Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.9% → 84.4%

Time: 9.5s

Alternatives: 15

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: 55.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 84.4% accurate, 0.4× speedup

Math

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

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
      (/ (fma (fma (fma y x z) y 27464.7644705) y 230661.510616) t_1)
      (/ t t_1))
     (- (+ x (* 2.0 (/ z y))) (/ z 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, (fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616) / t_1), (t / t_1));
	} else {
		tmp = (x + (2.0 * (z / y))) - (z / 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(y, Float64(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616) / t_1), Float64(t / t_1));
	else
		tmp = Float64(Float64(x + Float64(2.0 * Float64(z / y))) - Float64(z / 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[(y * N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(2.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 55.9%

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

   3. Applied rewrites 56.6%

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

   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 55.9%

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

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. flip-+ N/A

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

      8. lower-/.f64 N/A

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

   3. Applied rewrites 51.2%

      \[\leadsto \frac{\color{blue}{\frac{\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) - 53204732479.65508}{\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y - 230661.510616}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \left(\frac{z}{y} + \frac{a \cdot x}{y}\right) \]

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

      8. lower-*.f64 30.2

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

   6. Applied rewrites 30.2%

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

   7. Taylor expanded in x around 0

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

      1. lift-/.f64 31.9

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y} \]

   9. Applied rewrites 31.9%

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

Alternative 2: 83.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
           t)
          (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))))
   (if (<= t_1 INFINITY) t_1 (- (+ x (* 2.0 (/ z y))) (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x + (2.0 * (z / y))) - (z / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x + (2.0 * (z / y))) - (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (x + (2.0 * (z / y))) - (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = 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))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(2.0 * Float64(z / y))) - Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (x + (2.0 * (z / y))) - (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x + N[(2.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 55.9%

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

   if +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 55.9%

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

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. flip-+ N/A

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

      8. lower-/.f64 N/A

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

   3. Applied rewrites 51.2%

      \[\leadsto \frac{\color{blue}{\frac{\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) - 53204732479.65508}{\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y - 230661.510616}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \left(\frac{z}{y} + \frac{a \cdot x}{y}\right) \]

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

      8. lower-*.f64 30.2

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

   6. Applied rewrites 30.2%

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

   7. Taylor expanded in x around 0

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

      1. lift-/.f64 31.9

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y} \]

   9. Applied rewrites 31.9%

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

Alternative 3: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y}\\ \end{array} \end{array} \]

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))
      5e+307)
   (/
    (fma (fma (fma z y 27464.7644705) y 230661.510616) y t)
    (fma (fma (fma (+ a y) y b) y c) y i))
   (- (+ x (* 2.0 (/ z y))) (/ z 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)) <= 5e+307) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = (x + (2.0 * (z / y))) - (z / 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)) <= 5e+307)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = Float64(Float64(x + Float64(2.0 * Float64(z / y))) - Float64(z / 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], 5e+307], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(2.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 5e307

   1. Initial program 55.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 52.2%

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

   if 5e307 < (/.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 55.9%

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

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. flip-+ N/A

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

      8. lower-/.f64 N/A

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

   3. Applied rewrites 51.2%

      \[\leadsto \frac{\color{blue}{\frac{\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) - 53204732479.65508}{\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y - 230661.510616}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \left(\frac{z}{y} + \frac{a \cdot x}{y}\right) \]

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

      8. lower-*.f64 30.2

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

   6. Applied rewrites 30.2%

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

   7. Taylor expanded in x around 0

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

      1. lift-/.f64 31.9

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y} \]

   9. Applied rewrites 31.9%

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

Alternative 4: 76.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (* 2.0 (/ z y))) (/ z y))))
   (if (<= y -1.15e+16)
     t_1
     (if (<= y 3.1e-92)
       (/ (fma 230661.510616 y t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
       (if (<= y 1.1e+30)
         (/
          (+
           (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
           t)
          (fma c y i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (2.0 * (z / y))) - (z / y);
	double tmp;
	if (y <= -1.15e+16) {
		tmp = t_1;
	} else if (y <= 3.1e-92) {
		tmp = fma(230661.510616, y, t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else if (y <= 1.1e+30) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(2.0 * Float64(z / y))) - Float64(z / y))
	tmp = 0.0
	if (y <= -1.15e+16)
		tmp = t_1;
	elseif (y <= 3.1e-92)
		tmp = Float64(fma(230661.510616, y, t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	elseif (y <= 1.1e+30)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(2.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+16], t$95$1, If[LessEqual[y, 3.1e-92], N[(N[(230661.510616 * y + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+30], 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[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e16 or 1.1e30 < y

   1. Initial program 55.9%

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

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. flip-+ N/A

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

      8. lower-/.f64 N/A

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

   3. Applied rewrites 51.2%

      \[\leadsto \frac{\color{blue}{\frac{\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) - 53204732479.65508}{\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y - 230661.510616}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \left(\frac{z}{y} + \frac{a \cdot x}{y}\right) \]

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

      8. lower-*.f64 30.2

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

   6. Applied rewrites 30.2%

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

   7. Taylor expanded in x around 0

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

      1. lift-/.f64 31.9

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y} \]

   9. Applied rewrites 31.9%

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

   if -1.15e16 < y < 3.1000000000000001e-92

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 48.0

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

   4. Applied rewrites 48.0%

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

   if 3.1000000000000001e-92 < y < 1.1e30

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 46.0

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

   4. Applied rewrites 46.0%

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

Alternative 5: 75.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+28}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (* 2.0 (/ z y))) (/ z y))))
   (if (<= y -1.15e+16)
     t_1
     (if (<= y 3e+28)
       (/ (fma 230661.510616 y t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (2.0 * (z / y))) - (z / y);
	double tmp;
	if (y <= -1.15e+16) {
		tmp = t_1;
	} else if (y <= 3e+28) {
		tmp = fma(230661.510616, y, t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(2.0 * Float64(z / y))) - Float64(z / y))
	tmp = 0.0
	if (y <= -1.15e+16)
		tmp = t_1;
	elseif (y <= 3e+28)
		tmp = Float64(fma(230661.510616, y, t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(2.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+16], t$95$1, If[LessEqual[y, 3e+28], N[(N[(230661.510616 * y + 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], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e16 or 3.0000000000000001e28 < y

   1. Initial program 55.9%

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

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. flip-+ N/A

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

      8. lower-/.f64 N/A

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

   3. Applied rewrites 51.2%

      \[\leadsto \frac{\color{blue}{\frac{\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) - 53204732479.65508}{\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y - 230661.510616}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \left(\frac{z}{y} + \frac{a \cdot x}{y}\right) \]

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

      8. lower-*.f64 30.2

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

   6. Applied rewrites 30.2%

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

   7. Taylor expanded in x around 0

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

      1. lift-/.f64 31.9

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y} \]

   9. Applied rewrites 31.9%

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

   if -1.15e16 < y < 3.0000000000000001e28

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 48.0

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

   4. Applied rewrites 48.0%

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

Alternative 6: 73.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{\left(\left(y \cdot z + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (* 2.0 (/ z y))) (/ z y))))
   (if (<= y -2.1e+29)
     t_1
     (if (<= y 4.2e+19)
       (/
        (+ (* (+ (* (+ (* y z) 27464.7644705) y) 230661.510616) y) t)
        (fma c y i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (2.0 * (z / y))) - (z / y);
	double tmp;
	if (y <= -2.1e+29) {
		tmp = t_1;
	} else if (y <= 4.2e+19) {
		tmp = ((((((y * z) + 27464.7644705) * y) + 230661.510616) * y) + t) / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(2.0 * Float64(z / y))) - Float64(z / y))
	tmp = 0.0
	if (y <= -2.1e+29)
		tmp = t_1;
	elseif (y <= 4.2e+19)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(y * z) + 27464.7644705) * y) + 230661.510616) * y) + t) / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(2.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+29], t$95$1, If[LessEqual[y, 4.2e+19], N[(N[(N[(N[(N[(N[(N[(y * z), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000002e29 or 4.2e19 < y

   1. Initial program 55.9%

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

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. flip-+ N/A

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

      8. lower-/.f64 N/A

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

   3. Applied rewrites 51.2%

      \[\leadsto \frac{\color{blue}{\frac{\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) - 53204732479.65508}{\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y - 230661.510616}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \left(\frac{z}{y} + \frac{a \cdot x}{y}\right) \]

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

      8. lower-*.f64 30.2

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

   6. Applied rewrites 30.2%

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

   7. Taylor expanded in x around 0

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

      1. lift-/.f64 31.9

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y} \]

   9. Applied rewrites 31.9%

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

   if -2.1000000000000002e29 < y < 4.2e19

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 46.0

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

   4. Applied rewrites 46.0%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 44.3

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

   7. Applied rewrites 44.3%

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

Alternative 7: 71.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y}\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (* 2.0 (/ z y))) (/ z y))))
   (if (<= y -2.45e+29)
     t_1
     (if (<= y 1.7e+27)
       (/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (fma c y i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (2.0 * (z / y))) - (z / y);
	double tmp;
	if (y <= -2.45e+29) {
		tmp = t_1;
	} else if (y <= 1.7e+27) {
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(2.0 * Float64(z / y))) - Float64(z / y))
	tmp = 0.0
	if (y <= -2.45e+29)
		tmp = t_1;
	elseif (y <= 1.7e+27)
		tmp = Float64(Float64(Float64(Float64(Float64(27464.7644705 * y) + 230661.510616) * y) + t) / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(2.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.45e+29], t$95$1, If[LessEqual[y, 1.7e+27], N[(N[(N[(N[(N[(27464.7644705 * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4500000000000001e29 or 1.7e27 < y

   1. Initial program 55.9%

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

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. flip-+ N/A

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

      8. lower-/.f64 N/A

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

   3. Applied rewrites 51.2%

      \[\leadsto \frac{\color{blue}{\frac{\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) - 53204732479.65508}{\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y - 230661.510616}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \left(\frac{z}{y} + \frac{a \cdot x}{y}\right) \]

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

      8. lower-*.f64 30.2

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

   6. Applied rewrites 30.2%

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

   7. Taylor expanded in x around 0

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

      1. lift-/.f64 31.9

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y} \]

   9. Applied rewrites 31.9%

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

   if -2.4500000000000001e29 < y < 1.7e27

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 46.0

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

   4. Applied rewrites 46.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 42.3

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

   7. Applied rewrites 42.3%

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

Alternative 8: 71.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y}\\ \mathbf{if}\;y \leq -47000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+28}:\\ \;\;\;\;\frac{230661.510616 \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (* 2.0 (/ z y))) (/ z y))))
   (if (<= y -47000000000000.0)
     t_1
     (if (<= y 2.4e+28) (/ (+ (* 230661.510616 y) t) (fma c y i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (2.0 * (z / y))) - (z / y);
	double tmp;
	if (y <= -47000000000000.0) {
		tmp = t_1;
	} else if (y <= 2.4e+28) {
		tmp = ((230661.510616 * y) + t) / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(2.0 * Float64(z / y))) - Float64(z / y))
	tmp = 0.0
	if (y <= -47000000000000.0)
		tmp = t_1;
	elseif (y <= 2.4e+28)
		tmp = Float64(Float64(Float64(230661.510616 * y) + t) / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(2.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -47000000000000.0], t$95$1, If[LessEqual[y, 2.4e+28], N[(N[(N[(230661.510616 * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7e13 or 2.39999999999999981e28 < y

   1. Initial program 55.9%

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

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. flip-+ N/A

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

      8. lower-/.f64 N/A

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

   3. Applied rewrites 51.2%

      \[\leadsto \frac{\color{blue}{\frac{\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) - 53204732479.65508}{\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y - 230661.510616}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \left(\frac{z}{y} + \frac{a \cdot x}{y}\right) \]

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

      8. lower-*.f64 30.2

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z + a \cdot x}{y} \]

   6. Applied rewrites 30.2%

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

   7. Taylor expanded in x around 0

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

      1. lift-/.f64 31.9

         \[\leadsto \left(x + 2 \cdot \frac{z}{y}\right) - \frac{z}{y} \]

   9. Applied rewrites 31.9%

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

   if -4.7e13 < y < 2.39999999999999981e28

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 46.0

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

   4. Applied rewrites 46.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 42.4

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

   7. Applied rewrites 42.4%

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

Alternative 9: 69.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - a \cdot x}{y}\\ \mathbf{if}\;y \leq -47000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+28}:\\ \;\;\;\;\frac{230661.510616 \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* a x)) y))))
   (if (<= y -47000000000000.0)
     t_1
     (if (<= y 2.4e+28) (/ (+ (* 230661.510616 y) t) (fma c y i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (a * x)) / y);
	double tmp;
	if (y <= -47000000000000.0) {
		tmp = t_1;
	} else if (y <= 2.4e+28) {
		tmp = ((230661.510616 * y) + t) / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(a * x)) / y))
	tmp = 0.0
	if (y <= -47000000000000.0)
		tmp = t_1;
	elseif (y <= 2.4e+28)
		tmp = Float64(Float64(Float64(230661.510616 * y) + t) / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -47000000000000.0], t$95$1, If[LessEqual[y, 2.4e+28], N[(N[(N[(230661.510616 * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7e13 or 2.39999999999999981e28 < y

   1. Initial program 55.9%

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

   2. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

   4. Applied rewrites 24.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 31.0

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

   7. Applied rewrites 31.0%

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

   if -4.7e13 < y < 2.39999999999999981e28

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 46.0

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

   4. Applied rewrites 46.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 42.4

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

   7. Applied rewrites 42.4%

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

Alternative 10: 63.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - a \cdot x}{y}\\ \mathbf{if}\;y \leq -47000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* a x)) y))))
   (if (<= y -47000000000000.0)
     t_1
     (if (<= y 2.4e+28) (/ t (fma c y i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (a * x)) / y);
	double tmp;
	if (y <= -47000000000000.0) {
		tmp = t_1;
	} else if (y <= 2.4e+28) {
		tmp = t / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(a * x)) / y))
	tmp = 0.0
	if (y <= -47000000000000.0)
		tmp = t_1;
	elseif (y <= 2.4e+28)
		tmp = Float64(t / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(a * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -47000000000000.0], t$95$1, If[LessEqual[y, 2.4e+28], N[(t / N[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7e13 or 2.39999999999999981e28 < y

   1. Initial program 55.9%

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

   2. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

   4. Applied rewrites 24.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 31.0

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

   7. Applied rewrites 31.0%

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

   if -4.7e13 < y < 2.39999999999999981e28

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 46.0

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

   4. Applied rewrites 46.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 36.8%

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

Alternative 11: 56.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      2e+287)
   (/ t (fma c y i))
   (* (- x) -1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2e+287) {
		tmp = t / fma(c, y, i);
	} else {
		tmp = -x * -1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i)) <= 2e+287)
		tmp = Float64(t / fma(c, y, i));
	else
		tmp = Float64(Float64(-x) * -1.0);
	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], 2e+287], N[(t / N[(c * y + i), $MachinePrecision]), $MachinePrecision], N[((-x) * -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2.0000000000000002e287

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 46.0

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

   4. Applied rewrites 46.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 36.8%

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

   if 2.0000000000000002e287 < (/.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 55.9%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}}{x} + -1 \cdot \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   4. Applied rewrites 48.8%

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

   5. Taylor expanded in y around inf

      \[\leadsto \left(-x\right) \cdot -1 \]
   6. Step-by-step derivation

   7. Applied rewrites 25.5%

      \[\leadsto \left(-x\right) \cdot -1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 48.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      2e+287)
   (/ t i)
   (* (- x) -1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2e+287) {
		tmp = t / i;
	} else {
		tmp = -x * -1.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2d+287) then
        tmp = t / i
    else
        tmp = -x * (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2e+287) {
		tmp = t / i;
	} else {
		tmp = -x * -1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2e+287:
		tmp = t / i
	else:
		tmp = -x * -1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i)) <= 2e+287)
		tmp = Float64(t / i);
	else
		tmp = Float64(Float64(-x) * -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= 2e+287)
		tmp = t / i;
	else
		tmp = -x * -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], 2e+287], N[(t / i), $MachinePrecision], N[((-x) * -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2.0000000000000002e287

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 28.9

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

   4. Applied rewrites 28.9%

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

   if 2.0000000000000002e287 < (/.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 55.9%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}}{x} + -1 \cdot \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   4. Applied rewrites 48.8%

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

   5. Taylor expanded in y around inf

      \[\leadsto \left(-x\right) \cdot -1 \]
   6. Step-by-step derivation

   7. Applied rewrites 25.5%

      \[\leadsto \left(-x\right) \cdot -1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 35.5% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.66 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.66e+61) (/ z y) (if (<= y 6.2e+37) (/ t i) (/ z y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.66e+61) {
		tmp = z / y;
	} else if (y <= 6.2e+37) {
		tmp = t / i;
	} else {
		tmp = z / 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 <= (-1.66d+61)) then
        tmp = z / y
    else if (y <= 6.2d+37) then
        tmp = t / i
    else
        tmp = z / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.66e+61) {
		tmp = z / y;
	} else if (y <= 6.2e+37) {
		tmp = t / i;
	} else {
		tmp = z / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.66e+61:
		tmp = z / y
	elif y <= 6.2e+37:
		tmp = t / i
	else:
		tmp = z / y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.66e+61)
		tmp = Float64(z / y);
	elseif (y <= 6.2e+37)
		tmp = Float64(t / i);
	else
		tmp = Float64(z / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.66e+61)
		tmp = z / y;
	elseif (y <= 6.2e+37)
		tmp = t / i;
	else
		tmp = z / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.66e+61], N[(z / y), $MachinePrecision], If[LessEqual[y, 6.2e+37], N[(t / i), $MachinePrecision], N[(z / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.66000000000000004e61 or 6.2000000000000004e37 < y

   1. Initial program 55.9%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 11.3%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 7.4

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

   7. Applied rewrites 7.4%

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

   8. Taylor expanded in y around inf

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

      1. lower-/.f64 10.7

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

   10. Applied rewrites 10.7%

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

   if -1.66000000000000004e61 < y < 6.2000000000000004e37

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 28.9

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

   4. Applied rewrites 28.9%

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

Alternative 14: 12.0% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.35 \cdot 10^{+72}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.35e+72) (/ z y) (/ z a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.35e+72) {
		tmp = z / y;
	} else {
		tmp = z / a;
	}
	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 (a <= 2.35d+72) then
        tmp = z / y
    else
        tmp = z / a
    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 (a <= 2.35e+72) {
		tmp = z / y;
	} else {
		tmp = z / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.35e+72:
		tmp = z / y
	else:
		tmp = z / a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.35e+72)
		tmp = Float64(z / y);
	else
		tmp = Float64(z / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.35e+72)
		tmp = z / y;
	else
		tmp = z / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.35e+72], N[(z / y), $MachinePrecision], N[(z / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.35000000000000017e72

   1. Initial program 55.9%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 11.3%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 7.4

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

   7. Applied rewrites 7.4%

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

   8. Taylor expanded in y around inf

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

      1. lower-/.f64 10.7

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

   10. Applied rewrites 10.7%

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

   if 2.35000000000000017e72 < a

   1. Initial program 55.9%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 11.3%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 7.4

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

   7. Applied rewrites 7.4%

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

Alternative 15: 7.4% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \frac{z}{a} \end{array} \]

FPCore

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

C

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

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 = z / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 55.9%

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

2. Taylor expanded in z around inf

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

   1. associate-/l* N/A

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

   2. lower-*.f64 N/A

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

   3. unpow3 N/A

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

   4. unpow2 N/A

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

   5. lower-*.f64 N/A

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

   6. unpow2 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. +-commutative N/A

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

   10. *-commutative N/A

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

   11. lower-fma.f64 N/A

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

4. Applied rewrites 11.3%

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

5. Taylor expanded in a around inf

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

   1. lower-/.f64 7.4

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

7. Applied rewrites 7.4%

   \[\leadsto \frac{z}{\color{blue}{a}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025139 
(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)))