<= y -3.6e-56)
       (* (* (* y y) y) (/ z (fma c y i)))
       (if (<= y 7.5e+20)
         (/ (fma (fma (* x (* y y)) y 230661.510616) y t) 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 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -3.8e+49) {
		tmp = t_1;
	} else if (y <= -3.6e-56) {
		tmp = ((y * y) * y) * (z / fma(c, y, i));
	} else if (y <= 7.5e+20) {
		tmp = fma(fma((x * (y * y)), y, 230661.510616), y, t) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -3.8e+49)
		tmp = t_1;
	elseif (y <= -3.6e-56)
		tmp = Float64(Float64(Float64(y * y) * y) * Float64(z / fma(c, y, i)));
	elseif (y <= 7.5e+20)
		tmp = Float64(fma(fma(Float64(x * Float64(y * y)), y, 230661.510616), y, t) / i);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -3.8e+49], t$95$1, If[LessEqual[y, -3.6e-56], N[(N[(N[(y * y), $MachinePrecision] * y), $MachinePrecision] * N[(z / N[(c * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+20], N[(N[(N[(N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999999e49 or 7.5e20 < y

   1. Initial program 5.7%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 64.6

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

   4. Applied rewrites 64.6%

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

   if -3.7999999999999999e49 < y < -3.59999999999999978e-56

   1. Initial program 78.3%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

         \[\leadsto \left({y}^{2} \cdot y\right) \cdot \frac{z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 28.3%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(\left(y \cdot y\right) \cdot y\right) \cdot \frac{z}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 14.0%

      \[\leadsto \left(\left(y \cdot y\right) \cdot y\right) \cdot \frac{z}{\mathsf{fma}\left(c, y, i\right)} \]

   if -3.59999999999999978e-56 < y < 7.5e20

   1. Initial program 99.0%

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

   2. Taylor expanded in i around inf

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

      1. lower-/.f64 N/A

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

   4. Applied rewrites 67.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot {y}^{2}, y, \frac{28832688827}{125000}\right), y, t\right)}{i} \]
   6. Step-by-step derivation

      1. pow2 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot \left(y \cdot y\right), y, \frac{28832688827}{125000}\right), y, t\right)}{i} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot \left(y \cdot y\right), y, \frac{28832688827}{125000}\right), y, t\right)}{i} \]

      3. lift-*.f64 66.0

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

   7. Applied rewrites 66.0%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot \left(y \cdot y\right), y, 230661.510616\right), y, t\right)}{i} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 61.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot y\right) \cdot y\\ t_2 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;t\_1 \cdot \frac{z}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{\left(t\_1 \cdot x + 230661.510616\right) \cdot y + t}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* y y) y)) (t_2 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -3.8e+49)
     t_2
     (if (<= y -3.6e-56)
       (* t_1 (/ z (fma c y i)))
       (if (<= y 7.5e+20)
         (/ (+ (* (+ (* t_1 x) 230661.510616) y) t) i)
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * y) * y;
	double t_2 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -3.8e+49) {
		tmp = t_2;
	} else if (y <= -3.6e-56) {
		tmp = t_1 * (z / fma(c, y, i));
	} else if (y <= 7.5e+20) {
		tmp = ((((t_1 * x) + 230661.510616) * y) + t) / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * y) * y)
	t_2 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -3.8e+49)
		tmp = t_2;
	elseif (y <= -3.6e-56)
		tmp = Float64(t_1 * Float64(z / fma(c, y, i)));
	elseif (y <= 7.5e+20)
		tmp = Float64(Float64(Float64(Float64(Float64(t_1 * x) + 230661.510616) * y) + t) / i);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * y), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -3.8e+49], t$95$2, If[LessEqual[y, -3.6e-56], N[(t$95$1 * N[(z / N[(c * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+20], N[(N[(N[(N[(N[(t$95$1 * x), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / i), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999999e49 or 7.5e20 < y

   1. Initial program 5.7%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 64.6

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

   4. Applied rewrites 64.6%

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

   if -3.7999999999999999e49 < y < -3.59999999999999978e-56

   1. Initial program 78.3%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

         \[\leadsto \left({y}^{2} \cdot y\right) \cdot \frac{z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 28.3%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(\left(y \cdot y\right) \cdot y\right) \cdot \frac{z}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 14.0%

      \[\leadsto \left(\left(y \cdot y\right) \cdot y\right) \cdot \frac{z}{\mathsf{fma}\left(c, y, i\right)} \]

   if -3.59999999999999978e-56 < y < 7.5e20

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

         \[\leadsto \frac{\left(\left({y}^{2} \cdot y\right) \cdot x + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left({y}^{2} \cdot y\right) \cdot x + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. unpow2 N/A

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

      7. lower-*.f64 94.0

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

   4. Applied rewrites 94.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 66.0%

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

Alternative 13: 60.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-47}:\\ \;\;\;\;\left(\left(y \cdot y\right) \cdot y\right) \cdot \frac{z}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -3.8e+49)
     t_1
     (if (<= y -2.3e-47)
       (* (* (* y y) y) (/ z (fma c y i)))
       (if (<= y 3.2e+20) (/ (fma 230661.510616 y t) 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 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -3.8e+49) {
		tmp = t_1;
	} else if (y <= -2.3e-47) {
		tmp = ((y * y) * y) * (z / fma(c, y, i));
	} else if (y <= 3.2e+20) {
		tmp = fma(230661.510616, y, t) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -3.8e+49)
		tmp = t_1;
	elseif (y <= -2.3e-47)
		tmp = Float64(Float64(Float64(y * y) * y) * Float64(z / fma(c, y, i)));
	elseif (y <= 3.2e+20)
		tmp = Float64(fma(230661.510616, y, t) / i);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -3.8e+49], t$95$1, If[LessEqual[y, -2.3e-47], N[(N[(N[(y * y), $MachinePrecision] * y), $MachinePrecision] * N[(z / N[(c * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+20], N[(N[(230661.510616 * y + t), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999999e49 or 3.2e20 < y

   1. Initial program 5.8%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 64.5

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

   4. Applied rewrites 64.5%

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

   if -3.7999999999999999e49 < y < -2.29999999999999982e-47

   1. Initial program 76.5%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

         \[\leadsto \left({y}^{2} \cdot y\right) \cdot \frac{z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 28.8%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(\left(y \cdot y\right) \cdot y\right) \cdot \frac{z}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 14.4%

      \[\leadsto \left(\left(y \cdot y\right) \cdot y\right) \cdot \frac{z}{\mathsf{fma}\left(c, y, i\right)} \]

   if -2.29999999999999982e-47 < y < 3.2e20

   1. Initial program 99.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-/.f64 N/A

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

   4. Applied rewrites 67.5%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 64.6%

      \[\leadsto \frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 58.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;\left(-z\right) \cdot \left(-1 \cdot \frac{y \cdot y}{c}\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+31}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot z, y, t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -8.5e+46)
     t_1
     (if (<= y -1.45e-31)
       (* (- z) (* -1.0 (/ (* y y) c)))
       (if (<= y 2.9e+31) (/ (fma (* (* y y) z) y t) 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 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -8.5e+46) {
		tmp = t_1;
	} else if (y <= -1.45e-31) {
		tmp = -z * (-1.0 * ((y * y) / c));
	} else if (y <= 2.9e+31) {
		tmp = fma(((y * y) * z), y, t) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -8.5e+46)
		tmp = t_1;
	elseif (y <= -1.45e-31)
		tmp = Float64(Float64(-z) * Float64(-1.0 * Float64(Float64(y * y) / c)));
	elseif (y <= 2.9e+31)
		tmp = Float64(fma(Float64(Float64(y * y) * z), y, t) / i);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -8.5e+46], t$95$1, If[LessEqual[y, -1.45e-31], N[((-z) * N[(-1.0 * N[(N[(y * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+31], N[(N[(N[(N[(y * y), $MachinePrecision] * z), $MachinePrecision] * y + t), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4999999999999996e46 or 2.9e31 < y

   1. Initial program 4.5%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 65.4

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

   4. Applied rewrites 65.4%

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

   if -8.4999999999999996e46 < y < -1.45e-31

   1. Initial program 73.4%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}}{z} + -1 \cdot \frac{{y}^{3}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in c around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

   7. Applied rewrites 17.7%

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

   8. Taylor expanded in z around inf

      \[\leadsto \left(-z\right) \cdot \left(-1 \cdot \frac{{y}^{2}}{c}\right) \]
   9. Step-by-step derivation

      1. pow2 N/A

         \[\leadsto \left(-z\right) \cdot \left(-1 \cdot \frac{y \cdot y}{c}\right) \]

      2. lift-*.f64 9.6

         \[\leadsto \left(-z\right) \cdot \left(-1 \cdot \frac{y \cdot y}{c}\right) \]

   10. Applied rewrites 9.6%

       \[\leadsto \left(-z\right) \cdot \left(-1 \cdot \frac{y \cdot y}{c}\right) \]

   if -1.45e-31 < y < 2.9e31

   1. Initial program 98.5%

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

   2. Taylor expanded in i around inf

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

      1. lower-/.f64 N/A

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

   4. Applied rewrites 65.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto \frac{\mathsf{fma}\left({y}^{2} \cdot z, y, t\right)}{i} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left({y}^{2} \cdot z, y, t\right)}{i} \]

      2. pow2 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot z, y, t\right)}{i} \]

      3. lift-*.f64 57.6

         \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot z, y, t\right)}{i} \]

   7. Applied rewrites 57.6%

      \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot z, y, t\right)}{i} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 54.6% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      INFINITY)
   (/ (fma 230661.510616 y 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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = fma(230661.510616, y, t) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

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

Wolfram

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

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 90.1%

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

   2. Taylor expanded in i around inf

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

      1. lower-/.f64 N/A

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

   4. Applied rewrites 55.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 52.1%

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

   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. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 58.6%

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

Alternative 16: 51.2% accurate, 0.9× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      INFINITY)
   (/ 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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Java

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

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= math.inf:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[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], Infinity], N[(t / i), $MachinePrecision], x]

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 90.1%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 46.7

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

   4. Applied rewrites 46.7%

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

   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. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 58.6%

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

Alternative 17: 26.6% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+253}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{+57}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.3e+253) (/ z a) (if (<= z -1.08e+57) (/ z y) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.3e+253) {
		tmp = z / a;
	} else if (z <= -1.08e+57) {
		tmp = z / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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 (z <= (-1.3d+253)) then
        tmp = z / a
    else if (z <= (-1.08d+57)) then
        tmp = z / y
    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 (z <= -1.3e+253) {
		tmp = z / a;
	} else if (z <= -1.08e+57) {
		tmp = z / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.3e+253:
		tmp = z / a
	elif z <= -1.08e+57:
		tmp = z / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.3e+253)
		tmp = Float64(z / a);
	elseif (z <= -1.08e+57)
		tmp = Float64(z / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.3e+253)
		tmp = z / a;
	elseif (z <= -1.08e+57)
		tmp = z / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.3e+253], N[(z / a), $MachinePrecision], If[LessEqual[z, -1.08e+57], N[(z / y), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e253

   1. Initial program 51.2%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

         \[\leadsto \left({y}^{2} \cdot y\right) \cdot \frac{z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 22.4%

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

   5. Taylor expanded in a around inf

      \[\leadsto \frac{z}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 13.1

         \[\leadsto \frac{z}{a} \]

   7. Applied rewrites 13.1%

      \[\leadsto \frac{z}{\color{blue}{a}} \]

   if -1.3e253 < z < -1.08000000000000004e57

   1. Initial program 56.2%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

         \[\leadsto \left({y}^{2} \cdot y\right) \cdot \frac{z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 16.1%

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

   5. Taylor expanded in y around inf

      \[\leadsto \frac{z}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. lower-/.f64 17.3

         \[\leadsto \frac{z}{y} \]

   7. Applied rewrites 17.3%

      \[\leadsto \frac{z}{\color{blue}{y}} \]

   if -1.08000000000000004e57 < z

   1. Initial program 56.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 27.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 25.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leq 2 \cdot 10^{+81}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      2e+81)
   (/ z a)
   x))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2e+81) {
		tmp = z / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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 ((((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2d+81) then
        tmp = z / a
    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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2e+81) {
		tmp = z / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2e+81:
		tmp = z / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (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)) <= 2e+81)
		tmp = Float64(z / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2e+81)
		tmp = z / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[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], 2e+81], N[(z / a), $MachinePrecision], x]

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)) < 1.99999999999999984e81

   1. Initial program 91.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

         \[\leadsto \left({y}^{2} \cdot y\right) \cdot \frac{z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 18.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto \frac{z}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 6.9

         \[\leadsto \frac{z}{a} \]

   7. Applied rewrites 6.9%

      \[\leadsto \frac{z}{\color{blue}{a}} \]

   if 1.99999999999999984e81 < (/.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 16.9%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 48.6%

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

Alternative 19: 25.4% accurate, 46.9× 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return x;
}

Python

def code(x, y, z, t, a, b, c, i):
	return x

Julia

function code(x, y, z, t, a, b, c, i)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := x

Derivation

1. Initial program 56.1%

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

2. Taylor expanded in y around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 25.7%

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

Reproduce

herbie shell --seed 2025114 
(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)))