Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.8% → 85.3%

Time: 7.8s

Alternatives: 17

Speedup: 2.3×

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: 56.8% 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: 85.3% accurate, 0.4× speedup

Math

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

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)))
   (if (<=
        (/
         (+
          (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
          t)
         (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
        INFINITY)
     (fma
      (fma (fma x y z) y 27464.7644705)
      (* y (/ y t_1))
      (/ (fma y 230661.510616 t) t_1))
     (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y))))))

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 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(x, y, z), y, 27464.7644705), (y * (y / t_1)), (fma(y, 230661.510616, t) / t_1));
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	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)
	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 = fma(fma(fma(x, y, z), y, 27464.7644705), Float64(y * Float64(y / t_1)), Float64(fma(y, 230661.510616, t) / t_1));
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	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]}, 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[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * N[(y * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(y * 230661.510616 + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #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 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

      1. lift-fma.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. associate-*l* N/A

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 58.2%

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

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

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 85.1% accurate, 0.4× speedup

Math

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

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)))
   (if (<=
        (/
         (+
          (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
          t)
         (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
        INFINITY)
     (fma
      (/ y t_1)
      (fma (fma (fma y x z) y 27464.7644705) y 230661.510616)
      (/ t t_1))
     (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y))))))

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 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((y / t_1), fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), (t / t_1));
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	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)
	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 = fma(Float64(y / t_1), fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), Float64(t / t_1));
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	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]}, 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[(y / t$95$1), $MachinePrecision] * N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #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 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   if +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 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\\ \end{array} \end{array} \]

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 (fma y x z) y 27464.7644705) y 230661.510616) y t)
    (fma (fma (fma (+ a y) y b) y c) y i))
   (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y)))))

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(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	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(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	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[(N[(y * x + z), $MachinePrecision] * 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[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #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 56.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 56.8

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 56.8

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 56.8

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

      10. lift-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 56.8

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

      14. lift-+.f64 N/A

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

   3. Applied rewrites 56.8%

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

   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 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 78.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{z - a \cdot x}{y}\\ \mathbf{elif}\;y \leq 0.135:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(b, y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.1e+45)
   (+ x (/ (- z (* a x)) y))
   (if (<= y 0.135)
     (/
      (fma (fma (fma (fma y x z) y 27464.7644705) y 230661.510616) y t)
      (fma (fma b y c) y i))
     (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.1e+45) {
		tmp = x + ((z - (a * x)) / y);
	} else if (y <= 0.135) {
		tmp = fma(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(b, y, c), y, i);
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.1e+45)
		tmp = Float64(x + Float64(Float64(z - Float64(a * x)) / y));
	elseif (y <= 0.135)
		tmp = Float64(fma(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(b, y, c), y, i));
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.1e+45], N[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.135], N[(N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(b * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999988e45

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -3.09999999999999988e45 < y < 0.13500000000000001

   1. Initial program 56.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 56.8

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 56.8

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 56.8

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

      10. lift-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 56.8

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

      14. lift-+.f64 N/A

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

   3. Applied rewrites 56.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 51.6%

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

   if 0.13500000000000001 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{z - a \cdot x}{y}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-9}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(b \cdot y, y, i\right)}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(27464.7644705, y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.15e+40)
   (+ x (/ (- z (* a x)) y))
   (if (<= y -1.65e-9)
     (/
      (fma (fma (fma (fma y x z) y 27464.7644705) y 230661.510616) y t)
      (fma (* b y) y i))
     (if (<= y 1.26e+14)
       (/
        (fma (fma 27464.7644705 y 230661.510616) y t)
        (fma (fma (fma (+ a y) y b) y c) y i))
       (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.15e+40) {
		tmp = x + ((z - (a * x)) / y);
	} else if (y <= -1.65e-9) {
		tmp = fma(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma((b * y), y, i);
	} else if (y <= 1.26e+14) {
		tmp = fma(fma(27464.7644705, y, 230661.510616), y, t) / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.15e+40)
		tmp = Float64(x + Float64(Float64(z - Float64(a * x)) / y));
	elseif (y <= -1.65e-9)
		tmp = Float64(fma(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(Float64(b * y), y, i));
	elseif (y <= 1.26e+14)
		tmp = Float64(fma(fma(27464.7644705, y, 230661.510616), y, t) / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.15e+40], N[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.65e-9], N[(N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(b * y), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+14], N[(N[(N[(27464.7644705 * 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[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.14999999999999997e40

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -1.14999999999999997e40 < y < -1.65000000000000009e-9

   1. Initial program 56.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 56.8

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 56.8

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 56.8

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

      10. lift-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 56.8

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

      14. lift-+.f64 N/A

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

   3. Applied rewrites 56.8%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 38.8

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

   6. Applied rewrites 38.8%

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

   if -1.65000000000000009e-9 < y < 1.26e14

   1. Initial program 56.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 48.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 48.6

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 48.6

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 48.6

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

   6. Applied rewrites 48.6%

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

   if 1.26e14 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 75.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{z - a \cdot x}{y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(27464.7644705, y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.6e+33)
   (+ x (/ (- z (* a x)) y))
   (if (<= y -1.5e-51)
     (/
      (fma (fma (fma (fma y x z) y 27464.7644705) y 230661.510616) y t)
      (fma c y i))
     (if (<= y 1.26e+14)
       (/
        (fma (fma 27464.7644705 y 230661.510616) y t)
        (fma (fma (fma (+ a y) y b) y c) y i))
       (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.6e+33) {
		tmp = x + ((z - (a * x)) / y);
	} else if (y <= -1.5e-51) {
		tmp = fma(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(c, y, i);
	} else if (y <= 1.26e+14) {
		tmp = fma(fma(27464.7644705, y, 230661.510616), y, t) / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.6e+33)
		tmp = Float64(x + Float64(Float64(z - Float64(a * x)) / y));
	elseif (y <= -1.5e-51)
		tmp = Float64(fma(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(c, y, i));
	elseif (y <= 1.26e+14)
		tmp = Float64(fma(fma(27464.7644705, y, 230661.510616), y, t) / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.6e+33], N[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e-51], N[(N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+14], N[(N[(N[(27464.7644705 * 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[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6000000000000003e33

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -3.6000000000000003e33 < y < -1.50000000000000001e-51

   1. Initial program 56.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 56.8

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 56.8

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 56.8

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

      10. lift-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 56.8

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

      14. lift-+.f64 N/A

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

   3. Applied rewrites 56.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 46.5%

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

   if -1.50000000000000001e-51 < y < 1.26e14

   1. Initial program 56.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 48.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 48.6

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 48.6

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 48.6

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

   6. Applied rewrites 48.6%

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

   if 1.26e14 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 75.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{z - a \cdot x}{y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.6e+33)
   (+ x (/ (- z (* a x)) y))
   (if (<= y -1.5e-51)
     (/
      (fma (fma (fma (fma y x z) y 27464.7644705) y 230661.510616) y t)
      (fma c y i))
     (if (<= y 1.26e+14)
       (/ (fma 230661.510616 y t) (fma (fma (fma (+ a y) y b) y c) y i))
       (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.6e+33) {
		tmp = x + ((z - (a * x)) / y);
	} else if (y <= -1.5e-51) {
		tmp = fma(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(c, y, i);
	} else if (y <= 1.26e+14) {
		tmp = fma(230661.510616, y, t) / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.6e+33)
		tmp = Float64(x + Float64(Float64(z - Float64(a * x)) / y));
	elseif (y <= -1.5e-51)
		tmp = Float64(fma(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(c, y, i));
	elseif (y <= 1.26e+14)
		tmp = Float64(fma(230661.510616, y, t) / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.6e+33], N[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e-51], N[(N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+14], N[(N[(230661.510616 * y + t), $MachinePrecision] / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6000000000000003e33

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -3.6000000000000003e33 < y < -1.50000000000000001e-51

   1. Initial program 56.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 56.8

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 56.8

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 56.8

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

      10. lift-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 56.8

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

      14. lift-+.f64 N/A

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

   3. Applied rewrites 56.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 46.5%

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

   if -1.50000000000000001e-51 < y < 1.26e14

   1. Initial program 56.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 56.8

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 56.8

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 56.8

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

      10. lift-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 56.8

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

      14. lift-+.f64 N/A

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

   3. Applied rewrites 56.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 48.7%

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

   if 1.26e14 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 75.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{z - a \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.35e+30)
   (+ x (/ (- z (* a x)) y))
   (if (<= y 1.26e+14)
     (/ (fma 230661.510616 y t) (fma (fma (fma (+ a y) y b) y c) y i))
     (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.35e+30) {
		tmp = x + ((z - (a * x)) / y);
	} else if (y <= 1.26e+14) {
		tmp = fma(230661.510616, y, t) / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.35e+30)
		tmp = Float64(x + Float64(Float64(z - Float64(a * x)) / y));
	elseif (y <= 1.26e+14)
		tmp = Float64(fma(230661.510616, y, t) / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.35e+30], N[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+14], N[(N[(230661.510616 * y + t), $MachinePrecision] / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3499999999999999e30

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -1.3499999999999999e30 < y < 1.26e14

   1. Initial program 56.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 56.8

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 56.8

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 56.8

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

      10. lift-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 56.8

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

      14. lift-+.f64 N/A

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

   3. Applied rewrites 56.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 48.7%

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

   if 1.26e14 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 70.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{z - a \cdot x}{y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-215}:\\ \;\;\;\;\frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{c \cdot y + i}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.8e+47)
   (+ x (/ (- z (* a x)) y))
   (if (<= y 5e-215)
     (/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* c y) i))
     (if (<= y 1.26e+14)
       (/ t (fma (fma (fma (+ a y) y b) y c) y i))
       (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.8e+47) {
		tmp = x + ((z - (a * x)) / y);
	} else if (y <= 5e-215) {
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / ((c * y) + i);
	} else if (y <= 1.26e+14) {
		tmp = t / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.8e+47)
		tmp = Float64(x + Float64(Float64(z - Float64(a * x)) / y));
	elseif (y <= 5e-215)
		tmp = Float64(Float64(Float64(Float64(Float64(27464.7644705 * y) + 230661.510616) * y) + t) / Float64(Float64(c * y) + i));
	elseif (y <= 1.26e+14)
		tmp = Float64(t / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.8e+47], N[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-215], N[(N[(N[(N[(N[(27464.7644705 * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+14], N[(t / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999961e47

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -5.79999999999999961e47 < y < 4.99999999999999956e-215

   1. Initial program 56.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 48.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 42.5

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

   7. Applied rewrites 42.5%

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

   if 4.99999999999999956e-215 < y < 1.26e14

   1. Initial program 56.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 56.8

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 56.8

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 56.8

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

      10. lift-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 56.8

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

      14. lift-+.f64 N/A

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

   3. Applied rewrites 56.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 41.4%

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

   if 1.26e14 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 69.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{z - a \cdot x}{y}\\ \mathbf{elif}\;y \leq 0.13:\\ \;\;\;\;\frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{c \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.8e+47)
   (+ x (/ (- z (* a x)) y))
   (if (<= y 0.13)
     (/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* c y) i))
     (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.8e+47) {
		tmp = x + ((z - (a * x)) / y);
	} else if (y <= 0.13) {
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / ((c * y) + i);
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	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 (y <= (-5.8d+47)) then
        tmp = x + ((z - (a * x)) / y)
    else if (y <= 0.13d0) then
        tmp = ((((27464.7644705d0 * y) + 230661.510616d0) * y) + t) / ((c * y) + i)
    else
        tmp = x + ((-1.0d0) * ((z * ((a / y) - 1.0d0)) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.8e+47) {
		tmp = x + ((z - (a * x)) / y);
	} else if (y <= 0.13) {
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / ((c * y) + i);
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.8e+47:
		tmp = x + ((z - (a * x)) / y)
	elif y <= 0.13:
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / ((c * y) + i)
	else:
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.8e+47)
		tmp = Float64(x + Float64(Float64(z - Float64(a * x)) / y));
	elseif (y <= 0.13)
		tmp = Float64(Float64(Float64(Float64(Float64(27464.7644705 * y) + 230661.510616) * y) + t) / Float64(Float64(c * y) + i));
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -5.8e+47)
		tmp = x + ((z - (a * x)) / y);
	elseif (y <= 0.13)
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / ((c * y) + i);
	else
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.8e+47], N[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.13], N[(N[(N[(N[(N[(27464.7644705 * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999961e47

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -5.79999999999999961e47 < y < 0.13

   1. Initial program 56.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 48.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 42.5

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

   7. Applied rewrites 42.5%

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

   if 0.13 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 60.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{z - a \cdot x}{y}\\ \mathbf{elif}\;y \leq 0.13:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot z, y, 230661.510616\right), y, t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7.5e+16)
   (+ x (/ (- z (* a x)) y))
   (if (<= y 0.13)
     (/ (fma (fma (* y z) y 230661.510616) y t) i)
     (+ x (* -1.0 (/ (* z (- (/ a y) 1.0)) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7.5e+16) {
		tmp = x + ((z - (a * x)) / y);
	} else if (y <= 0.13) {
		tmp = fma(fma((y * z), y, 230661.510616), y, t) / i;
	} else {
		tmp = x + (-1.0 * ((z * ((a / y) - 1.0)) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7.5e+16)
		tmp = Float64(x + Float64(Float64(z - Float64(a * x)) / y));
	elseif (y <= 0.13)
		tmp = Float64(fma(fma(Float64(y * z), y, 230661.510616), y, t) / i);
	else
		tmp = Float64(x + Float64(-1.0 * Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7.5e+16], N[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.13], N[(N[(N[(N[(y * z), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / i), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5e16

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -7.5e16 < y < 0.13

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 56.5

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

   3. Applied rewrites 56.5%

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

   4. Taylor expanded in y around 0

      \[\leadsto \frac{1}{\frac{\color{blue}{i}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 33.6%

      \[\leadsto \frac{1}{\frac{\color{blue}{i}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip-rev N/A

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

      4. lower-/.f64 33.9

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

   8. Applied rewrites 33.9%

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

   9. Taylor expanded in z around inf

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

       1. lower-*.f64 32.8

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

   11. Applied rewrites 32.8%

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

   if 0.13 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 32.9

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

   9. Applied rewrites 32.9%

      \[\leadsto x + -1 \cdot \frac{z \cdot \left(\frac{a}{y} - 1\right)}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 59.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - a \cdot x}{y}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.13:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot z, y, 230661.510616\right), y, t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* a x)) y))))
   (if (<= y -7.5e+16)
     t_1
     (if (<= y 0.13) (/ (fma (fma (* y z) 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 = x + ((z - (a * x)) / y);
	double tmp;
	if (y <= -7.5e+16) {
		tmp = t_1;
	} else if (y <= 0.13) {
		tmp = fma(fma((y * z), 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(x + Float64(Float64(z - Float64(a * x)) / y))
	tmp = 0.0
	if (y <= -7.5e+16)
		tmp = t_1;
	elseif (y <= 0.13)
		tmp = Float64(fma(fma(Float64(y * z), 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[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+16], t$95$1, If[LessEqual[y, 0.13], N[(N[(N[(N[(y * z), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e16 or 0.13 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -7.5e16 < y < 0.13

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 56.5

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

   3. Applied rewrites 56.5%

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

   4. Taylor expanded in y around 0

      \[\leadsto \frac{1}{\frac{\color{blue}{i}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 33.6%

      \[\leadsto \frac{1}{\frac{\color{blue}{i}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip-rev N/A

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

      4. lower-/.f64 33.9

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

   8. Applied rewrites 33.9%

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

   9. Taylor expanded in z around inf

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

       1. lower-*.f64 32.8

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

   11. Applied rewrites 32.8%

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

Alternative 13: 58.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - a \cdot x}{y}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.13:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* a x)) y))))
   (if (<= y -7.2e+16)
     t_1
     (if (<= y 0.13) (fma y (/ 230661.510616 i) (/ 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 = x + ((z - (a * x)) / y);
	double tmp;
	if (y <= -7.2e+16) {
		tmp = t_1;
	} else if (y <= 0.13) {
		tmp = fma(y, (230661.510616 / i), (t / i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(a * x)) / y))
	tmp = 0.0
	if (y <= -7.2e+16)
		tmp = t_1;
	elseif (y <= 0.13)
		tmp = fma(y, Float64(230661.510616 / i), Float64(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[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+16], t$95$1, If[LessEqual[y, 0.13], N[(y * N[(230661.510616 / i), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e16 or 0.13 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -7.2e16 < y < 0.13

   1. Initial program 56.8%

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

   2. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \color{blue}{\frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{\color{blue}{c \cdot t}}{{i}^{2}}, \frac{t}{i}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot \color{blue}{t}}{{i}^{2}}, \frac{t}{i}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{\color{blue}{{i}^{2}}}, \frac{t}{i}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{\color{blue}{i}}^{2}}, \frac{t}{i}\right) \]

      7. lower-pow.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{\color{blue}{2}}}, \frac{t}{i}\right) \]

      8. lower-/.f64 25.7

         \[\leadsto \mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

   4. Applied rewrites 25.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 31.8

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

   7. Applied rewrites 31.8%

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

Alternative 14: 58.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - a \cdot x}{y}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.13:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* a x)) y))))
   (if (<= y -7.2e+16)
     t_1
     (if (<= y 0.13) (/ (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 = x + ((z - (a * x)) / y);
	double tmp;
	if (y <= -7.2e+16) {
		tmp = t_1;
	} else if (y <= 0.13) {
		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(x + Float64(Float64(z - Float64(a * x)) / y))
	tmp = 0.0
	if (y <= -7.2e+16)
		tmp = t_1;
	elseif (y <= 0.13)
		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[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+16], t$95$1, If[LessEqual[y, 0.13], N[(N[(230661.510616 * y + t), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e16 or 0.13 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

   3. Applied rewrites 57.6%

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

   4. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{-1 \cdot \left(z - a \cdot x\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + \left(-1 \cdot \left(a \cdot \left(z - a \cdot x\right)\right) + -1 \cdot \left(b \cdot x\right)\right)}{y}}{\color{blue}{y}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 30.6

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

   9. Applied rewrites 30.6%

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

   if -7.2e16 < y < 0.13

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 56.5

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

   3. Applied rewrites 56.5%

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

   4. Taylor expanded in y around 0

      \[\leadsto \frac{1}{\frac{\color{blue}{i}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 33.6%

      \[\leadsto \frac{1}{\frac{\color{blue}{i}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip-rev N/A

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

      4. lower-/.f64 33.9

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

   8. Applied rewrites 33.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 31.9%

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

Alternative 15: 52.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{1}{x}}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ 1.0 x))))
   (if (<= y -6.5e+16)
     t_1
     (if (<= y 1.26e-26) (/ (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 = 1.0 / (1.0 / x);
	double tmp;
	if (y <= -6.5e+16) {
		tmp = t_1;
	} else if (y <= 1.26e-26) {
		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(1.0 / Float64(1.0 / x))
	tmp = 0.0
	if (y <= -6.5e+16)
		tmp = t_1;
	elseif (y <= 1.26e-26)
		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[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+16], t$95$1, If[LessEqual[y, 1.26e-26], N[(N[(230661.510616 * y + t), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e16 or 1.26000000000000002e-26 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 56.5

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

   3. Applied rewrites 56.5%

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

   4. Taylor expanded in y around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 24.6

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{x}}} \]

   6. Applied rewrites 24.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x}}} \]

   if -6.5e16 < y < 1.26000000000000002e-26

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 56.5

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

   3. Applied rewrites 56.5%

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

   4. Taylor expanded in y around 0

      \[\leadsto \frac{1}{\frac{\color{blue}{i}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 33.6%

      \[\leadsto \frac{1}{\frac{\color{blue}{i}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip-rev N/A

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

      4. lower-/.f64 33.9

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

   8. Applied rewrites 33.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 31.9%

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

Alternative 16: 49.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{1}{x}}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ 1.0 x))))
   (if (<= y -6.8e+16) t_1 (if (<= y 2.3e-40) (/ 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 = 1.0 / (1.0 / x);
	double tmp;
	if (y <= -6.8e+16) {
		tmp = t_1;
	} else if (y <= 2.3e-40) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / (1.0d0 / x)
    if (y <= (-6.8d+16)) then
        tmp = t_1
    else if (y <= 2.3d-40) then
        tmp = t / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 1.0 / (1.0 / x);
	double tmp;
	if (y <= -6.8e+16) {
		tmp = t_1;
	} else if (y <= 2.3e-40) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 1.0 / (1.0 / x)
	tmp = 0
	if y <= -6.8e+16:
		tmp = t_1
	elif y <= 2.3e-40:
		tmp = t / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(1.0 / Float64(1.0 / x))
	tmp = 0.0
	if (y <= -6.8e+16)
		tmp = t_1;
	elseif (y <= 2.3e-40)
		tmp = Float64(t / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 1.0 / (1.0 / x);
	tmp = 0.0;
	if (y <= -6.8e+16)
		tmp = t_1;
	elseif (y <= 2.3e-40)
		tmp = t / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+16], t$95$1, If[LessEqual[y, 2.3e-40], N[(t / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e16 or 2.3e-40 < y

   1. Initial program 56.8%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 56.5

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

   3. Applied rewrites 56.5%

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

   4. Taylor expanded in y around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 24.6

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{x}}} \]

   6. Applied rewrites 24.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x}}} \]

   if -6.8e16 < y < 2.3e-40

   1. Initial program 56.8%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 29.0

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

   4. Applied rewrites 29.0%

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

Alternative 17: 29.0% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \frac{t}{i} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (/ t i))

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.8%

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

2. Taylor expanded in y around 0

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

   1. lower-/.f64 29.0

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

4. Applied rewrites 29.0%

   \[\leadsto \color{blue}{\frac{t}{i}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025155 
(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)))