Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.4% → 84.8%

Time: 10.3s

Alternatives: 15

Speedup: 3.2×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+101}:\\ \;\;\;\;\frac{t \cdot \mathsf{fma}\left(27464.7644705, \frac{1}{t \cdot y}, \mathsf{fma}\left(230661.510616, \frac{1}{t \cdot \left(y \cdot y\right)}, \frac{1}{\left(y \cdot y\right) \cdot y} + \frac{z + x \cdot y}{t}\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2e+64)
     t_1
     (if (<= y 5.6e+33)
       (/
        (+
         (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
         t)
        (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
       (if (<= y 6.2e+101)
         (/
          (*
           t
           (fma
            27464.7644705
            (/ 1.0 (* t y))
            (fma
             230661.510616
             (/ 1.0 (* t (* y y)))
             (+ (/ 1.0 (* (* y y) y)) (/ (+ z (* x y)) t)))))
          a)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2e+64) {
		tmp = t_1;
	} else if (y <= 5.6e+33) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else if (y <= 6.2e+101) {
		tmp = (t * fma(27464.7644705, (1.0 / (t * y)), fma(230661.510616, (1.0 / (t * (y * y))), ((1.0 / ((y * y) * y)) + ((z + (x * y)) / t))))) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2e+64)
		tmp = t_1;
	elseif (y <= 5.6e+33)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	elseif (y <= 6.2e+101)
		tmp = Float64(Float64(t * fma(27464.7644705, Float64(1.0 / Float64(t * y)), fma(230661.510616, Float64(1.0 / Float64(t * Float64(y * y))), Float64(Float64(1.0 / Float64(Float64(y * y) * y)) + Float64(Float64(z + Float64(x * y)) / t))))) / a);
	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[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+64], t$95$1, If[LessEqual[y, 5.6e+33], N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+101], N[(N[(t * N[(27464.7644705 * N[(1.0 / N[(t * y), $MachinePrecision]), $MachinePrecision] + N[(230661.510616 * N[(1.0 / N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / N[(N[(y * y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + N[(N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000004e64 or 6.19999999999999998e101 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -2.00000000000000004e64 < y < 5.6000000000000002e33

   1. Initial program 56.4%

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

   if 5.6000000000000002e33 < y < 6.19999999999999998e101

   1. Initial program 56.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 52.4%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

   7. Applied rewrites 10.5%

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

Alternative 2: 84.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+79}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2e+64)
     t_1
     (if (<= y 3e+79)
       (/
        (+
         (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 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 + (z / y);
	double tmp;
	if (y <= -2e+64) {
		tmp = t_1;
	} else if (y <= 3e+79) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-2d+64)) then
        tmp = t_1
    else if (y <= 3d+79) then
        tmp = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2e+64) {
		tmp = t_1;
	} else if (y <= 3e+79) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -2e+64:
		tmp = t_1
	elif y <= 3e+79:
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 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(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2e+64)
		tmp = t_1;
	elseif (y <= 3e+79)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -2e+64)
		tmp = t_1;
	elseif (y <= 3e+79)
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+64], t$95$1, If[LessEqual[y, 3e+79], 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], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000004e64 or 2.99999999999999974e79 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -2.00000000000000004e64 < y < 2.99999999999999974e79

   1. Initial program 56.4%

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

Alternative 3: 84.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2e+64)
     t_1
     (if (<= y 3e+79)
       (*
        (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
        (/ 1.0 (fma (fma (fma (+ 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 + (z / y);
	double tmp;
	if (y <= -2e+64) {
		tmp = t_1;
	} else if (y <= 3e+79) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) * (1.0 / fma(fma(fma((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(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2e+64)
		tmp = t_1;
	elseif (y <= 3e+79)
		tmp = Float64(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) * Float64(1.0 / fma(fma(fma(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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+64], t$95$1, If[LessEqual[y, 3e+79], N[(N[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] * N[(1.0 / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000004e64 or 2.99999999999999974e79 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -2.00000000000000004e64 < y < 2.99999999999999974e79

   1. Initial program 56.4%

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

   3. Applied rewrites 56.3%

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

Alternative 4: 79.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(y \cdot y\right) \cdot \left(b + y \cdot \left(a + y\right)\right) + i}\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-59}:\\ \;\;\;\;\frac{\left(230661.510616 - -27464.7644705 \cdot y\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
           t)
          (+ (* (* y y) (+ b (* y (+ a y)))) i)))
        (t_2 (+ x (/ z y))))
   (if (<= y -8e+63)
     t_2
     (if (<= y -9e-7)
       t_1
       (if (<= y 2.3e-59)
         (/
          (+ (* (- 230661.510616 (* -27464.7644705 y)) y) t)
          (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
         (if (<= y 3e+79) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((y * y) * (b + (y * (a + y)))) + i);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -8e+63) {
		tmp = t_2;
	} else if (y <= -9e-7) {
		tmp = t_1;
	} else if (y <= 2.3e-59) {
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else if (y <= 3e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((y * y) * (b + (y * (a + y)))) + i)
    t_2 = x + (z / y)
    if (y <= (-8d+63)) then
        tmp = t_2
    else if (y <= (-9d-7)) then
        tmp = t_1
    else if (y <= 2.3d-59) then
        tmp = (((230661.510616d0 - ((-27464.7644705d0) * y)) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
    else if (y <= 3d+79) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((y * y) * (b + (y * (a + y)))) + i);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -8e+63) {
		tmp = t_2;
	} else if (y <= -9e-7) {
		tmp = t_1;
	} else if (y <= 2.3e-59) {
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else if (y <= 3e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 * y) * (b + (y * (a + y)))) + i)
	t_2 = x + (z / y)
	tmp = 0
	if y <= -8e+63:
		tmp = t_2
	elif y <= -9e-7:
		tmp = t_1
	elif y <= 2.3e-59:
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
	elif y <= 3e+79:
		tmp = t_1
	else:
		tmp = t_2
	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(y * y) * Float64(b + Float64(y * Float64(a + y)))) + i))
	t_2 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -8e+63)
		tmp = t_2;
	elseif (y <= -9e-7)
		tmp = t_1;
	elseif (y <= 2.3e-59)
		tmp = Float64(Float64(Float64(Float64(230661.510616 - Float64(-27464.7644705 * y)) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	elseif (y <= 3e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((y * y) * (b + (y * (a + y)))) + i);
	t_2 = x + (z / y);
	tmp = 0.0;
	if (y <= -8e+63)
		tmp = t_2;
	elseif (y <= -9e-7)
		tmp = t_1;
	elseif (y <= 2.3e-59)
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	elseif (y <= 3e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(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[(y * y), $MachinePrecision] * N[(b + N[(y * N[(a + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+63], t$95$2, If[LessEqual[y, -9e-7], t$95$1, If[LessEqual[y, 2.3e-59], N[(N[(N[(N[(230661.510616 - N[(-27464.7644705 * y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+79], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000046e63 or 2.99999999999999974e79 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -8.00000000000000046e63 < y < -8.99999999999999959e-7 or 2.29999999999999979e-59 < y < 2.99999999999999974e79

   1. Initial program 56.4%

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

   2. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 43.7

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

   4. Applied rewrites 43.7%

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

   if -8.99999999999999959e-7 < y < 2.29999999999999979e-59

   1. Initial program 56.4%

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

   2. Taylor expanded in y around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. metadata-eval 48.1

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

   4. Applied rewrites 48.1%

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

Alternative 5: 76.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+79}:\\ \;\;\;\;\frac{\left(230661.510616 - -27464.7644705 \cdot y\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2.2e+19)
     t_1
     (if (<= y 3e+79)
       (/
        (+ (* (- 230661.510616 (* -27464.7644705 y)) 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 + (z / y);
	double tmp;
	if (y <= -2.2e+19) {
		tmp = t_1;
	} else if (y <= 3e+79) {
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-2.2d+19)) then
        tmp = t_1
    else if (y <= 3d+79) then
        tmp = (((230661.510616d0 - ((-27464.7644705d0) * y)) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2.2e+19) {
		tmp = t_1;
	} else if (y <= 3e+79) {
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -2.2e+19:
		tmp = t_1
	elif y <= 3e+79:
		tmp = (((230661.510616 - (-27464.7644705 * y)) * 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(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.2e+19)
		tmp = t_1;
	elseif (y <= 3e+79)
		tmp = Float64(Float64(Float64(Float64(230661.510616 - Float64(-27464.7644705 * y)) * 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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -2.2e+19)
		tmp = t_1;
	elseif (y <= 3e+79)
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+19], t$95$1, If[LessEqual[y, 3e+79], N[(N[(N[(N[(230661.510616 - N[(-27464.7644705 * y), $MachinePrecision]), $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], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e19 or 2.99999999999999974e79 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -2.2e19 < y < 2.99999999999999974e79

   1. Initial program 56.4%

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

   2. Taylor expanded in y around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. metadata-eval 48.1

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

   4. Applied rewrites 48.1%

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

Alternative 6: 76.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(27464.7644705, y, 230661.510616\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2.2e+19)
     t_1
     (if (<= y 3e+79)
       (*
        (fma (fma 27464.7644705 y 230661.510616) y t)
        (/ 1.0 (fma (fma (fma (+ 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 + (z / y);
	double tmp;
	if (y <= -2.2e+19) {
		tmp = t_1;
	} else if (y <= 3e+79) {
		tmp = fma(fma(27464.7644705, y, 230661.510616), y, t) * (1.0 / fma(fma(fma((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(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.2e+19)
		tmp = t_1;
	elseif (y <= 3e+79)
		tmp = Float64(fma(fma(27464.7644705, y, 230661.510616), y, t) * Float64(1.0 / fma(fma(fma(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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+19], t$95$1, If[LessEqual[y, 3e+79], N[(N[(N[(27464.7644705 * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] * N[(1.0 / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e19 or 2.99999999999999974e79 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -2.2e19 < y < 2.99999999999999974e79

   1. Initial program 56.4%

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

   3. Applied rewrites 56.3%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 48.0%

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

Alternative 7: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+79}:\\ \;\;\;\;\frac{t - -230661.510616 \cdot y}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2.2e+19)
     t_1
     (if (<= y 3e+79)
       (/
        (- t (* -230661.510616 y))
        (+ (* (+ (* (+ (* (+ 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 + (z / y);
	double tmp;
	if (y <= -2.2e+19) {
		tmp = t_1;
	} else if (y <= 3e+79) {
		tmp = (t - (-230661.510616 * y)) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-2.2d+19)) then
        tmp = t_1
    else if (y <= 3d+79) then
        tmp = (t - ((-230661.510616d0) * y)) / (((((((y + a) * y) + b) * y) + c) * y) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2.2e+19) {
		tmp = t_1;
	} else if (y <= 3e+79) {
		tmp = (t - (-230661.510616 * y)) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -2.2e+19:
		tmp = t_1
	elif y <= 3e+79:
		tmp = (t - (-230661.510616 * y)) / (((((((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(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.2e+19)
		tmp = t_1;
	elseif (y <= 3e+79)
		tmp = Float64(Float64(t - Float64(-230661.510616 * y)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -2.2e+19)
		tmp = t_1;
	elseif (y <= 3e+79)
		tmp = (t - (-230661.510616 * y)) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+19], t$95$1, If[LessEqual[y, 3e+79], N[(N[(t - N[(-230661.510616 * y), $MachinePrecision]), $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 < -2.2e19 or 2.99999999999999974e79 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -2.2e19 < y < 2.99999999999999974e79

   1. Initial program 56.4%

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

   2. Taylor expanded in y around 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. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. metadata-eval 48.1

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

   4. Applied rewrites 48.1%

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

Alternative 8: 75.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(230661.510616, y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -1.5e+19)
     t_1
     (if (<= y 3e+79)
       (* (fma 230661.510616 y t) (/ 1.0 (fma (fma (fma a y b) y c) y i)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.5e+19) {
		tmp = t_1;
	} else if (y <= 3e+79) {
		tmp = fma(230661.510616, y, t) * (1.0 / fma(fma(fma(a, y, b), y, c), y, i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -1.5e+19)
		tmp = t_1;
	elseif (y <= 3e+79)
		tmp = Float64(fma(230661.510616, y, t) * Float64(1.0 / fma(fma(fma(a, y, b), y, c), y, i)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+19], t$95$1, If[LessEqual[y, 3e+79], N[(N[(230661.510616 * y + t), $MachinePrecision] * N[(1.0 / N[(N[(N[(a * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e19 or 2.99999999999999974e79 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -1.5e19 < y < 2.99999999999999974e79

   1. Initial program 56.4%

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

   3. Applied rewrites 56.3%

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

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{28832688827}{125000}}, y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)} \]
   5. Step-by-step derivation

   6. Applied rewrites 48.0%

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

   7. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{28832688827}{125000}, y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{a}, y, b\right), y, c\right), y, i\right)} \]
   8. Step-by-step derivation

   9. Applied rewrites 47.6%

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

Alternative 9: 68.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-126}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+79}:\\ \;\;\;\;\frac{230661.510616 \cdot y + t}{\left(y \cdot y\right) \cdot \left(b + y \cdot \left(a + y\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2.2e+19)
     t_1
     (if (<= y 1.1e-126)
       (/ t (fma (fma (fma (+ y a) y b) y c) y i))
       (if (<= y 3e+79)
         (/ (+ (* 230661.510616 y) t) (+ (* (* y y) (+ b (* y (+ a 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 / y);
	double tmp;
	if (y <= -2.2e+19) {
		tmp = t_1;
	} else if (y <= 1.1e-126) {
		tmp = t / fma(fma(fma((y + a), y, b), y, c), y, i);
	} else if (y <= 3e+79) {
		tmp = ((230661.510616 * y) + t) / (((y * y) * (b + (y * (a + y)))) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.2e+19)
		tmp = t_1;
	elseif (y <= 1.1e-126)
		tmp = Float64(t / fma(fma(fma(Float64(y + a), y, b), y, c), y, i));
	elseif (y <= 3e+79)
		tmp = Float64(Float64(Float64(230661.510616 * y) + t) / Float64(Float64(Float64(y * y) * Float64(b + Float64(y * Float64(a + 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[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+19], t$95$1, If[LessEqual[y, 1.1e-126], N[(t / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+79], N[(N[(N[(230661.510616 * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(y * y), $MachinePrecision] * N[(b + N[(y * N[(a + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2e19 or 2.99999999999999974e79 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -2.2e19 < y < 1.10000000000000007e-126

   1. Initial program 56.4%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 41.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 41.0

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 41.0

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 41.0

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

   6. Applied rewrites 41.0%

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

   if 1.10000000000000007e-126 < y < 2.99999999999999974e79

   1. Initial program 56.4%

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

   2. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 43.7

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

   4. Applied rewrites 43.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 37.6

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

   7. Applied rewrites 37.6%

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

Alternative 10: 68.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+79}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2.2e+19)
     t_1
     (if (<= y 3e+79) (/ t (fma (fma (fma (+ 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 + (z / y);
	double tmp;
	if (y <= -2.2e+19) {
		tmp = t_1;
	} else if (y <= 3e+79) {
		tmp = t / fma(fma(fma((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(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.2e+19)
		tmp = t_1;
	elseif (y <= 3e+79)
		tmp = Float64(t / fma(fma(fma(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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+19], t$95$1, If[LessEqual[y, 3e+79], N[(t / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e19 or 2.99999999999999974e79 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -2.2e19 < y < 2.99999999999999974e79

   1. Initial program 56.4%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 41.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 41.0

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 41.0

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 41.0

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

   6. Applied rewrites 41.0%

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

Alternative 11: 66.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{\left(\left(y \cdot y\right) \cdot z\right) \cdot y + t}{c \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -1.5e+19)
     t_1
     (if (<= y 9.2e+68) (/ (+ (* (* (* y y) z) y) t) (+ (* 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 / y);
	double tmp;
	if (y <= -1.5e+19) {
		tmp = t_1;
	} else if (y <= 9.2e+68) {
		tmp = ((((y * y) * z) * y) + t) / ((c * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-1.5d+19)) then
        tmp = t_1
    else if (y <= 9.2d+68) then
        tmp = ((((y * y) * z) * y) + t) / ((c * y) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.5e+19) {
		tmp = t_1;
	} else if (y <= 9.2e+68) {
		tmp = ((((y * y) * z) * y) + t) / ((c * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -1.5e+19:
		tmp = t_1
	elif y <= 9.2e+68:
		tmp = ((((y * y) * z) * y) + t) / ((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(z / y))
	tmp = 0.0
	if (y <= -1.5e+19)
		tmp = t_1;
	elseif (y <= 9.2e+68)
		tmp = Float64(Float64(Float64(Float64(Float64(y * y) * z) * y) + t) / Float64(Float64(c * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -1.5e+19)
		tmp = t_1;
	elseif (y <= 9.2e+68)
		tmp = ((((y * y) * z) * y) + t) / ((c * y) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+19], t$95$1, If[LessEqual[y, 9.2e+68], N[(N[(N[(N[(N[(y * y), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e19 or 9.1999999999999999e68 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -1.5e19 < y < 9.1999999999999999e68

   1. Initial program 56.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 44.7

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

   4. Applied rewrites 44.7%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 38.4%

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

Alternative 12: 60.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(230661.510616, y, t\right) \cdot \frac{1}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2.7e+14)
     t_1
     (if (<= y 1.7e+45) (* (fma 230661.510616 y t) (/ 1.0 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 / y);
	double tmp;
	if (y <= -2.7e+14) {
		tmp = t_1;
	} else if (y <= 1.7e+45) {
		tmp = fma(230661.510616, y, t) * (1.0 / i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.7e+14)
		tmp = t_1;
	elseif (y <= 1.7e+45)
		tmp = Float64(fma(230661.510616, y, t) * Float64(1.0 / 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[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+14], t$95$1, If[LessEqual[y, 1.7e+45], N[(N[(230661.510616 * y + t), $MachinePrecision] * N[(1.0 / i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e14 or 1.7e45 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -2.7e14 < y < 1.7e45

   1. Initial program 56.4%

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

   3. Applied rewrites 56.3%

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

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{28832688827}{125000}}, y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)} \]
   5. Step-by-step derivation

   6. Applied rewrites 48.0%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 31.9

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

   9. Applied rewrites 31.9%

      \[\leadsto \mathsf{fma}\left(230661.510616, y, t\right) \cdot \color{blue}{\frac{1}{i}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 57.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -5.2e+19) t_1 (if (<= y 9.2e+68) (/ t i) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -5.2e+19) {
		tmp = t_1;
	} else if (y <= 9.2e+68) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-5.2d+19)) then
        tmp = t_1
    else if (y <= 9.2d+68) then
        tmp = t / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -5.2e+19) {
		tmp = t_1;
	} else if (y <= 9.2e+68) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -5.2e+19:
		tmp = t_1
	elif y <= 9.2e+68:
		tmp = t / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -5.2e+19)
		tmp = t_1;
	elseif (y <= 9.2e+68)
		tmp = Float64(t / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -5.2e+19)
		tmp = t_1;
	elseif (y <= 9.2e+68)
		tmp = t / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+19], t$95$1, If[LessEqual[y, 9.2e+68], N[(t / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e19 or 9.1999999999999999e68 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if -5.2e19 < y < 9.1999999999999999e68

   1. Initial program 56.4%

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

   2. Taylor expanded in y around 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: 35.3% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 0.0069:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.7e+19) (/ z y) (if (<= y 0.0069) (/ 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 <= -6.7e+19) {
		tmp = z / y;
	} else if (y <= 0.0069) {
		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 <= (-6.7d+19)) then
        tmp = z / y
    else if (y <= 0.0069d0) 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 <= -6.7e+19) {
		tmp = z / y;
	} else if (y <= 0.0069) {
		tmp = t / i;
	} else {
		tmp = z / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.7e+19:
		tmp = z / y
	elif y <= 0.0069:
		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 <= -6.7e+19)
		tmp = Float64(z / y);
	elseif (y <= 0.0069)
		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 <= -6.7e+19)
		tmp = z / y;
	elseif (y <= 0.0069)
		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, -6.7e+19], N[(z / y), $MachinePrecision], If[LessEqual[y, 0.0069], N[(t / i), $MachinePrecision], N[(z / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7e19 or 0.0068999999999999999 < y

   1. Initial program 56.4%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 30.8

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

   4. Applied rewrites 30.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 10.3

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

   7. Applied rewrites 10.3%

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

   if -6.7e19 < y < 0.0068999999999999999

   1. Initial program 56.4%

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

   2. Taylor expanded in y around 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 15: 10.3% accurate, 10.8× speedup

Math

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

FPCore

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

C

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

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 / y
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 / y;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.4%

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

2. Taylor expanded in y around -inf

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

   1. lower-+.f64 N/A

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

   2. mul-1-neg N/A

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

   3. lower-neg.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. lower--.f64 N/A

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

   6. mul-1-neg N/A

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

   7. lower-neg.f64 N/A

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

   8. mul-1-neg N/A

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

   9. lower-neg.f64 N/A

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

   10. lower-*.f64 30.8

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

4. Applied rewrites 30.8%

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

5. Taylor expanded in x around 0

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

   1. lower-/.f64 10.3

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

7. Applied rewrites 10.3%

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

Reproduce

herbie shell --seed 2025134 
(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)))